nmat-mock-paper-answers

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NMAT

®

1 IMS-35-UG-AL-SIMNM-1

SECTION - I

1. Required a verage =4

25402035 +++ = 30

Hence, [3].

2 . Requ ir ed percent age ch an ge =25

25 – 40 × 100 = 60%

Hence, [4].

3. Number of girls who played chess in the years 2005

and 2006 = 20 + 45 = 65

Number of boys who played chess in the years 2005

and 2006 = 40 + 60 = 100

\ Required ratio = 65 : 100 = 13 : 20. Hence, [4].

4. Required average =6

452015352530 +++++

=6

170 » 28. Hence, [3].

5. 12x3y2 = 2 × 2 × 3 × x × x × x × y × y

3xy5 = 3 × x × y × y × y × y × y

8x2y2z = 2 × 2 × 2 × x × x × y × y × z

\ HCF = xy2 and LCM = 24x3y5z. Hence, [4].

6. 32x× 5y = 2254 × 813 = 38 × 58 × 312

Þ 32x× 5y = 320

× 58

Þ 2x = 20 or x = 10 and y = 8.

Þ x + y = 10 + 8 = 18. Hence, [5].

7. 3

1

x + 3

1

y + 3

1

z = 0

Þ 3

1

x + 3

1

y = 3

1

z-

Þ

3

3

1

3

1

yx÷÷

ø

ö

çç

è

æ + =

3

3

1

z÷÷

ø

ö

çç

è

æ -

Þ x + y + 3

1

3

1

yx3 ( 3x

1

+ 3y

1

)

Þ x + y + 3

1

3

1

yx3 ( 3

1

z ) = – z

Þ x + y + z = 3

1

3

1

3

1

zyx3

Þ (x + y + z)3 = 27xyz. Hence, [1].

8. Number of officers = 15

Let number of non-officers be x.

SimNMAT-1

EXPLANATORY ANSWERS

Thus, total staff = x + 15

\ 120(x + 15) = 460 × 15 + 110 × x

\ x = 510

\ Number of non-officers = 510. Hence, [3].

9 . Ra tio of capit al in ves ted b y A, B an d C

=3

1 :

4

1 :

5

1 = 20 : 15 : 12

Let the capital invested by A, B and C be Rs.20x,

Rs.15x and Rs.12x respectively.

For first four months, A’s investment = Rs.20x

For next 8 months, A’s investment = Rs.10x

Thus, A’s share in the profit

= x1212x1512x108x204

x108x204

´+´+´+´

´+´

=160x

484x× 847 = Rs.280. Hence, [3].

10. Let An denote the amount after n years.

Let I be the simple interest for 1 year.

\ A3 = P + 3I

\ A2 = P + 2I

\ I = A3 – A

2 = 816 – 744 = Rs.72

744 = P + 2 × 72

\ P = 744 – 144 = Rs.600

I =100

R P ´ (Interest for one year)

\ 72 =100

R 600 ´

\ R = 12%

\ Rate of interest = 12% p.a. Hence, [5].

11. Let DE denote the stick and AB denote the tower.Let DF and AC denote the shadows made by the stick and the tower respectively.

Since angle of depression would be same in both the

cases, m Ð EFD = m Ð BCA

Also, m Ð EDF = m Ð BAC = 90º

Thus, D DEF ~ D ABC (By AA test of similarity)

\ AB

DE =

AC

DF

\ x

20 =

50

10



NMAT

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IMS-35-UG-AL-SIMNM-1 2

\ x = 100 m

\ Height of the tower = 100 m. Hence, [1].

12. Let the number of red and blue marbles be 2x and

3x respectively.Then, 2x + 3x = 30 Þ x = 6

\ Number of red and blue marbles is 12 and 18

respectively.

\ Probability of drawing two red balls, one after

other with replacement.

30

12 ×

30

12 =

25

4. Hence, [5].

13 . Let the number to be added be x.

Then,x9

x4

+

+ =

3

2

Þ 12 + 3x = 18 + 2x

Þ x = 6. Hence, [5].

