number series

29 IBPS PO EXAM 2013 : Quantitative Aptitude

Chapter: Number Series In Number Series, questions are asked on the basis of relation between numbers given in a series. The questions asked can be divided into different types:

Type I: In this type of questions, a series of numbers is given with one number missing represented by a question mark. Candidate has to select from the options choices to correct option in place of the question mark. The given sequences of numbers will be such that each number follows its predecessor in the same way, i.e., according to a particular pattern. Candidates are required to find out the correct ways in which the sequence is formed and there after find out the number to complete the series.

1. 30, 34, 43, 59, 84, 120,?

(1) 169

(2) 148

(3) 153

(4) 176

(5) None of these

Solution: (1) The given pattern is:

+22, 32, +42, + 62, +72

So, missing term is 169=120 +72

2. 40, 54, 82,?, 180,250

(1) 142

(2) 124

(3) 136

(4) 163

(5) None of these

Solution: (2) The pattern is: +14, + 28, + 42, + 52, + 70


So, missing term is 82 + 42=124

Type II: Here, we are given a sequence of number. Whole sequence, except the odd number follow a certain rule. You have to find that number which does not follow the rule.

1. 0, 1,3,8,18,35,264

(1) 62

(2) 35

(3) 18

(4) 8

(5) None of these

Solution: (1) The pattern is +(02+1), +(12+1), + (22+1) ,+ (32+1), + (42+1), + (52+1)

So, 62 is wrong and must be replaced by 35 + (52+1) = 62

2. 1, 9, 125, 49, 729, 121, 2147

(1) 2147

(2) 729

(3) 125

(4) 1

(5) None of these

Solution: (1)

Type III: In this type of questions, a number series is given. After the series is over, in the next line, a number is followed by (A), (B), (C), (D) and (E). The candidates have to complete the series starting with the number given following the sequence of the given series.

1. 2, 4, 9, 20, 43, 90

3 (A) (B) (C) (D) (E)

Which number will come in place of (D)?

(1) 58

(2) 99


(3) 48

(4) 59

(5) None of these

Solution: (4)

Similarly,

Hence, the number 59 will come in place of D.

2. 3, 4, 10, 33, 136,

3 (A) (B) (C) (D) (E)

Which number will come in place of (E)?

(1) 1035

(2) 1165

(3) 1039

(4) 891

(5) None of these

Solution: (2)


Similarly,

Hence, the number 1165 will come in place of E.


Solved Examples (Number Series)

Directions: (1-5) In each of these questions a number series is given. In each series only one number is wrong. Find out the wrong number. (IBPS CWE PO MT 2012) 1. 5531 5506 5425 5304 5135 4910 4621 (1) 5531 (2) 5425 (3) 4621 (4) 5135 (5) 5506 Solution: The number should be 5555 in place of 5531. -72, -92, -112, -132, -152, -172... Ans: (1) 2. 6 7 9 13 26 37 69 (1) 7 (2) 26 (3) 69 (4) 37 (5) 9 Solution: The number should be 21 in place of 26. +1, +2, +4, +8, +16, +32 Ans: (2) 3. 1 3 10 36 152 760 4632 (1) 3 (2) 36 (3) 4632 (4) 760


(5) 152 Solution: The number should be 770 In place of 760. ×1 +2, ×2 +4, ×3 +6, ×4 + 8, ×5 +10, ×6 + 12, ... Ans: (4) 4. 4 3 9 34 96 219 435 (1) 4 (2) 9 (3) 34 (4) 435 (5) 219 Solution: The series is 02+ 4, 12+2, 32+0, 62-2, 102-4, 152- 6,212 - 8... Hence, 435 should be replaced with 433 Ans: (1) 5. 157.5 45 15 6 3 2 1 (1) 1 (2) 2 (3) 6 (4) 157.5 (5) 45 Solution: The number should be 2 in place of 1.

3.5, 3, 2.5, 2, 1.5, 1, ... Ans: (1)

Directions (6-10): In the following number series only one number is wrong.

Find out the wrong number.

6. 7 12 40 222 1742 17390 208608

(1) 7

(2) 12

(3) 40


(4) 1742

(5) 208608

Solution: The pattern of number series is as follows:

7 2 - 2 = 12

12 4 - (2 + 6) = 48 - 8 = 40

40 6 - (8 + 10) = 240 - 18 = 222

222 8 - (18 + 14) = 1776 - 32 = 1744 1742

1744 10 - (32 + 18) = 17440 - 50 = 17390

Ans: (4)

7. 6 91 584 2935 11756 35277 70558

(1) 91

(2) 70558

(3) 584

(4) 2935

(5) 35277


6 7 + 72 = 42 + 49 = 91

91 6 + 62 = 546 + 36 = 582 584

582 5+52 =2910 + 25=2935

2935 4 + 42 = 11740 + 16 = 11756

11756 x 3 + 32 = 35268 + 9 = 35277

Ans: (3)


8. 9050 5675 3478 2147 1418 1077 950

(1) 3478

(2) 1418

(3) 5675

(4) 2147

(5) 1077


9050 – I53 = 9050 - 3375 = 5675

5675 - 133 = 5675 - 2197 = 3478

3478 - 113 = 3478 - 1331 = 2147

2147 - 93 = 2147 - 729 = 1418

1418 - 73 = 1418 - 343 = 1075 1077

Ans: (5)

9. 1 4 25 256 3125 46656 823543

(1)3125

(2) 823543

(3) 46656

(4) 25

(5) 256


11 = 1;-22 = 4; 33 = 27 25; 44 = 256; 55 = 3125; 66 = 46656;

77 = 823543

Ans: (4)


10. 8424 4212 2106 1051 526.5 263.25 131.625

(1) 131.625

(2) 1051

(3) 4212

(4) 8424

(5) 263.25


8424 2 = 4212

4212 2 = 2106

2106 2 = 1053 1051

1053 2 = 526.5

526.5 ÷ 2 = 263.25 263.25 ÷ 2 = 13 1.625

Ans: (2)


Practice Set (Number Series)

Directions (Q. 1-3): What will come in place of question mark (?) in the following number series? (IBPS RRB Grade Officer Exam 2012)

1. 987 587 331 187 123 (?)

(1) 104

(2) 113

(3) 107

(4) 114

(5) None of these

2. 125 171 263 401 585 (?)

(1) 835

(2) 815

(3) 792

(4) 788

(5) None of these

3. 121 132 167 226 309 (?)

(1) 424

(2) 413

(3) 427

(4) 416

(5) None of these

Directions (Q. 4-5): In the following number series, only one is wrong. Find out the wrong number.

4. 454 327 648 524 842 713 1036

(1) 327

(2) 648

(3) 521

(4) 842

(5) 713

5. 72.5 86 113 168 275 491 923

(1) 86

(2)113

(3)168

(4)275

(5)491

Directions (Q. 6-10): What will come in place of question mark (?) in the following number series? (RBI Grade’B’ Officer’s Exam 2011)

6. 17 19 33 (?) 129 227

(1) 64 (2) 73 (3) 67 (4) 72 (5) None of these

7. 35 256 451 620 763 (?)


(1) 680 (2) 893 (3) 633 (4) 880 (5) None of these

8. 18 139 868 917 (?) 1051

(1) 1042 (2) 1036 (3) 942 (4) 996 (5) None of these

9. 2890 (?) 1162 874 730 658

(1) 1684 (2) 1738 (3) 1784 (4) 1672 (5) None of these

10. 14 1004 1202 1251.5 1268 (?)

(1) 1267.5 (2) 1276.25 (3) 1324.5 (4) 1367.25 (5) None of these

Directions (Q. 11-15): What will come in place of question mark (?) in the following number series? (Corporation Bank PO 2011)

11. 8 11 20 47 128 (?)

(1) 483 (2) 488 (3) 397 (4) 371 (5) None of these

12. 71 78 99 134 183 (?)

(1) 253 (2) 239 (3) 246 (4) 253 (5) None of these

13. 342 337.5 328.5 315 297 (?)

265.5

274.5

270

260

None of these

14. 161 164 179 242 497 (?)

(1) 1540 (2) 1480 (3) 1520 (4) 1440 (5) None of these

15. 239 254 284 344 464 (?)

(1) 726 (2) 716 (3) 724 (4) 714 (5) None of these

Directions-(Q. 16-20) What will come in place of question-mark (?) in the following number series? (Allahabad Bank Probationary Officers Exam 2011)

16. 958 833 733 658 608, (?)

(1) 577 (2) 583 (3) 567 (4) 573 (5) None of these


17. 11 10 18 51 200, (?)

(1) 885 (2) 1025 (3) 865 (4) 995 (5) None of these

18. 25 48 94 186 370 (?)

(1) 738 (2) 744 (3) 746 (4) 724 (5) None of these

19. 14 24 43 71 108 (?)

(1) 194 (2) 154 (3) 3) 145 (4) 4) 155 (5) 5) None of these

20. 144 173 140 169 136 (?)

(1) 157 (2) 148 (3) 164 (4) 132 (5) None of these


Number Series Practice Set (Answers)

1) 3

2) 2

3) 4

4) 5

5) 3

6) 3

7) 4

8) 1

9) 2

10) 2

11) 4

12) 3

13) 2

14) 3

15) 5

16) 2

17) 4

18) 1

19) 2

20) 5


Chapter: Number System Introduction: Number is a symbol which represents quantity. There are three types of numbers:

1. Real Numbers: Real numbers are those numbers which can be easily indentify and quantify. For example: -10, -7.33, -1, 0, 1, 2, 5.77 etc.

2. Imaginary Numbers: Imaginary numbers are those numbers which we can just imagine but cannot physically perceive.

For example: , etc, is represented by i . Square root of all negative numbers are imaginary.

3. Complex Number: Combination of Real and Imaginary number is called complex numbers. For example: (2+5i) , (1+3i) etc .

Here we will only discuss about the real numbers . Types of Real Numbers: there are two types of real numbers

1. Rational numbers: - All that numbers which can be expressed in the form of where p

& q are integers and q 0 are called rational numbers.

For example: - -1, 2, , 0, 1 , 2.7 etc. , here -1 = =

Again Rational numbers are classified as:

(a) Integers: All rational numbers which do not have decimal or fractional parts are called integers. For example: -3, -1, 0 , 1 , 2 etc .

Integers are of two type whole numbers and natural numbers. All the non negative integers are whole numbers , for example 0 , 1 , 2 , 3 etc and all the whole numbers except 0 are natural numbers , for example 1, 2 , 3 etc


(b) Fractions: All rational numbers which are in the form of where p & q are integers and

q 0 and p is not a multiple of q are called fractions.

For example: - 1.2, , , 1.7, .3 etc.

Fractions are of three types: Proper Improper Mixed fractions

A proper fraction is a fraction whose numerator is smaller than denominator, for example

, etc. An improper fraction is a fraction whose numerator is equal to or greater than its

denominator for example , etc. and a mixed fraction is an integer plus a fraction, for

example , etc.

2. Irrational Numbers:- All that numbers which cannot be expressed in the form of are

called irrational numbers. They have non-terminating and non-recurring decimal parts.

For example: , , etc.

On the basis of origin:

1. Prime Numbers: All the natural numbers greater than 1 which are only divisible by 1 and the number itself are called prime numbers. For example: 2, 3, 5, 7, 11, 13, 17 etc.

2. Composite Numbers: All the natural numbers greater than 1 which are divisible by at least one more number other than 1 and the number itself are called composite numbers. For example: 4, 6, 8, 9, 10, 12 etc. Note: 1 is neither a prime number nor a composite.

On basis of divisor:

1. Even Numbers: All the natural numbers which are multiple of 2 are called even numbers. For example: 2, 4, 6, 8, 10 etc.


Odd Numbers: All the natural numbers which are not a multiple of 2 are called odd

numbers. They are denoted as 2k 1, where k is a natural number. For example: 3, 5, 7, 9, 11 etc.

To find whether a number is prime or not. Step 1: Find the approximate square root of a number . Step 2: Check if any prime number from 2 to that square root divides that number or not. Step 3: If none of those prime number divides the number than the number must be prime number. Example: Take 631 , the approx square root of 631 is 25 , now from 2 to 25 there are 2 , 3 ,5 , 7 , 11 , 13 , 17 , 19 and 23 prime number . Since none of these divides 631, so 631 must be a prime number.

Conversion of recurring decimal into fraction.

The form of purely recurring number =

Let x = 0.77777…. 10x = 7.77777……

If x = 0.27272727 …. 100 x = 27.272727 ……

The form of purely recurring number =

Let x= 0.143333333…….. 100x = 14.333333……. 1000x = 143.3333….

= 129


Quotient and remainder:

Dividend = (Divisor Quotient) + remainder.

For example: If dividend = 15968, Quotient = 89 and remainder = 37 then Divisor is?

Divisor =

=


Divisibility Rules:

For Number

Divisibility Rule Example Note

2 If the last digit of a number is 0,2,4,6,8 , then the number is divisible by 2

742 is divisible by 2 but 743 is not.

3 If the sum of all the digits of a number is divisible by 3 , then the number is divisible by 3

1458 (sum of digits = 18) is divisible by 3, but 766 (sum of digits =19) is not divisible by 3.

766 (sum of digits =19) the remainder when 19 is divided by 3 i.e. 1 will also be the remainder when 766 is divided by3

4 If the last two digits of a number are divisible by 4, then the number is also divisible by 4

6732 is divisible by 4 as 32 is divisible by 4, but 2142 is not divisible by 4.

Similarly the remainder when 42 is divided by 4 i.e 2 will also be the remainder when 2142 is divided by 4.

5 If the last digits of a number are 0 and 5, then the number is divisible by 5.

1465, 1320 are divisible by 5 as their last digit is 5 and 0 respectively.

6 If the number is divisible by 2 and 3 both, then it is also divisible by 6.

1452 is divisible by both 2 and 3 so it is divisible by 6 also, but 3362 is not divisible by 6 as it is not divisible by 3.

If the number is divisible by 4 and 6 both, then it is not necessary that it is

divisible by 24 (6 4).

8 If the last three digit of a number are divisible by 8 or are 000, then the number is divisible by 8 .

43102 and 13000 are divisible by 8 since 102 is divisible by 8 and 13000 have 000 as last three digits, but 2148 is not as

The remainder when 148 is divided by 8 i.e. 4 will also be the remainder of 2148


148 is not divisible by 8 when divided by 8.

9 If the sum of all digits of a number is divisible by 9 , then the number is also divisible by 9.

25344 (sum of digits = 18) is divisible by 9 , 764 (sum of digits =17) is not.

The remainder when 17 is divided by 9 i.e 8 will also be the remainder when 764 is divided by 9.

11 If the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or is divisible by 11 , then the number is also divisible by 11.

9415956 is divisible by 11 as the difference of 9+1+9+6 =25 and 4+5+5 = 14 is 11, but 31872 is not as the sum of even places = 13 and sum of odd is 8 their difference is neither 0 nor 11.


Solved Examples (Number System)

1. When X is subtracted from the numbers 9, 15 and 27, the remainders are in continued proportion. What is the value of X? (IBPS CWE PO MT 2012)

(1) 8 (2) 6 (3) 4 (4) 5 (5) None of these Solution: Let be subtracted from the numbers 9, 15 and 27 we get continue proportion. Now, 9 – : 15 – : 27 –

b2 = ac (15 – )2 = (9 – ) (27 – ) or, 225 – 30 + 2 = 243 + 2 – 36 or, 6 = 243 – 225 = 18

X = 3 Hence number become 9 - x = 9-3=6 15 – x = 15 -3 = 12 And 27-x = 27 -3 = 24

6 : 12 : 24 = 1: 2: 4 Thus 1: 2: 4 is continued proportion Ans: (5) 2. Sum of three consecutive numbers is 2262. What is 41% of the highest number? (IBPS CWE PO MT 2012)

(1) 301.5.1 (2) 303.14 (3) 308.73 (4) 306.35 (5) 309.55 Solution: Let the three consecutive number be x, x + 1 and x + 2. Then, x + x + 1 + x + 2 =2262 or, 3x = 2262 – 3 = 2259

x = = 753


The Numbers are 753, 754, 755. The highest number is 755 41% of 755 = 755 = 41 7.55 = 309.55

Ans: (5)

3. Rachita enters a shop to buy ice-creams, cookies and pastries. She has to buy at least 9 units of each. She buys more cookies than ice-creams and more pastries than cookies. She picks up a total of 32 items. How many cookies does she buy? (IBPS CWE PO MT 2012) (1) Either 12 or 13 (2) Either 11 or 12 (3) Either 10 or 11 (4) Either 9 or 11 (5) Either 9 or 10 Solution: Total number of items = 32 Maximum number of ice creams = 9

pastries> cookies> ice cream So, 13 10 9 12 11 9 Hence number of cookies is either 10 or 11. Number of pastries is either 13 or 12. Ans: (3) 4. The fare of a bus is Rs. x for the first five kilometres and Rs. 13/- per kilometre thereafter. If a passenger pays Rs. 2402/- for a journey of 187 kilometres, what is the value of X? (IBPS CWE PO MT 2012) (1) Rs. 29 (2) Rs. 39 (3) Rs. 36 (4) Rs. 31 (5) None of these Solution: Let the fare of first five kilometres be Rs. x. Total distance = 187 km Remaining distance = 187 - 5 = 182 km Now, x + 182 13 = 2402


x = 2402 - 2366= Rs.36 Ans: (3) 5. The product of three consecutive even numbers is 4032. The product of the first and the third number is 252. What is five times the second number? (1) 80 (2) 100 (3) 60 (4) 70 (5) 90 Solution: Let the three consecutive even numbers be 2x, 2x + 2 and 2x+4. Then, (2x) (2x + 2) (2x + 4) = 4032 ... (I) Again, product of first and third number 2x (2x + 4) = 252 ... (II) Putting the values of the product of first and third number in eqn (I), we have (2x + 2) 252 = 4032 or, 2x + 2 = = 16

x = 7 Hence, first number = 7 8 = 14 Second number = 7 x 2 + 2 = 16 And third number = 7 x 2 + 4 = 18 Five times of second number = 5 x 16 = 80 Ans: (1)

6. Rubina could get equal number of Rs. 55, Rs. 85 and Rs. 105 tickets for a movie. She spends Rs. 2,940 for all the tickets. How many of each did she buy?

(1) 12 (2) 14 (3) 16 (4) Cannot be determined (5) None of these

Solution: Let she buy x tickets. Then total money spent = 55x + 85x + 105x or, 245x = 2940 or, x = 12

Ans: (1)


7. Seema bought 20 pens, 8 packets of wax colours, 6 calculators and 7 pencil boxes. The price of one pen is Rs. 7, one packet of wax colour is for Rs. 22, one calculator is for Rs. 175 and one pencil box costs Rs. 14 more than the combined price of one pen and one packet of wax colours. How much amount did Seema pay to the shopkeeper?

(1) Rs. 1,491 (2) Rs. 1,725 (3) Rs. 1,667 (4) Rs. 1,527 (5) None of these

Solution: Price of one pencil box = 14 + (Price of one pen + Price of one packet of wax colours)= 14+ (7+22) = Rs. 43 Total amount paid by Seema = {(20 × 7) + (8 × 22) + (6 × 175) + (7 × 43)} = Rs 1667

Ans: (3)

8. In a cricket match, Sachin and Viru scored a century each (more than 100 runs) and Yuvi and Gauti scored a half century each. Gauti scored 76 runs and Yuvi scored 12 runs less than Gauti. Viru scored 102 runs. The sum of the scores of all the four players is 442. How many runs did Sachin score? (Corporation Bank PO 2011)

(1) 200 (2) 210 (3) 180 (4) 160 (5) None of these

Solution: Sachin's score = 442 – 76 – (76 – 12) – 102 = 200

Ans: (1)

9. The sum of seven consecutive even numbers of Set A is 378. What is the sum of a different set of four consecutive numbers whose lowest number is 23 less than the mean of Set A?

(1) 132 (2) 146 (3) 156 (4) 124 (5) None of these


Solution: Mean of Set A

Lowest number of Set B = (54 – 23) = 31 Sum of the four numbers of Set B = 31 + 32 + 33 + 34 = 130

Ans: (5)

10. The sum of six consecutive even numbers of Set-A is 402. What is the sum of another Set-B of four consecutive numbers whose lowest number is 15 less than double the lowest number of set- A? (Allahabad Bank Probationary Officers Exam 2011)

(1) 444 (2) 442 (3) 440 (4) 446 (5) None of these

Solution: Third even number = = 67 - 1 = 66

smallest even number = 62

smallest number of set B = 2 x 62 - 15 = 109

required sum = 109 + 110 + 111+ 112 = 442

Ans: (2)


Practice Set-1 (Number System)

1. A person on tour has Rs 360 for his daily expense. He decides to extend his tour programme by 4 days which leads to cutting down daily expense by Rs 3 a day. The number of days of his tour programme is

(1) 15 (2) 20 (3) 18 (4) 16

2. Two times a two-digit number is 9 times the number obtained by reversing the digits and sum of the digits is 9. The number is

(1) 72 (2) 54 (3) 63 (4) 81

3. If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15 students?

(1) 10 days (2) 12 days (3) 11 days (4) None of these

4. A man has certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcel, none is left over. What is the number of boxes he may have to pack?

(1) 106 (2) 301 (3) 309 (4) 400

5. Out of a group of swans, 7/2 times the square foot of the number are playing on the shore of the pond. The two remaining are inside the pond. What is the total number of swans?

(1) 10 (2) 14 (3) 12


(4) 16

6. In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?

(1) 4 (2) 3 (3) 2 (4) 5

7. A yearly payment to a servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and received 65 and a turban. Then find the price of the turban.

(1) Rs 10 (2) Rs 15 (3) Rs 7.50 (4) Cannot be determined

8. Mr. Mukherjee is 5 yr older to his wife and they have one son and one daughter. If the daughter is 23 yr younger to his mother, what is the difference in the ages of the brother and the sister?

(1) 7 yr (2) 12 yr (3) 4 yr (4) 2 yr

9. The expenses of a hotel consist of two parts. The first one varies with the number of inmates, while the second one is fixed. When the numbers of inmates are 275 and 350, the expenses are Rs 1600 and Rs 1900 respectively. The expenses when the number of inmates is 315, are

(1) Rs 1760 (2) Rs 1680 (3) Rs 1780 (4) Rs 1660

10. If the numerator of a fraction is doubled and the denominator is increased by 3, the new fraction is 3/5 what is the original fraction, if its denominator is more than twice the numerator by 1?