14 . 3 3y x y = k × xÞ (where k – constant)

new

xx

2=

\ newy = k ×8

x3

\ Percentage decrease in value of y =y

yy new- × 100

= 3

33

kx

8

kx –kx

× 100 = 87.5%. Hence, [1].

15 . By all igation rule, we have:

\ Alcohol and wine must be mixed in the ratio of 7.5 : 2.5 = 3 : 1. Hence, [2].

16 . Volume of ball = Volume of cone

3123

4´p´ = h8

3

2 ´´p

Þ h =2

2

83

1234

´p´

´p´´ = 108 cm.

\ Height of the cone = 108 cm. Hence, [3].

17. x! = 56 ´ (x – 2)!

Þ x(x – 1)(x – 2)! = 56(x – 2)!

Þ x2 – x = 56

Þ x = –7 or 8.

Thus, x = 8. (Factorials of negative numbers are not

defined). Hence, [5].

18 . 125

1

25

1

5

1

818181 ´´ ×... =

32

5

1

5

1

5

1

818181÷ ø

öçè

æ ÷ ø

öçè

æ

´´ × ...

....51

51

51 32

81+÷

ø öç

è æ +÷

ø öç

è æ +

= 5

11

5

1

81-

= 4

1

81 = 3. Hence, [2].

19 . Let one pa rt be x.

So, other part = (78 – x).

\ x(78 – x) = 1512

\ x2 – 78x + 1512 = 0

Þ (x – 36)(x – 42) = 0

\ x = 36 or x = 42. Hence, [3].

2 0. Requ ir ed amou nt = 25 00 0 ×

100

104 ×

100

105

= Rs.27300. Hence, [2].

2 1. T ime taken t o comple te 1 ro un d by :

A º 150

1200 = 8 minutes

B º 80

1200 = 15 minutes

\ Time after which they meet at the starting point

for the first time = LCM(15, 8) = 120 minutes

= 2 hours. Hence, [3].

22. A and B will meet each other for the first time when

A has gained one complete round over B.

A gains 150 – 80 = 70 m over B in 1 minute

Thus, A will gain 1200 m in70

1200 =7117 minutes

\ They will meet each other for the first time after

117

7 minutes. Hence, [4].

23. Working together, in 1 day, part of work finished

20

1

10

1+ = th

20

3

\ In 5 days, part of work finished =20

)35( ´ = th

20

15

\ Part of work remaining =20

5 = th

4

1 work, which

has to be finished by B.

\ Time taken by B to finish the remaining work

=4

1 × 20 = 5 days. Hence, [5].

24 . Let the total number o f vo tes po lled be x.

\ 100

x)41100( - = 18526



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Þ x =59

10018526 ´ = 31400

\ Total votes polled = 31400. Hence, [4].

25 .2

1

h

h =

2

1

area

area

=16

9 =

4

3. Hence, [1].

26. Population after n years is given byn

100

R 1P ÷

ø

öçè

æ + ;

where P is present population.

\ 800 × 106

n

100

101 ÷

ø

öçè

æ + > 109

Þ

n

10

11÷

ø

öçè

æ >

100

103

Þ (1.1)n > 1.25

Þ n = 3

The population will cross 1 billion at the end of

3 years. Hence, [3].

2 7. Given expr es sion

= 2

3

q4

p- × 4

2

q3

p2 × 2

3

p

q

= pq6

1-. Hence, [1].

28 . Let f(x) = px3 + x2 – 2x – q

Since f(x) is divisible by (x – 1) and (x + 1),

f(1) = p + 1 – 2 – q = 0

\ p – q = 1 ... (i)

and f(–1) = p(–1)3 + (–1)2 – 2(–1) – q = 0

\ p + q = 3 ... (ii)

Solving (i) and (ii), we get,

p = 2, q = 1. Hen ce, [1 ].

29 . Let the f irs t f ive terms of the G.P. be

,r

a ,

r

a2

a, ar, ar 2.

The third term = a = 5.

Product of the first five terms

= 2r

a

× r

a

× a × ar × ar

2

= a

5

= 5

5

. Hence, [4].

30. There are 10 subjects to choose from and only 5

classes in a day.