(1) 3/7 (2) 6/13 (3) 1/3 (4) 5/11


Practice Set-2 (Number System)

1. The sum and product of two numbers are 5 and 6, respectively. The sum of reciprocals of their squares is

(1)

(2)

(3)

(4)

2. The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is

(1) 30 (2) 33 (3) 36 (4) 45

3. The sum of a natural number and its square equals the product of the first three prime numbers. The number is

(1) 2 (2) 3 (3) 5 (4) 6

4. 47 is added to the product of 71 and an unknown number. The new number is divisible by 7, giving the quotient 98. The unknown number is a multiple of

(1) 2 (2) 7 (3) 5 (4) 3


5. Two natural numbers are in the ratio 3: 5 and their product is 2160. The smaller of the number is

(1) 36 (2) 24 (3) 18 (4) 12

6. The sum of two numbers is 10. Their product is 20. Find the sum of the reciprocals of the two numbers.

(1) 1

(2)

(3)

(4)

7. The sum of the digits of a two digit numbers is 10. The number formed by reversing the digits is 18 less than the original number. Find the original number.

(1) 81 (2) 46 (3) 64 (4) 60

8. The least number to be subtracted from 36798 to get a number which is exactly divisible by 78 is

(1) 18 (2) 60 (3) 38 (4) 68

9. The sum of first sixty number from one to sixty is divisible by

(1) 13 (2) 59 (3) 60 (4) 61


10. Eight consecutive number are given. If the average of the two numbers that appear in the middle is 6, then the sum of the eight given numbers is

(1) 36 (2) 48 (3) 54 (4) 64


Number System Practice Set-1 (Answers)

1 (2)

2 (4)

3 (3)

4 (2)

5 (4)

6 (2)

7 (1)

8 (4)

9 (1)

10 (1)


Number System Practice Set-2 (Answers)

1 (1)

2 (2)

3 (3)

4 (4)

5 (1)

6 (3)

7 (3)

8 (2)

9 (4)

10 (2)


Chapter: Data Interpretation Introduction:

Analyzing data is the major part of our daily routine. Financial data as in P & L sheet, marketing

and sales data, data on productivity, data on performance appraisal, data on each and every

thing that we can imagine. In some companies entire department generates and manages every

conceivable data that we can imagine.

To collect information from all the amount of data it needs to be presented in a lucid and

concise manner. Therefore we use data representation as it immediately provides the overall

scenario and it is also sufficient to compute any detailed information.

Strategies:

While studying the DI section one should follow few strategies given below:

1. Solve the graph with which you are most comfortable for example some are more

comfortable with line graph while the other may be with pie chart.

2. The problems with numbers with 2 or 3 digits like 82, 114 etc are easier to solve then

the problem with number of 4 or 5 digits like 3457, 52468.

3. In pie charts if sectors are 15% 20% etc then it will be easier calculation then the sectors

like 17.5%, 23.6 % etc.

4. We must also look at the number in answer option, if the answers are 12.5 5 6.33% etc

then it will be easier to arrive at.

5. Wider are the choices in answer, easier will be the elimination process and lesser will be

the calculation.

6. The answer choice “ Cannot be determined “ makes the question much easier as it

becomes data sufficiency question and if the question can be answered then only four

options are left.


7. Pick the alternative which is the middle one and check if your answer is less than, equal

to or greater than this value. In this way only one iteration will give you the correct

answer.

8. Te answer choice “None of these “on the other hand make it more difficult as we have

to calculate the question to the exact value.

9. It is better to solve a line chart with two lines and 5 points than to solve a table with 5

rows and 6 columns. But this may not be the case always looking at the other factors.

Growth rate and Growth:

Growth and Growth rate are two different cases. Growth refers to just increase in the

underlying value, while the Growth rate refers to the percentage increase. For example

following table shows the sales and profit of a company A in Rs. Lakhs

1999 2000 2001 2002 2003

Sales 240 290 320 350 380

Profit 50 55 70 50 40

Here,

Growth during the period from 2000 to 2002 is simple the difference of sales = 350-290 = 60

But the Growth rate during this period is the percentage of growth =

Profit Percentages:

The profit percentage is not but it is . For example in above

table the profit percentage of year 1999 is not = .


But the profit percentage of year 1999 is = as cost price of this year is 190

Also the percentage change in profit percentage is percent of profit percent of two years with

base as previous year profit percent. For example the percentage change in profit percentage in

the year 2002 over that in year 2001 is:

=

=

But in line graph growth rate is related to slope of line. There are few points to understand:

1. The slope of each segment is same across all years of company B but still the growth

rate is not the same in all years. The same slope simply means the sales grow by a

constant amount each year. But the growth rate depends on the base value so in

company B it’s decreasing from 2000 to 2004.

2. The line representing sales of A in 2002-03 is steeper but 2003 is not the year with

highest growth rate of sales of A . The highest growth rate of sale of A is in year 2001.


Chapter: Data Interpretation-Table Chart In studying problems on statistics, the data collected by the investigator are arranged in systematic form, called the tabular form. In order to avoid some heads again and again, we make tables, consisting of horizontal lines called rows and vertical lines called columns with distinctive heads, known as captions. Units of measurements are given along with the captions.

Example:

The table given below shows the population, literates and illiterates (in thousands) and the percentage of literacy in 3 states, in a year:

State Population Literates Illiterates Percentage of literacy

Madras 49342 6421 …………….. ……………………

Bombay ……………. 4068 16790 ……………………..

Bengal 60314 …………… …………… 16.1

After reading the table, mark a tick ( ) against the correct answer in each question given below and hence complete the table.

1) Percentage of literacy in Madras is (a) 14.9% (b) 13.01% (c) 12.61% (d) 15.04%

2) Percentage of literacy in Bombay is (a) 19.5% (b) 16.7% (c) 18.3% (d) 14.6%


3) Number of literates in Bengal (in thousands) is: (a) 50599 (b) 9715 (c) 76865 (d) 9475

Solution:

1) (b) percentage of literacy in Madras = (6421/49342)×100% = 13.01% 2) (a) Population of Bombay = (4068+16790) thousands = 20858 thousands.

Therefore, percentage of literacy in Bombay = (4068/20858)×100% = 19.5% 3) (b) Number of literates in Bengal =(16.1/100)×60314 = 9715 thousands


Solved Examples (Data Interpretation-Table Chart)

Direction (1-5): Study the table carefully to answer the questions that follow :- (IBPS PO Exam 2011)

Number of people visiting six different Super-markets and the percentage of Men, Women and Children visiting those Super-markets

Names of the Total Number of Percentage of

Super- markets

People Men Women Children

A 34560 35 55 10

B 65900 37 43 20

C 45640 35 45 20

0 55500 41 26 33

E 42350 06 70 24

F 59650 24 62 14


1. The Number of men visiting Super-market D forms approximately what percent of the total number of people visiting all the Super-markets together?

(1) 11 (2) 5.5 (3) 13 (4) 9 (5) 7.5

Solution: Number of men visiting supermarket D

= 41% of 55500

= = 41×55500 = 22755

Total number of people visiting all the supermarkets together

= 34560 + 65900 + 45640 + 55500 + 42350 + 59650

= 303600

required probability = × 100 = 7.5% (Aprox)

Ans: (5)

2. The Number of children visiting Super-market C forms what percent of number of children visiting Super- market F? (rounded off to two digits after decimal)

(1) 91.49 (2) 49.85 (3) 121.71 (4) 109.30 (5) None of these

Solution: Number of children visiting supermarkets C

= 20% of 45640 = 20 x 45640 = = 9128

Number of children visiting supermarket F

= 14% of 59650 = = 8351


required percentage = x 100 = 109.30%

Ans: (4)

3. What-is the total number of children visiting Super-markets B and D together?

(1) 18515 (2) 28479 (3) 31495 (4) 22308 (5) None of these

Solution: Total number of children visiting supermarket B and D together

= 20% of 65900 + 33% of 55500

= +

= 13180 + 18315 = 31495

Ans: (3)

4. What is the average number of women visiting all the Super-markets together?

(1) 24823.5 (2) 22388.5 (3) 26432.5 (4) 20988.5 (5) None of these

Solution: Total number of women = 55% of 34560 + 43% of 65900 + 45% of 45640 + 26% of 55500+ 70% of 42350 + 62% of 59650

= 19008 +'28337 + 20538 + 14430 + 29645 + 36983

= 148941

required average = = 24823.5

Ans: (1)


5. What is the ratio of number of women visiting Super-markets A to that visiting Super- market C?

(1) 35: 37 (2) 245: 316 (3) 352: 377 (4) 1041: 1156 (5) None of these

Solution: Required ratio = 19008: 20538 = 1056: 1141

Ans : (3)

(Directions Q.6-10): Study the table carefully to answer the questions that follow :- (IBPS PO Exam 2011)

Percentage of Marks SUBJECTS (Maximum Marks)

Students Strategic Brand Compensation Consumer Service Training &

Management Management Management Behaviour Marketing Development (150) (100) (150) (125) (75) (50)

Anushka 66 75 88 56 56 90

Archit 82 76 84 96 92 88

Arpan 76 66 78 88 72 70

Garvita 90 88 96 76 84 86

Gunit 64 70 68 7.2 68 , 74

Pranita 48 56 50 64 64 58

6. How many marks did Anushka get in all the Subjects together?

(1) 369 (2) 463 (3) 558 (4) 496 (5) None of these

Solution: Total marks of Anuska

= + 75 + + + + 45


= = 99 + 75 + 132 + 70 + 42 + 45 = 463

Ans: (2)

7. The Marks obtained by Garvita in Brand Management are what percent of marks obtained by Archit in the same Subject? (rounded off to two digits after decimal)

(1) 86.36 (2) 101.71 (3) 115.79 (4) 133.33 (5) None of these

Solution: Marks obtained by Garvita in Brand Management

= 88% of 100 = 88

Marks obtained by Archita in Brand Management

= 76% of 100 = 76

required percentage = x 100 115.79%

Ans: (3)

8. What is the average marks obtained by all students together in Compensation Management?

(1) 116 (2) 120 (3) 123 (4) 131 (5) None of these

Solution: Average marks obtained by all students together in Compensation Management

=


= × 150=116

Ans: (1)

9. Who has scored the highest total marks in all the subjects together?

(1) Archit (2) Gunit (3) Pranita (4) Garvita (5) Arpan

Solution: Total obtained in all the subjects together by

Arapn: 76% of 150 + 66% of 100 + 78% of 150 + 88% of 125 + 72% of 75 + 70% of 50

= + + + + +

= 114 + 66 + 117 + 110 + 54 + 35 = 496

Archit: 82% of 150 + 76% of 100 + 84% of 150 + 96% of 125 + 92% of 75 + 88% of 50

= + + + + +

= 123 + 76 + 126 + 120 + 69 + 44 = 558

Garvita: 90% of 150 + 88% of 100 + 96% of 150 + 76% of 125 + 84% of 75 + 86% of 50 .

= 135 + 88 + 144 + 95 + 63 + 43 = 568

= + + + + +

= 135 + 88 + 144 + 95 + 63 + 43 = 568

Gunit: 64% of 150 + 70% of 100 + 68% of 150 + 72% of 125 + 68% of 75 + 74% of 50

= + + + + +

= 96 + 70 + 102 + 90 + 51 + 37 = 446

Pranita: 48% of 150 + 56% of 100 + 50% of 150 + 64% of 125 + 64% of 75 + 58% of 50


= + + + + +

= 72 + 56 + 75 + 80 + 48 + 29 = 360

Clearly, Garvita scored the highest total marks in all the subjects together.