\ Number of ways of mak ing the time -table

= 10P5 =

)!510(

!10

-

=!5

!10 = 30240. Hence, [5].

31 .1 1

1 12 2

1 43 3

1 51

4

=

+ ++ +

+

=

19

5 2

1

+ =

43

19. Hence, [1].

32 . Rat io of sides of the t riangle =3

1 :

4

1 :

5

1

= 20 : 15 : 12

Let the lengths of the three sides be 20x, 15x and 12xÞ perimeter of the triangle = 20x + 15x + 12x

= 47x = 94 cm\ x = 2 cmThus, the lengths of the three sides are:20 × 2, 15 × 2 and 12 × 2 = 40 cm, 30 cm, 24 cmThus, smallest side = 24 cm. Hence, [3].

33 . 10 0.5 4 7.0

14.0´´´

= 10 0.5 4 2.0 ´´´ = 4 = 2. Hence, [5].

34 . The given express ion i s o f the form22

33

baba

ba

+-

+

=) baba(

) baba)( ba(22

22

+-

+-+ = a + b.

\ L.H.S. equals 0.32 + 0.64 = 0.96. Hence, [2].

35. (a + 1)4 = 212

\ a + 1 = ( )4

1122 = +23 = +8

\ a = –9 or a = 7. Hence, [5].

36. x +x

1 = 2

Squaring both sides,

x2 + 2 +2x

1 = 4

\ x2 +2x

1 = 2. Hence, [1].

37 . Let the or ig inal number be 10x + y .

\ x + y = 9 and 10y + x – (10x + y) = 27

Þ 9y – 9x = 27 Þ y – x = 3

\ 2y = 12 Þ y = 6 and x = 3

\ The number required is 36. Hence, [5].



NMAT

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38. 4(z – 2)2 + 9z – 27 = 0

Þ 4(z2 – 4z + 4) + 9z – 27 = 0

Þ 4z2 – 16z + 16 + 9z – 27 = 0

Þ 4z2 – 7z – 11 = 0

Þ (4z – 11) (z + 1) = 0

Þ z =4

11 or z = –1. Hence, [2].

39. 1]4

3

y

x=

From componendo

4

7

y

yx=

+, is true

2]4

3

y

x=

1 –y

x = 1 –

4

3 Þ

y

xy - =

4

1

\ 1

4

xy

y=

- is true

3]3

11

x

y2x=

+

\ 3

11

y3

y11

4

y3

y24

y3

==+

is true.

4]4

3

y2

x=

\ 8

3

y2

4

y3

= is not true. Hence, [4].

4 0 . L .C .M . of 6 , 7, 8 and 13 = 2 18 4Hence, we have to find some multiple of 2184.\ 2184 × 3 + 4 = 6556Also, this number is divisible by 11. Hence, [5].

SECTION - II

4 1 . F ro m t he gi ven d at a, we get :

Now since ther e are only 6 members , A has to be

C’s brother’s daughter, hence the family tree is:

Thus, there are 3 generations. Hence, [3].

42. Since the grand-father in the family has to be C’s bro ther, the fam ily can be represente d as :

Hence, E is C’s niece’s husband. Hence, [4].

43. It is not known whether C is D’s brother or sister.Hence, C could either be A’s paternal aunt or paternaluncle. Hence, [5].

44 . In th e fa mily t ree,

If B adopts X, his great grand-father will be D.

Hence, [1].

45. With 2 females in the family; C is definitely a male.

Thus, there are 2 possible combinations.

Hence, [2].

46. Every letter is moved forward one place to get the

corresponding letter of the code.

\ NEMESIS º OFNFTJT. Hence, [2].

47 .



NMAT

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D ABC is a right-angled triangle.

\ AC = 22 86 + = 10 km. Hence, [5].

48. The odd positioned letters (B, E, I, H) are moved back one place while the even posit ioned letters (L,

M, S) are moved forward three places to get the cor-

responding letters of the code.

\ CHAPTER º BKZSSHQ. Hence, [2].

49. As D has to be immediately before E and A cannot

come immediately before B, so, either C or F can

be sch eduled for Sat urday. Hence, [2] .