Ans: (4)

10. How many Students have scored the highest marks in more than one Subject?

(1) three (2) two (3) one (4) none (5) Now of these

Solution: Archit (consumer behaviour and service marketing) and Garvita (strategic management, brand management and compensation management).

Ans: (2)


Practice Set (Data Interpretation-Table Chart)

Directions (Q. 1-5): Study the table carefully to answer the questions that follow

Number of cars (in thousand) of two models (Basic and Premium) produced by five different companies in five different years (IBPS RRB Grade Officer Exam 2012)

Company

A

B C D E

Year

Basic

Premium

Basic

Premium

Basic

Premium

Basic

Premium

Basic

Premium

2006 4.4 2.5 5.6 2.4 5.4 6.1 7.6 7.5 2.7 5.1

2007 4.9 7.2 9.4 7.2 7.5 8.3 8.4 4.9 4.2 5.5

2008 13.6 15.5 14.8 9.5 12.8 9.9 9.2 8.2 7.7 11.5

2009 6.6 13.9 11.8 11.4 16.6 18.2 10.6 10.4 7.2 12.8

2010 5.8 14.9 12.2 7.2 19.9 22.3 14.6 12.2 13.2 12.2

1. The number of cars of premium model produced by Company D in the year 2009 was approximately what per cent of the total number of cars (both models) produced by Company C in the year 2007?

(1) 70 (2) 51 (3) 56 (4) 61 (5) 66


2. What was the approximate percentage decrease in the number of cars of basic model produced by Company B in the year 2009 as compared to the previous year?

(1) 15 (2) 20 (3) 10 (4) 80 (5) 85 3. What was the average number of cars of premium model produced by Company A over all the years together?

(1) 9000 (2) 8000 (3) 6000 (4) 48000 (5) None of these

4. In which year was the difference between the basic model and the premium model of cars produced by Company E the second highest?

(1) 2010 (2) 2006 (3) 2007 (4) 2008 (5) 2009

5. In which company did the production of cars of premium model consistently increase from the year 2006 to the year 2010?

(1) Both C and E (2) Both C and d (3) C only (4) D only (5) E only


Directions (Q. 6-10): Study the table carefully to answer the questions that follow.

Number of animals in grasslands of four different countries in five different years (RBI Grade’B’ Officer’s Exam 2011)

Year

Country

South Africa China Sri Lanka England

Tiger Lion Bear Tiger Lion Bear Tiger Lion Bear Tiger Lion Bear

1990 145 156 250 320 346 436 280 468 255 423 342 234

1995 134 165 354 445 256 542 354 354 343 368 136 345

2000 120 135 324 583 325 454 433 345 545 354 267 456

2005 110 184 285 466 475 322 343 324 546 562 235 567

2010 160 224 264 411 535 534 535 532 453 349 345 324

6. What is the average of the number of tigers in the grassland of Sri Lanka over all the years together?

(1) 386 (2) 389 (3) 369 (4) 276 (5) None of these

7. What is the difference between the total number of lions and bears in the grassland of England in the year 2005 and the number of tigers in the grassland of South Africa in the year 1995?

(1) 597 (2) 558 (3) 677 (4) 668 (5) None of these


8. The total number of animals together in the grassland of China in the year 1990 is approximately what per cent of the total number of bears in the grassland of Sri Lanka over all the years together?

(1) 44% (2) 56% (3) 41% (4) 47% (5) 51%

9. If 35 per cent of the total number of animals in the grassland of China in the year 2010 died due to an epidemic, how many animals remained in the grassland of China in the year2010?

(1) 976 (2) 952 (3) 986 (4) 962 (5) None of these

10. What is three-fourths of the total number of lions in the grasslands of all the four countries in the year 2000?

(1) 848 (2) 868 (3) 804 (4) 824 (5) None of these


Directions (Q. 11-5): Study the table carefully to answer the questions that follow:

Number of girls and boys (in hundreds) in six different years in five different schools

School

Years

A B C D E

Boys Girls Boys Girls Boys Girls Boys Girls Boys Girls

2005 3.3 3.6 5.2 3.1 5.5 4.5 2.4 1.4 6.5 6.6

2006 6.6 4.2 4.9 2.2 6.9 3.3 4.4 2.3 5.5 3.6

2007 9.3 6.9 4.7 4.2 5.8 4.9 6.4 3.3 2.7 2.4

2008 5.4 9.6 6.3 5.4 6.6 5.2 5.3 5.4 5.4 5.7

2009 8.4 12.9 7.5 5.9 8.7 6.6 12.1 5.2 6.8 6.5

2010 12.3 14.4 9.8 4.4 11.7 4.2 12.2 9.4 10.8 12.7

11. What is the approximate percentage decrease in the number of boys in School D in the year 2008 as compared to that in the previous year?

(1) 17 (2) 12 (3) 9 (4) 5 (5) 23

12. The number of girls in School B in the year 2009 is approximately what per cent of the total number of students (both boys and girls) in School E in the year 2006?

(1) 46 (2) 52 (3) 70 (4) 58 (5) 65

13. What is the average number of girls in School A in all the years taken together?

(1) 760 (2) 800 (3) 860


(4) 600 (5) None of these

14. What is the ratio of the number of boys in School C in the year 2009 to the number of girls in School A in the year 2009?

(1) 29 : 41 (2) 36 : 11 (3) 29 : 43 (4) 36: 13 (5) None of these

15. In which year is the total number of students (both girls and boys together) the third highest in School E?

(1) 2006 (2) 2007 (3) 2008 (4) 2005 (5) 2010


Directions-(Q. 16-20) Study the table carefully to answer the questions that follow:

Number of Athletes (in hundreds) who participated in a Sports Event from Five Different Countries over the years (Allahabad Bank Probationary Officers Exam 2011)

Countries

Year

A B C D E

Male Fem Male Fem Male Fem Male Fem Male Fem

2005 4.4 3.3 6.3 4.2 4.5 3.1 5.6 4.1 4.7 2.1

2006 6·6 4·2 8·4 6·2 6·9 3·3 8·4 6·3 7·8 5·2

2007 4·6 1·8 7·4 4·8 4·8 2·8 9·3 7·3 8·7 6·5

2008 9.6 4·9 11.4 8·4 6·6 4·2 12·6 9·4 8·9 5·8

2009 11.8 6·4 10·6 5·2 7·9 6·3 14.4 10·2 11·8 9·2

2010 8·2 5·2 6·4 7·2 10·8 6·9 15·6 12·1 13·6 9·8

16. In which of the following years was the total number of participants (athletes) second highest from Country C?

(1) 2005 (2) 2006 (3) 2007 (4) 2008 (5) None of these

17. What was the average number of female athletes who participated from Country B over all the years together?

(1) 1200 (2) 400 (3) 600 (4) 1800 (5) 3600


18. What was the approximate percentage decrease in the number of male athletes who participated from Country C in the year 2007 as compared to the previous year?

(1) 21 (2) 30 (3) 35 (4) 39 (5) 25

19. The Number of female athletes who participated from Country E in the year 2009 was approximately what percentage of the 42 total number of athletes who participated from Country-B in the year 2008?

(1) 40 (2) 46 (3) 50 (4) 56 (5) 60

20. In which of the following country is the difference between the number of male and female participants second highest in the year 2006?

(1) A (2) B (3) C (4) D (5) E


Data Interpretation-Table Chart Practice Set (Answers)

1) 5 2) 2 3) 5 4) 5 5) 3 6) 2 7) 4 8) 5 9) 4 10) 3

11) 1 12) 5 13) 3 14) 3 15) 5 16) 5 17) 3 18) 2 19) 2 20) 5


Chapter: Data Interpretation-Line Graphs Line graphs of a frequency distribution is obtained from the histogram of the frequency distribution by joining the mid points of respective tops of the rectangles in a histogram.

To complete the line graphs, the mid-points at each end are joined to the immediately lower or higher mid-points (as the case may be) at zero frequency.

Example: Study the following graph and answer the following questions:

1.) The total expenditure of which of the following pairs of years was equal to the income in 1992?

(a) 1987 and 1988 (b) 1987 and 1989 (c) 1988 and 1989 (d) 1988 and 1990 (e) none of these

2.) What was the percentage decrease in expenditure from 1988 and 1989?


(a) 80 (b) 50 (c) 40 (d) 10 (e) none of these

3.) In how many of the given years was the expenditure more than the average expenditure of the given years?


4.) In which of the following years was the percentage of expenditure to income, the highest?


5.) What was the approximate percentage increase in income from 1991 to 1992?

(a) 35 (b) 40 (c) 20 (d) 15 (e) 25

Solution:

1.) (c) : income in 1992= 475 crores

Total expenditure in 1988 and 1989 = Rs.( 250+225) crores

=Rs. 475 crores.

2.) (d) : expenditure in 1988 = Rs. 250 crores

Expenditure in 1989 = Rs. 225 crores.

Decrease % = = 10%

3.) (b): average expenditure =Rs.

=Rs. 287.5

The expenditure is greater than the average expenditure during the years 1987, 1990 and 1992.

Required no. of years =3

4.) (e): the required percentage :

In 1987 is (300×100/450)% = 66.66%

In 1988 is (250×100/400)% = 62.5%

In 1989 is (225×100/350)% = 64.29%


In 1990 is (375×100/425)% = 88.24%

In 1991 is (175×100/375)% = 46.6%

In 1992 is (400 ×100/475)% = 84.21%

Clearly the percentage is highest in 1990.

5.) (e): income in 1991 = 375 crores

Income in 1992 = 475 crores

Therefore increase % = (100×100/375)% = 26.6% = 25% nearly


Solved Examples (Data Interpretation-Line Graphs)

Directions-(Q.1-5): Study the following graph carefully to answer the questions that follow: (Allahabad Bank Probationary Officers Exam 2011)

1. In which state was the total number of trees planted by NGO A and NGO B together second lowest?

(1) Bihar (2) Punjab (3) Haryana (4) Assam (5) Tamil Nadu

Solution: Number of tree planted by NGO-A and NGO-B together in

Bihar: 100 + 60 = 160

Punjab: 120 + 80 = 200

Haryana: 80 + 140 = 220

Assam: 150 + 160 = 310


Tamil Nadu: 140 + 180 = 320

Ans: (2)

2. What was the difference between the trees planted by NGO A in Haryana and the number of trees planted by NGO C in Tamil Nadu?

(1) 90 (2) 60 (3) 120 (4) 100 (5) None of these

Solution: Required difference = 160 – 80 = 80

Ans: (5)

3. What was the average number of trees planted in Haryana by all the NGOs together?

(1) 420 (2) 140 (3) 120 (4) 390 (5) None of these

Solution: Required average = = 129

Ans: (5)

4. The total number of trees planted by NGO A and NGO B together in Bihar was approximately what per cent of the total number of trees planted by NGO-B and NGO-C together in Punjab?

(1) 85 (2) 90 (3) 105 (4) 110 (5) 95

Solution: Required percentage = × 100 = × 100 95%

Ans: (5)


5. What was the ratio of the number of trees planted by NGO B in Tamil Nadu, number of trees planted by NGO C in Assam and the number of trees planted by NGO A in Assam?

(1) 5: 3 : 6 (2) 5: 6 : 3 (3) 6: 4 : 5 (4) 6: 5 : 3 (5) None of these

Solution: Required ratio: 180: 120 + 150 = 6: 4: 5

Ans: (3)

Direction (Q. 6 – 10): Study the graph carefully and answer the questions that follow:

Per cent profit made by two companies over the years

6. If in the year 2006 the expenditures incurred by company P and Q were same, what was the ratio of the income of company Q to that of company P in that year?

(a) 26 : 27 (b) 27 : 26 (c) 24 : 25 (d) 25 : 24 (e) None of these

Answer: (c)


7. If the amount of profit earned by company Q in the year 2007 was Rs. 2.4 lakhs, what was its expenditure in that year?

(a) Rs. 13 lakhs (b) Rs. 15 lakhs (c) Rs. 24 lakhs (d) Rs. 16 lakhs (e) Rs. 20 lakhs

Answer: (d) 8. What is the average per cent profit earned by company P over all the years together?

(a) 30 (b) 25 (c) 40 (d) 33 (e) None of these

Answer: (b) 9. If in the year 2009, the incomes of both the companies P and Q were same, what was the ratio of the expenditure of company P to the expenditure of company Q in the same year?


Answer: (a) 10. What is the ratio of the amount of profit earned by company A to that by company B in the year 2010?

(a) 27 : 24 (b) 24 : 27 (c) 23 : 24 (d) 24 : 23 (e) None of these Cannot be determined

Answer: (e)


Practice Set (Data Interpretation-Line Graphs)

Directions (1-5): Study the following graph carefully and answer the questions given below: (Allahabad Bank PO Exam: 2010)

Profit earned by Three Companies over the years (Rs. in crores)

1. What was the average profit earned by all the three companies in the year 2008?

(a) Rs. 300 crore

(b) Rs. 400 crore

(c) Rs. 350 crore

(d) Rs. 520 crore

(e) None of these

2. In which of the following years was the difference between the profits earned by company B and company A the minimum?

(a) 2003

(b) 2004


(c) 2005

(d) 2008

(e) None of these

3. In which of the following years was the total profit earned by all three comapnies together the highest?

(a) 2004

(b) 2007

(c) 2008

(d) 2009

(e) None of these

4. What was the approximate percentage increase in the profit earned by Company A from 2006 to 2007?

(a) 36

(b) 24

(c) 40

(d) 20

(e) 54

5. What was the difference between the profit earned by company A in 2004 and the profit earned by company C in 2009?

(a) Rs. 50 crore

(b) Rs. 1 crore

(c) Rs. 100 crore

(d) Rs. 200 crore

(e) None of these


Direction (Q. 6 – 10): Study the given graph carefully and answer the questions that follow:

The line diagram shows the cost of production and profit of six companies for the year 2011-12. (The figures are in 'Lakhs').

Revenue = Cost of Production + Profit.

6. The ratio of profits of company B and D to the profits of A and E is:


7. The profit of company C is what percentage of the revenue of company F?

(a) 20% (b) 25% (c) 30% (d) 35% (e) None of these

8. The revenue of company C is how many times of company E's profit?

(a) 5.5 (b) 5.25 (c) 5.75 (d) 5 (e) None of these


9. Which company has the maximum percentage of profit?

(a) C (b) D (c) E (d) F (e) None of these

10. What is the average profit of the last five companies (B, C, D, E and F)?

(a) Rs. 500 (b) Rs. 5,000 (c) Rs. 50,000 (d) Rs. 4,66,667 (e) None of these


Data Interpretation-Line Graphs Practice Set (Answers)

1. (b)

2. (e)

3. (d)

4. (a)

5. (c)

6. (d)

7. (a)

8. (c)

9. (b)

10. (e)


Chapter: Data Interpretation-Bar Graphs In a bar diagram, information is presented by means of rectangles, whose lengths indicate the quantity of the variable which the bar is representing. The following points are important:

1) All bars are in the form of rectangles and the width of the bars is uniform throughout the diagram.

2) The height of each bar is proportional to the frequency of the variable. 3) The gap between various bars is uniform. 4) The base line of all the bars is the same. 5) The bars can be either horizontal or vertical depending on the space available.

Example: The expenditure of a company under different heads (in thousands of rupees) is given below:

Head Expenditure(in thousands of rupees)

Salary of employees 400

Travelling allowance (TA) 100

Rent 150

Equipment 200

Miscellaneous 300

Draw a bar chart to depict the above data.


Example: The following bar diagram represents the percentages of total expenditure incurred by a state during the years 1981- 90 for different items. In each bar the blue portion stands for the expenditure during the first five years and the red portion stands for the next five years. Study the graph and answer questions 1-5.

1) Which of the items listed below accounts for the maximum expenditure during the year 1981 to 1985?


(a) Communication (b) education (c) health (d) housing 2) Which of the items listed below accounts for the maximum expenditure during 1986

to 1990? (a) Agriculture (b) communication (c) education (d) health 3) The amount of expenditure on Agriculture is approximately what proportion of that

on industry during the year 1986-90? (a) 1/5 (b) ¼ (c) 1/3 (d) data inadequate 4) If the total expenditure on housing is Rs. 610 crores during 1981-85, the total

expenditure on industry during the same period would (approximately) (a) Rs 2440 crores (b) Rs 1220 crores (c) Rs 4620 crores (d) none of these 5) Out of every 10,000 rupees spent during 1981-90 approximately, how much was spent

during the years 1981-85 on housing? (a) Rs 1400 (b) Rs 700 (c) Rs 1000 (d) Rs 2800

Answer:

1) (d) out of the items listed in the question, clearly maximum expenditure during 1981-85 is on housing.

2) (a) out of the items listed in the question, clearly the maximum expenditure during 1986-90 is on agriculture.

3) (a) expenditure on agriculture during 1986-90 a. = (15-10)% of total expenditure = 5x/100 = x/20 b. Expenditure on industry during 1986-90 c. = (52.5-27.5)% of total expenditure = 25x/100 =x/4. d. Required ratio = x/20 : x/4 = 1:5

4) (d) expenditure on housing during 1981-85 = 10% of total expenditure. a. Let the total expenditure be Rs. x. b. Then , 105 of x = 610 crores or 10x/100 =610 crores c. x=6100 crores d. total expenditure on industry during 1981-85 = 25% of 6100 crores e. = Rs 1525 crores.

5) (c) 20% of total expenditure during 1981-90 was spent on housing. a. Expenditure on housing during 1981-90 for a total expenditure of Rs 10000 =

(20×10000/100) = Rs 2000 b. Ratio of expenditure on housing during 1981-85 and that during 1986-90=

10%/(20-10)% = 1/1 c. Expenditure on housing during 1981-85 = Rs 1000


Solved Examples (Data Interpretation-Bar Graphs)

Directions (Q. 1-5): Study the following graph and answer the questions given below:

1. Out of the total number of students who opted for the given three subjects, in the year 2009, 38% were girls. How many boys opted for Mathematics in the same year?

(1) 1322 (2) 1332 (3) 1312 (4) Cannot be determined (5) None of these

Solution: Number of students who opted for all three subjects in 2009 = (20 + 20 + 5) thousand = 45000

Number of boys = = 27900

Since, we do not know the number of girls in Mathematics, number of boys opted for Mathematics cannot be determined.

Ans : (4)


2. If the total number of students in the University in the year 2007 was 455030, then, the total number of students who opted for the given three subjects were approximately what percent of the total students?

(1) 19 (2) 9 (3) 12 (4) 5 (5) 23

Solution: Required percentage = 100

= 100 9

Ans: (2)

3. What is the total number of students who opted for Hindi and who opted for Mathematics in the years 2006, 2007 and 2009 together?

(1) 97000 (2) 93000 (3) 85000 (4) 96000 (5) None of these

Solution: Required number of students

= (5 + 35 + 15 + 15 + 20 + 5) x 1000

= 95 x 1000 = 95000

Ans: (5)

4. The total number of students who opted for Mathematics in the years 2005 and 2008 together are approximately what percent of the total number of students who opted for all three subjects in the same years?

(1) 38 (2) 28 (3) 42 (4) 32 (5) 48


Solution: Required percentage

= ×100

= × 100 = × 100 32

Ans: (4)

5. What is the respective ratio between the number of students who opted for English in the years 2006 and 2008 together and the number of students who opted for Hindi in the year 2005 and 2009 together?

(1) 11: 5 (2) 12: 7 (3) 11: 7 (4) 12:5 (5) None of these

Solution: Required ratio = (25 + 30): (5+20) = 55:25 = 11:15

Ans: (1)

Directions (Q. 6-10): Study the following graph carefully to answer the questions that follow:

Monthly income (Rs in thousand) of three different persons in six different years (IBPS RRB Grade ‘A’ Officers Exam 2012)


6. What was the difference between the total monthly salary of Arun in all the years together and Suman's monthly income in the year 2007?

(1) Rs. 1.24 Iakh (2) Rs. 1.14 Iakh (3) Rs. 11.4 lakh (4) Rs. 12.4 lakh (5) None of these

Solution. Arun monthly income in all year together

Suman's monthly income in the year 2007

= 15 thousand

Difference = 129 – 15 = 114 = 114 1000 = 114000 lakh

Ans: 2

7. What is the ratio of Arun's monthly income in the year 2006, Suman's monthly income in the year 2007 and Jyoti's monthly income in the year 2005?

(1) 6:3:5 (2) 6:4:5 (3) 5:6:4 (4) 5:4:7 (5) None of these

Solution. Ratio = Arun : Suman : Jyoti

18 : 15 : 9

6 : 5 : 3

Ans: 5


8. In which year was the difference between Jyoti's and Arun's monthly income the second highest?

(1) 2005 (2) 2006 (3) 2007 (4) 2009 (5) 2010

Solution. Difference in 2005 14 – 9 = 5

2006 18 – 10 = 8

2007 23 – 18 = 5

2008 27 – 21 = 6

2009 27 – 26 = 1

2010 35 – 26 = 9

Ans: 2

9. The monthly income of Suman in the year 2009 was approximately what percentage of the monthly income of Jyoti in the year 2010?

(1) 72 (2) 89 (3) 83 (4) 67 (5) 95

Solution. Monthly income of Suman in 2009 = 29000

Monthly income of Jyoti in 2010 = 35000

Ans: 3


10. What was the percentage increase in the monthly income of Jyoti in the year 2008 as compared to the previous year?

(1) 50 (2) 150 (3) 160 (4) 60 (5) None of these

Solution.

Ans: 1


Practice Set (Data Interpretation-Bar Graphs)

Directions (Q. 1-5): Study the following graph carefully to answer the questions that follow: (Corporation Bank PO 2011)

1. What is the percentage increase in the number of runs scored by Team B in Match 4 as compared to that in the previous match (Match 3)?

(1) 40 (2) 30 (3) 20 (4) 25 (5) None of these


2. What is the ratio of the number of runs scored by Team A in Match 2 to the number of runs scored by Team C in Match 6?

(1) 5 : 4 (2) 2 : 5 (3) 2 : 3 (4) 3 : 4 (5) None of these

3. What is the average number of runs scored by Team B in all the matches together?

(1) 250 (2) 275 (3) 200 (4) 300 (5) 225

4. The number of runs scored by all the teams together in Match 3 is approximately what percentage of the total runs scored by Team C in all the matches together?

(1) 37 (2) 57 (3) 52 (4) 47 (5) 42

5. In which match is the total runs scored by all the teams together the second highest?

(1) Match 2 only (2) Match 6 only (3) Match 4 only (4) Both Match 2 and Match 6 (5) Both Match 2 and Match 4


Directions (Q. 6-10): Study the given graph carefully to answer the questions that follow:

6. What is the average number of people using mobile service M for all the years together?

1) 16

2) 14444

3) 16666

4) 14

5) None of these

7. The total number of people using all the three mobile services in the year 2007 is what per cent of the total number of people using all the three mobile services in the year 2008? (rounded off to two digits after decimal)

1) 89.72 2) 93.46 3) 88.18


4) 91.67 5) None of these

8. The number of people using mobile service N in the year 2006 forms a proximately what per cent of the total number of people using all the three mobile services in that year?

1) 18 2) 26 3) 11 4) 23 5) 29

9. What is the ratio of the number of people using mobile service L in the year 2005 to that of those using the same service in the year 2004?

1) 8: 7 2) 3 : 2 3) 19: 13 4) 15: 11 5) None of these

10. What is the total number of people using mobile service M in the years 2008 and 2009 together?

1) 35,000 2) 30,000 3) 45,000 4) 25,000 5) None of these


Data Interpretation-Bar Graphs Practice Set (Answers)

1) 3

2) 3

3) 1

4) 5

5) 4

6) 5

7) 4

8) 1

9) 2

10) 3


Chapter: Data Interpretation-Pie Diagram In a pie chart, the values of different components of a frequency distribution are represented by the sectors of a circle. These sectors are so constructed that the area of each sector is proportional to the corresponding value of the component.

Since the sum of all the central angles is 360 degrees, we have

Central angle of a component = degrees

Example: The following pie diagram shows the expenditure incurred on the preparation of a book by a publisher, under various heads.

A: Paper 20, B: Printing 25%, C: Binding, Canvassing, Designing etc 30%

D: Miscellaneous 10% E: Royalty 15%

Study the diagram carefully and answer the questions 1-5:

1) What is the angle of pie diagram showing the expenditure incurred on paying the royalty?

(a) 15 degrees (b) 24 degrees (c) 48 degrees (d) 54 degrees


2) The marked price of a book is 20% more than the C.P. If the marked price of the book be Rs 30, what is the cost of paper used in a single copy of the book?

(a) Rs. 6 (b) Rs. 5 (c) Rs 4.50 (d) Rs 6.50 3) Which two expenditures together will form an angle of 108 degrees at the centre of the

pie diagram: (a) A and E (b) B and E (c) A and D (d) D and E 4) If the difference between two expenditures be represented by 18 degrees in the pie-

diagram, these expenditures are : (a) B and E (b) A and C (c) B and D (d) none of these

Answers: 1) (d) Angle representing royalty D = (15×360/100)degrees = 54 degrees 2) (b) C.P. of a book = Rs ( 100×30/120) = Rs 25 Cost of paper = Rs (20×25/100) = Rs 5 3) (c) angle A = (20×360/100)degrees =72 degrees Angle B = (25×360/100) degrees = 90 degrees Angle C = (30×360/100)degrees = 108 degrees Angle D = (10×360/100) degrees = 36 degrees Angle E = (15×360/100) degrees = 54 degrees Thus, A and D together will form an angle of 108 degrees. 4) (d) These expenditures are A and B; Band C; D and E; and A and E.


Solved Examples (Data Interpretation-Pie Diagram)

Direction (Q. 1-5): Study the following pie-chart and answer the questions given below:

Preferences of students among six beverages in terms of degree of angle in the pie-chart

Total No. of students = 6800

1. What is the difference between the total number of students who prefer Beverage A and C together and the total number of students who prefer beverage D and F together?

(1) 959 (2) 955 (3) 952 (4) 954 (5) None of these

Solution: Difference of corresponding angles = (122.4 + 21.6)0 - (79.2 + 14.4)0 = 50.40

required difference = x 6800 = 952

Ans: 3


2. What is the ratio of the number of students who prefer beverage F and the number of students who prefer beverage A?

(1) 3: 11 (2) 3: 13 (3) 6: 11 (4) 5: 11 (5) None of these

Solution: Required Ratio = 21.6: 79.2 = 3: 11

Ans: 1

3. The number of student who prefer beverage E and F together is what per cent of the total of student?

(1) 18 (2) 14 (3) 26 (4) 24 (5) None of these

Solution: Required percentage = ( ) × 100 =24%

Ans: 4

4. The number of students who prefer beverage C are approximately what percent of the number of students who prefer Beverage D?

(1) 7 (2) 12 (3) 18 (4) 22 (5) 29

Solution: Required percentage = × 100 = 11.76 12%

Ans: 2

5. How many students prefer beverage B and beverage E together?

(1) 2312 (2) 2313 (3) 2315 (4) 2318


(5) None of these

Solution: Number of students who prefer beverages B and E together

= × 68000 = = 2312

Ans: 1

Directions (Q. 6-10): Study the following pie-chart and answer the following questions. (IBPS RRB Group ‘A’ Officers Exam 2012)

Percentagewise distribution of teachers in six different universities.

Total number of teachers = 6400

6. The number of teachers in University B is approximately what per cent of the total number of teachers in University D and University E together?

(1) 55 (2) 59 (3) 49 (4) 45 (5) 65

Solution: Number of teachers in University B


Number of teachers in University D

Number of teachers in University E

Required percentage

Ans: 3

7. If twenty five per cent of the teachers in University C are females, what is the number of male teachers in University C?

(1) 922 (2) 911 (3) 924 (4) 912 (5) None of these

Solution: Number of teachers in University C

Number of female teachers in University C

Number of male teachers in University C

= 1216 – 304 = 912

Ans: 4

8. The difference between the total number of teachers in University A, University B and University C together and the total number of teachers in University D, University E and University F together is exactly equal to the number of teachers of which University?

(1) University A (2) University B (3) University C (4) University D


(5) University F

Solution: Number of teachers in University A

Number of teachers in University B

Number of teachers in University C

Number of teachers in University D

Number of teachers in University E

Number of teachers in University F

Difference = 3392 – 3008 = 384

Quicker method:

Difference = (D + E + F)% – (A + B + C)%

= (53 – 47) = 6%

6% of 6400 = 384

Hence, University of D is equal to 6%.

Ans: 4

9. If one-thirty sixth of the teachers from University F are professors and the salary of each professor is Rs. 96000, what will be the total salary of all the professors together from University F?

(1) Rs. 307.2 lakh (2) Rs. 32.64 lakh (3) Rs. 3.072 lakh (4) Rs. 3.264 lakh (5) None of these

Solution: Number of teachers in University F


Number of professors in University F

Total Salary of professors in University F

= 32 96000 = 30.72 lakh

Ans: 5

10. What is the average number of teachers in University A, University C, University D and University F together?

(1) 854 (2) 3546 (3) 3456 (4) 874 (5) None of these

Solution: Average

Ans: 5


Practice Set (Data Interpretation-Pie Diagram)

Directions (1-5): Study the following pie-charts carefully and answer the questions given below: Discipline-wise Breakup of the Number of candidates appeared in Interview and Discipline-wise Break up of the Number of candidates selected by an organisation

Discipline-wise Breakup of Number of candidates appeared in Interview

Total Number of Candidates Appeared In the Interview = 25780 Percentage Distribution

Discipline-wise Break-up of Number of candidates selected after Interview by the organization

Total Number of Candidates selected After Interview = 7390

Percentage Distribution


1. What was the ratio of the number of candidates appeared . in interview from other disciplines and the number of candidates selected from Engineering discipline respectively (rounded off to the nearest integer)?

1) 3609: 813 2) 3094: 813 3) 3094: 1035 4) 4125: 1035 5) 3981: 767

2. The total number of candidates appeared in interview from Management and other discipline was what percentage of number of candidates appeared from Engineering discipline?

1) 50 2) 150 3) 200 4) Cannot be determined 5) None of these

3. Approximately what was the difference between the number of candidates selected from Agriculture discipline and number of candidates selected from Engineering discipline?

1) 517 2) 665 3) 346 4) 813 5) 296

4. For which discipline was the difference in number of candidates selected to number of candidates appeared in interview the maximum?

1) Management 2) Engineering 3) Science 4) Agriculture 5) None of these

5. Approximately what was the total number of candidates selected from Commerce and Agricultural discipline together?

1) 1700


2) 1800 3) 2217 4) 1996 5) 1550

Directions (Q.6-10): Study the following pie-chart carefully to answer these questions. (Central Bank of India (PO) 2010)

Percentagewise Distribution of teachers who teach six different subjects Total number of Teachers = 1800

Percentage of teachers

6. If two-ninths of the teachers who teach Physics are female, then the number of male Physics teachers is approximately what percentage of the total number of teachers who teach Chemistry?

1) 57

2) 42

3) 63

4) 69

5) 51

7. What is the total number of teachers teaching Chemistry, English and Biology?

1) 1, 226


2) 1, 116

3) 1, 176

4) 998

5) None of these

8. What is the difference between the total number of teachers who teach English and Physics together and the total number of teachers who teach Mathematics and Biology together?

1) 352

2) 342

3) 643

4) 653

5) None of these

9. What is the ratio of the number of teachers who teach Mathematics to the number of teachers who teach Hindi?

1) 13:7

2) 7:13

3) 7: 26

4) 8: 15

5) None of these

10. If the percentage of Mathematics teachers is increased by 50 per cent and the percentage of Hindi teachers decreased by 25 per cent then what will be the total number of Mathematics and Hindi teachers together?

1) 390

2) 379

3) 459

4) 480

5) None of these


Direction (Q. 11 – 15): Study the given pie-charts carefully and answer the questions that follow:

Discipline-wise breakup of the number of candidates appeared in Interview and Discipline-wise breakup of the candidates selected by and organisation.

Total number of candidates appeared in the interview = 25,600 and total number of candidates selected after interview = 7,500.

11. What was the ratio of the number of candidates appeared in interview from other disciplines and the number of candidates selected from art disciplines?

(a) 256 : 125

(b) 125 : 256

(c) 125 : 216

(d) Cannot be determined

(e) None of these

12. The total number of candidates appeared in interview from Management and Art disciplines was what per cent of the number of candidates from Engineering discipline?

(a) 66.67


(b) 75

(c) 80

(d) 120

(e) 150

13. What was the difference between the number of candidates selected from Science discipline and the number of candidates selected from Commerce discipline?

(a) 1,000

(b) 1,100

(c) 1,200

(d) 1,250

(e) None of these

14. From which discipline was the difference in number of candidates selected to number of candidates appeared in interview the maximum?

(a) Management

(b) Engineering

(c) Commerce

(d) Science

(e) Art

15. What was the total number of candidates selected from Commerce and Art discipline together?

(a) 1,800

(b) 1,950

(c) 2,100

(d) 2,250

(e) 2,400


Data Interpretation- Pie Diagram Practice Set (Answers)

1. 2

2. 2

3. 5

4. 3

5. 1

6. 1

7. 2

8. 2

9. 5

10. 3

11. a

12. e

13. c

14. d

15. b


Chapter: Data Interpretation-Case lets Direction for questions 1 to 5: Answer these questions on the basis of the following information.

Shekhar bought 10 acres of land for Rs.250000 in 2011. That year he cultivated Sugarcane and Soya bean in the 10 acres with the ratio of area under Sugarcane and Soya bean being 5:4. The profit obtained from Sugarcane and Soya bean was in the ratio 3:2 with the total profit being Rs.58500. This was 15% of the amount he invested in cultivation that year. The next year he again cultivated Sugarcane and Soya bean, with the areas being same as before and reaped a profit of Rs.66000 in total with that from Sugarcane and Soya bean being in the ratio 8:7 but his return on his investment that year was only 14%.

1. What is the amount invested by Shekhar for cultivation in 2011?

(a) Rs.356000

(b) Rs.374800

(c) Rs.380000

(d) Rs. 390000

Solution: (d) Shekhar had a profit of Rs.58500 and this profit was 15% of the money he invested, his investment was

2. What is the profit obtained by Shekhar by cultivating Sugarcane in 2011?

(a) Rs.43800

(b) Rs.35100

(c) Rs.36200

(d) None of these

Solution: (b)

The profit obtained by Shekhar by cultivating Sugarcane in 2012 =


3. What is the profit obtained by cultivating Soya bean in 2012?

(a) Rs.30800

(b) Rs.36100

(c) Rs.24200

(d) None of these

Solution: (a)

The profit obtained by cultivating Soya bean in 2012 =

4. What is the ratio of the profit obtained from Sugarcane and Soya bean in the two years together?

(a) 89 : 79

(b) 167 : 211

(c) 703 : 542

(d) None of these

Solution: (c)

The profit obtained in 2011 from Sugarcane = Rs.35100

The profit obtained in 2012 from Sugarcane = 66000 - 30800 = Rs.35200

Total profit from Sugarcane = Rs.70300

Total profit in the two years = Rs.58500 + Rs.66000 = Rs.124500

Therefore, Profit from Soya bean Rs.54200.

Now, the required ratio = 70300: 54200 = 703 : 542.


5. What is the approximate amount invested by Shekhar for cultivation in 2012?

(a) Rs.428500

(b) Rs.471400

(c) Rs.495300

(d) Rs.518650

Solution: (b) Here the profit of 66,000 is 14% of the amount invested, therefore, the invested =


Solved Examples (Data Interpretation-Caselets)

Directions: (1-5) Study the following information and answer the questions that follow: (IBPS CWE PO MT 2012) The premises of a bank are to be renovated. The renovation is in terms of flooring. Certain areas are to be floored either with marble or wood. All rooms/halls and pantry are rectangular. The area to be renovated comprises of a hall for customer transaction measuring 23 m by 29 m, branch manager’s room measuring 13 m by 17 m, a pantry measuring 14 m by 13 m, a record keeping cum server room measuring 21 m by 13 m and locker area measuring 29 m by 21 m. The total area of the bank is 2000 square meters. The cost of wooden flooring is f 170/- per square meter and the cost of marble flooring is Rs. 190/- per square meter. The locker area, record keeping cum server room and pantry are to be floored with marble. The branch manager's room and the hall for customer transaction are to be floored with wood. No other area is to be renovated in terms of flooring. 1. What is the respective ratio of the total cost of wood en flooring to the total cost of marble flooring? (1) 1879: 2527 (2) 1887: 2386 (3) 1887: 2527 (4) 1829: 2527 (5) 1887: 2351 Solution: Total flooring area with marble = locker area + record keeping + pantry = 182+273 +609 = 1064 sqm Cost of flooring = 1064 190 Total flooring area with wooden = Branch Manager room + Hall = 221 + 667 = 888 sqm Cost of flooring = 888 170 Ratio= 888 170: 1064 190 = 888 17: 1064 19 = 15096 : 20216 = 1887: 2527 Ans: 3


2. If the four walls and ceiling of the branch manager’s room (The height of the room is 12 meters) are to be painted at the cost off 190/- per square meter, how much will be the total cost of renovation of the branch manager's room including the cost of flooring? (1) Rs. 1, 36,800/- (2) Rs. 2, 16,660/- (3) Rs. 1, 78,790/- (4) Rs. 2, 11,940/- (5) None of these Solution: Cost of flooring of branch manager room =221 170= Rs. 37570 Cost of painting = [2(17 12+ 13 12)+ 13 x 17] 190 = [2( 204 + 156) + 221] 190= (2 360 + 221) 190 = (720 + 221) 190 = 941 190 = Rs. 178790 Total cost = 178790 + 31570 = Rs.216360 Ans: (5) 3. If the remaining area of the bank is to be carpeted at the rate of Rs. 110/- per square meter, how much will be the increment in the total cost of renovation of bank premises? (1) Rs. 5,820/- (2) Rs. 4,848/- (3) Rs. 3,689/- (4) Rs. 6,890/- (5) None of these Solution: Total area of bank = 2000 sqm Total flooring area = 1952 sqm Remaining area = 2000 - 1952 = 48 sqm

Cost of carpeting = 48 110 = Rs.5280 Ans: (5) 4. What is the percentage area of the bank that is not to be renovated? (1) 2.2 % (2) 2.4 % (3) 4.2 % (4) 4.4 %


(5) None of these Solution: Area not to be renovated = 48 sq m

Reqd % = l00 = 2.4% Ans: 2 5. What is the total cost of renovation of the hall for customer transaction and the locker area? (1) Rs. 2, 29,100 (2) Rs. 2, 30,206 (3) Rs. 2, 16,920 (4) Rs. 2, 42,440 (5) None of these Solution: Cost of renovation of hall + locker area = 667 170 + 609 190 = 113390 + 115710= Rs. 229100 Ans: (1)

Directions (Q. 6 – 10): Study the given information carefully to answer the questions that follow:

An organization consists of 3500 employees working in different departments, viz HR, Marketing, IT, Production and Accounts. The ratio of male to female employees in the organisation is 3 : 2. 8% of the males work in the HR department. 22% of the female work in the account department. The ratio of males to females working in the HR department is 3 : 5. One-seventh of the females work in the IT department. 46% of the males work in the Production department. The number of females is one-sixth of the males working in the same. The remaining females work in the Marketing department. The total number of employees working in the IT department is 375. 22% of the males work in the Marketing department and remaining work in the Account department.

6. The number of males working in the Account department forms approximately what per cent of the total number of males in the organisation?

(a) 6 (b) 8 (c) 10


(d) 11 (e) 12

Answer: (a) 7. How many females work in Production department?

(a) 140 (b) 200 (c) 180 (d) 160 (e) None of these

Answer: (e) 8. The total number of employees working in the Account department forms approximately what per cent of the total number of female employees in the organisation?

(a) 28 (b) 32 (c) 29 (d) 31 (e) 30

Answer: (d) 9. The ratio of the numbers of females working in IT department to the numbers of males working in the same department is

(a) 15 : 8 (b) 1 : 2 (c) 8 : 15 (d) 2 : 1 (e) 7 : 11

Answer: (c) 10. What is the total number of employees working in the Marketing and Production departments together?

(a) 1900 (b) 2040 (c) 2020 (d) 2031 (e) 2042

Answer:(b)


PracticeSet-(Data Interpretation- Caselets)

Directions (Q. 1-5): Study the information carefully to answer the questions that follow.

A company produced five different products, viz mobile phone, pen drive, calculator, television and washing machine. The total number of all the five products is 1650.24% of the total number of products is mobile phones. One-sixth of the total number of products is pen drives. 14% of the total number of products is calculators. Remaining products are either television or washing machine. The number of washing machines is 50 more than the number of televisions produced. (IBPS RRB Grade Officer Exam 2012)

1. What is the ratio of the number of washing machines to the number of calculators produced by the company?

(1) 17:11 (2) 19:11 (3) 11:17 (4) 19: 13 (5) None of these

2. If 24 per cent of the pen drives are defective, what is the number of pen drives which are not defective?

(1) 209 (2) 215 (3) 219 (4) 225 (5) None of these

3. The number of televisions produced is approximately what per cent of the total number of calculators and washing machines produced together?

(1) 63 (2) 55 (3) 59 (4) 51 (5) 67

4. What is the difference between the total number of televisions and mobile phones together and the number of calculators produced? (1) 534 (2) 524 (3) 511 (4) 523 (5) None of these

5. What is the total number of pen drives, calculators and washing machines produced by the company? (1) 907 (2) 917 (3) 925 (4) 905 (5) None of these


Directions (Q. 6-10): Study the following information carefully to answer the questions that follow: (RBI Grade’B’ Officer’s Exam 2011)

There are two trains, Train A and Train B. Both trains have four different types of coaches, viz General, Sleeper, First Class and AC. In Train A, there are total 700 passengers. Train B has thirty per cent more passengers than Train A. Twenty per cent of the passengers of Train A are in General Coach. One-fourth of the total number of passengers of Train A are in AC coach. Twenty three per cent of the passengers of Train A are in Sleeper Coach. Remaining passengers of Train A are in First Class Coach. The total number of passengers in AC Coach in both the trains together is 480. Thirty per cent of the number of passengers of Train B are in Sleeper Coach. Ten per cent of the total passengers of Train B are in First Class Coach. The remaining passengers of Train B are in General Coach.

6. What is the ratio of the number of passengers in First Class Coach of Train A to the number of passengers in Sleeper Coach of Train B?

(1) 13 : 7 (2) 7 : 13 (3) 32 : 39 (4) Data Inadequate (5) None of these

7. What is the total number of passengers in the General Coach of Train A and the AC Coach of Train B together?

(1) 449 (2) 459

(3) 435 (4) 445 (5) None of these

8. What is the difference between the number of passengers in the AC Coach of Train A and the total number of passengers in Sleeper and First Class Coach together of Train B?

(1) 199 (2) 178 (3) 187 (4) 179 (5) None of these

9. The total number of passengers in General Coaches of both the trains together is approximately what percentage of the total number of passengers in Train B?

(1) 35 (2) 42 (3) 46 (4) 38 (5) 31

10. If the cost per ticket of First Class coach is Rs.450, what will be the total amount generated from First Class Coach of Train A?

(1) Rs.1, 00, 080 (2) Rs.1, 08, 000 (3) Rs.1, 00, 800 (4) Rs.10, 800 (5) None of these


Directions (Q. 11-15): Study the information carefully to answer the questions that follow:

A company produces five different products, viz Television, Refrigerator, Mobile Phone, Oven and Water Heater. The total number of all the five products manufactured is 1200. 15 per cent of the total number of products are Televisions. Three-tenths of the total number of products are Refrigerators. The number of Mobile Phones manufactured is 40 more than the number of Televisions. 22 per cent of the total number of products is Oven and the remaining number of products is Water Heaters. (Corporation Bank PO 2011)

11. What is the total number of Refrigerators and Water Heaters?

(1) 436 (2) 476 (3) 576 (4) 536 (5) None of these

12. The number of Mobile Phones is approximately what per cent of the number of Televisions? (1) 115 (2) 140 (3) 135 (4) 130 (5) 120

13. If the cost of one Oven is Rs. 8,200, what is the cost of all the Ovens manufactured by the company?

(1) Rs. 2,16,480

(2) Rs. 21,68,400 (3) Rs. 2,16,48,000 (4) Rs. 2,16,840 (5) None of these

14. What is the difference between the number of Refrigerators and the number of Mobile Phones manufactured?

(1) 160 (2) 140 (3) 120 (4) 130 (5) None of these

15. If 25 per cent of the number of Ovens are defective, what is the number of non-defective Ovens? (1) 176 (2) 188 (3) 198 (4) 186 (5) None of these


Directions-(Q. 16-20): Study the information carefully to answer the questions that follows:

In a ship there are 1200 passengers. 18 per cent of the total number of passengers is from Britain. Two- fifth of the total number of passengers is from South Africa 6 per cent of the total number of passengers is from Madagascar. Remaining number of passengers is from India. 25 per cent of the number of passengers from Britain is females. Half the numbers of passengers from South Africa are male. There is no female passenger from Madagascar. Two- third of the number of passengers from India are females. (Allahabad Bank Probationary Officers Exam 2011)

16. What is the ratio of the number of passengers from Madagascar, number of female passengers from South Africa and the total number of passengers from India?

(1) 2: 5 : 18 (2) 3: 10 : 18 (3) 3: 11 : 18 (4) 2: 18 : 5 (5) None of these

17. The number of male passengers from South Africa is approximately what percentage of the total number of passengers from Britain?

(1) 111 (2) 115 (3) 120 (4) 125 (5) 131

18. What is the average number of male passengers from all the four countries?

(1) 154.5 (2) 164.5 (3) 145 (4) 164 (5) None of these

19. What is the difference between the number of male passengers from Madagascar and the number of male passengers from India?

(1) 64 (2) 82 (3) 74 (4) 72 (5) None of these

20. What is the total number of male from Britain passengers’ female passengers from India together?

(1) 340 (2) 420 (3) 350 (4) 460 (5) None of these


Data Interpretation-Caselets Practice Set (Answers)

1) 2 2) 1 3) 2 4) 5 5) 4 6) 3 7) 4 8) 5 9) 2 10) 3

11) 4 12) 5 13) 5 14) 2 15) 3 16) 2 17) 1 18) 1 19) 4 20) 5


Solved Examples (Data Interpretation-Miscellaneous)

Directions: (1-5) Study the following graph and table carefully and answer the questions given below:

Time Taken To Travel (In Hours) By Six Vehicles On Two Different Days

Distance covered (in kilometers) by six vehicles on each day

(IBPS CWE PO MT 2012)

1. Which of the following vehicles travelled at the same speed on both the days? (1) Vehicle A (2) Vehicle C (3) Vehicle F


(4) Vehicle B (5) None of these Solution: The speed of Vehicle B on both the days is 43 km/hr. Ans: (4) 2. What was the difference between the speed of vehicle A on day 1 and the speed of vehicle C on the same day? (1) 7 km/hr (2) 12 km/hr (3) 11 km/hr (4) 8 km/hr (5) None of these Solution: Speed of A on 1st day = 52 km/hr Speed of C on 1st day = 63 km/hr

Difference = 65 - 52 = 11 km/hr Ans: 2 3. What was the speed of vehicle C on day 2 in terms of meters per second? (1) 15.3 (2) 12.8 (3) 11.5 (4) 13.8 (5) None of these Solution: Speed of Vehicle C on 2nd day = 45 km/hr = 45 × = 2.5 × 5 = 12.5 m/sec

Ans: (5) 4. The distance travelled by vehicle F on day 2 was approximately what percent of the distance travelled by it on day 1? (1) 80 (2) 65 (3) 85


(4) 95 (5) 90 Solution: Reqd % = 100 = 90.46 90%

Ans: (5) 5. What is the respective ratio between the speeds of vehicle 0 and vehicle E on day 2? (1) 15: 13 (2) 17: 13 (3) 13: 11 (4) 17: 14 (5) None of these

Solution: Reqd Ratio =

= = = 17:13

Ans: (2)


Directions (6-10) Study the following pie-chart and table carefully and answer the questions given below: Percentagewise distribution of the number of mobile phones sold a shopkeeper during six months Total number of mobile phones sold = 45000

The respective ratio between the numbers of mobile phones sold of company A and company B during six months

6. What is the respective ratio between the number of mobile phones sold of company B during July and those sold during December of the same company? (1) 119: 145 (2) 116: 135 (3) 119: 135 (4) 119: 130 (5) None of these Solution: Total number of mobiles sold in the month of July


= 45000 = 7650

Mobile phones sold by Company B in the month of July = 7650 = 3570

Total number of mobile phones sold in the month of December = 45000 = 7200

Mobile phones sold by Company B in the month of December = 7200 = 4050

Reqd ratio = = = = 119: 135

Ans: (3) 7. If 35% of the mobile phones sold by company A during November were sold at a discount, how many mobile phones of company A during that month were sold without a discount? (1) 882 (2) 1635 (3) 1638 (4) 885 (5) None of these Solution: Number of mobile phones sold in the month of November = 45000 = 5400

Number of mobile phones sold by Company A in the month of November = 5400 = 2520

Number of mobile phones without discount in the month of November by Company A = 2520 = 2520 0.65 = 1638

Ans: 3 8. If the shopkeeper earned a profit of Rs. 433/- on each mobile phone sold of company B during October, what was his total profit earned on the mobile phones of that company during the same month? (1) Rs. 6,49,900 (2) Rs. 6,45,900 (3) Rs. 6,49,400 (4) Rs 6,49,500 (5) None of these


Solution: Number of mobile phones sold in the month of October = 45000 = 3600

Number of mobile phones sold by Company B in the month of October = 3600 = 1500

Total profit earned by Company B in the month of October = 1500 433 = 649500 Ans: (4) 9. The number of mobile phones sold of company A during July is approximately what percent of the number of mobile phones sold of company A during December? (1) 110 (2) 140 (3) 150 (4) 105 (5) 130 Solution: Number of mobile phones sold in the month of July = 45000 = 7650

Number of mobile phones sold by Company A in the month of July = 7650 = 4080

Number of mobile phones sold in the month of December = 45000 = 7200

Number of mobile phones sold by Company A in the month of December = 7200 = 3150

Reqd % = = 129.52 130

Ans: (5) 10. What is the total number of mobile phones sold of company B during August and September together? (1) 10000 (2) 15000 (3) 10500 (4) 9500 (5) None of these


Solution: Number of mobile phones sold in the month of August = 45000=9900

Number of mobile phones sold in the month of September = 45000 = 45000 = 11250

Number of mobile phones sold by Company B in the month of August = 9900 = 5500

Number of mobile phones sold by Company B in September= 11250 = 4500

Total number of mobile phones sold in August and September by Company B = 5500+4500= 10000 Quicker Method: Total number of mobile phones sold by Company B in August and September .

= 10000

Ans: (1)


Directions: (11-15) Study the following information and answer the questions that follow: The graph given below represents the production (in tonnes) and sales (in tonnes) of company a from 2006-2011.

The table given below represents the respective ratio of the production (in tonnes) of Company A to the production (in tonnes) of Company B, and the respective ratio of the sales (in tonnes) of Company A to the sales (in tonnes) of Company B.

11. What is the approximate percentage increase in the production of Company A (in tonnes) from the year 2009 to the production of Company A (in tonnes) in the year 2010? (1) 18% (2) 38% (3) 23% (4) 27% (5) 32% Solution: Production of Company A in year 2009 = 550 Production of Company A in year 2010 = 700


Reqd % = 100 = 100 = = 27.27 27% Ans: (4) 12. The sale of Company A in the year 2009 was approximately what percent of the production of Company A in the same year? (1) 65% (2) 73% (3) 79% (4) 83% (5) 69% Solution: Sales of Company A in year 2009 = 400 Production of Company A in year 2009 = 550

Reqd % = 100 = = 72.72 73%

Ans: (2) 13. What is the average production of Company B (in tonnes) from the year 2006 to the year 2011? (1) 574 (2) 649 (3) 675 (4) 593 (5) 618 Solution: Average production of Company B

=

= = 675

Ans: (3)


14. What is the respective ratio of the total ‘production (in tonnes) of Company A to the total sales (in tonnes) of Company A? (1) 81: 64 (2) 64: 55 (3) 71: 81 (4) 71: 55 (5) 81: 55 Solution:

= = = 81: 55

Ans: (5) 15. What is the respective ratio of production of Company B (in tonnes) in the year 2006 to production of Company B (in tonnes) in the year 2008? (1) 2: 5 (2) 4: 5 (3) 3: 4 (4) 3: 5 (5) 1: 4 Solution: Production of Company B in the year 2006 = 150 = 600 Production of Company B in the year 2008 = 200 Ratio = = 3: 4 Ans: (3)


Practice Set (Data Interpretation-Miscellaneous)

Directions (Q. 1-5): Study the radar-graph carefully and answer the questions that follow.

Monthly salary (in thousands) of five different persons in three different years (RBI Grade’B’ Officer’s Exam 2011)

1. What is the average of the monthly salary of Sumit in the year 2008, Anil in the year 2009 and Jyoti in the year 2010?

(1) Rs.20, 000 (2) Rs.5, 000 (3) Rs.45, 000 (4) Rs.15, 000 (5) None of these

2. The total monthly salary of Arvind in all years together is what per cent of the total monthly salary of all the five persons together in the year 2008?

(1) 55% (2) 60% (3) 75% (4) 70% (5) None of these


3. Among the five persons, whose earning per month over all the years together is the second lowest?

(2) Sumit (3) Anil (4) Jyoti (5) Arvind (6) Poonam

4. What is the per cent decrease in the monthly salary of Poonam in the year 2009 as compared to her monthly salary in the previous year?

(1) 40% (2) 10% (3) 20% (4) 80% (5) None of these

5. If Jyoti's monthly salary in the year 2010 was increased by 30 per cent what would her monthly salary be in that year?

(1) Rs.36, 000 (2) Rs.39, 000 (3) Rs.45, 000 (4) Rs.42, 000 (5) None of these


Directions (Q. 6-10): Study the following pie-chart and bar-graph and answer the following questions. (Corporation Bank PO 2011)

Percentage wise distribution of teachers in six different districts

Total number of Teachers = 4500

Percentage of Teachers


6. What is the total number of male teachers in District F, female teachers in District C and female teachers in District B together?

(1) 1080 (2) 1120 (3) 1180 (4) 1020 (5) None of these

7. The number of female teachers in District D is approximately what per cent of the total number of teachers (both male and female) in District A?

(1) 70 (2) 75 (3) 80 (4) 95 (5) 90

8. In which district is the number of male teachers more than the number of female teachers?

(1) B only (2) D only (3) Both B and E (4) Both E and F (5) None

9. What is the difference between the number of female teachers in District F and the total number of teachers (both male and female) in District E?

(1) 625 (2) 775 (3) 675 (4) 725 (5) None of these

10. What is the ratio of the number of male teachers in District C to the number of female teachers in District B?

(1) 11 : 15 (2) 15 : 11 (3) 15 : 8 (4) 30 : 13 (5) None of these


Directions-(Q. 11-15) Study the following pie-chart and bar chart and answer the following questions. (Allahabad Bank Probationary Officers Exam 2011)

Percentagewise Distribution of students in six different Schools

Total number of Students = 6000

Percentage of Students

Number of Boys out of the 6000 Students in each School Separately.


11. What is the sum of the number of girls in School C. Number of girls in School-E and the number of boys in school-D together?

(1) 1700 (2) 1900 (3) 1600 (4) 1800 (5) None of these

12. What is the respective ratio of the number of boys in School-C, number of girls in School B and total number of students in School E?

(1) 45: 7: 97 (2) 43: 9: 97 (3) 45: 7: 87 (4) 43: 9: 87 (5) None of these

13. What is the difference between the total number of students in School-P and the number of boys in School E?

(1) 820 (2) 860 (3) 880 (4) 900 (5) None of these

14. In which school the total numbers of students (both boys and girls) together are equal to the number of girls in School E?

(1) A (2) B (3) C (4) D (5) F 15. The Number of girls in School A is approximately what per cent of total number of students in School B? (1) 55 (2) 50 (3) 35 (4) 45 (5) 4


Data Interpretation-Miscellaneous Practice Set (Answers)

1 (1)

2 (2)

3 (4)

4 (4)

5 (2)

6 (1)

7 (5)

8 (3)

9 (2)

10 (3)

11 (4)

12 (3)

13 (5)

14 (2)

15 (5)

number series

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