50. F has to come on Tuesday because of condition (iii)

and D and E will come on Friday and Saturday. So

B will come on Wednesday. Hence, [1].

51. As D has to come before E, so, E cannot come on

Monday. Hence, [5].

52. As D has to come on Wednesday and F on Friday,

so, either B or C can come on Monday. Hence, [4].

Answe rs to quest ions 53 to 57:

B is A's mother.

About the points obtained:

B > B's husband;

Als o, F > D > E.

E's niece got the lowest points.

B's husband > F.

Thus, we get,

B > B's husband > F > D > E > E's neice

Out of A and C, one will be A's father (i.e. B's husband)

and the other will be E's niece.

Since, A cannot be B's husband, thus C is A's father and

A is E's neice.

Thus, B > C > F > D > E > A.

Since, A is E's neice, thus A is a female.

Now, all the ques tions can be answered.

53-[2] 54-[5]

55-[4] 56-[1]

57-[3]


From the given data, we get the following family tree:

58. Thus, Amit is Sonu's cousin. Hence, [2].

59. Raja has two nephews (Amit and Sonu).

Hence, [2].

60 . Raja i s Sarika’s b rother. Hence, [2 ].

61. Option [4]:

If all beach is bed and all bed is murky we can conclude

that all beach is murky. Hence, [4].

62. Option [2]:

If all politician is insane and no insane is fair, we

can conclude that no politician is fair. Hence, [2].

63. Option [2]:

If no predator is herbivore and all lion is predator, we

can conclude that no lion is herbivore. Hence, [2].

64. The first statement is a quote. So, B flows from it,

as it names the source behind the quote. A links

the past with the present. And thus connects the

last sentence to the rest of the paragraph. Hence,

[2].

65. A narrows down the impact of Internet on business

and B elaborates on it. Thus, B flows from A.

Hence, [1].

66. The Venn dia gr am:

From the diagram, we can conclude that some noise

may be music but it is not definite. II cannot be

deduced as no concrete relationship between soundand wave is given. Also, some music may be wave.

Only IV can be concluded - some sound is wave.

Hence, [1].



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6 7. The Venn diagra m:

From the diagram, it is clear that no winter or autumnis summer. So, I and II are true. All and not somewinter is season. So, III is ruled out. Similarly, allautumn is season. Thus, IV too is false. Hence, [3].

6 8. The Ven n diagr ams :

From the diagrams, we can see that we cannot arriveat any of the conclusions. We cannot say for sure that

no merit is fail. Similarly, III and IV cannot be concluded.II is contradictory to the given diagram. Hence, [5].

69. ‘Step back’ means to think about a situation calmly.‘Step aside’ means to leave a job or position and let

somebody else take over. ‘Go over’ means to check;

to study; to examine, etc. ‘Bounce back’ means to become healthy, successful; recover. If the senior political

leaders have to make way for the young generationof leaders, they have to ‘step aside’ Hence, [5].

70. ‘Watch out for’ means to be careful of something.‘Stock up on’ means to buy a lot of something sothat you can use it. ‘Wear away’ means to gradually become wea k. ‘Walk awa y with ’ means to win or obtain something easily. In the given context only‘watch out for’ can fit in. Hence, [1].

71 .

or

As seen from the diagram, II and III follow. II followsfrom premises 1 and 3. III follows from premises2 and 3. Hence, [2].

72 .

or

As seen in the diagram, none of the options ar e logical.

Hence, [5].

73 .

II follows from the premises 2 and 3. III follows from premises 1 and 3. Thus, II and III follow. Hence, [2].

74 .

None of the given options are corr ect . Hence, [5 ].



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75 .

‘Some warriors are famous’ follows from premises

1 and 2 only and thus valid here. Hence, [3].


In this coding, the first step is to reverse the given word

and then in the reversed word the odd placed letters are coded

by next lette r in the alph abe tical ser ies and the even placed

letters are coded as previous in the alphabetical series.

76. Reversed word of SPARKLE is ELKRAPS

\ Code for SPARKLE is FKLQBOT. Hence, [5].

77. Reversed word of ALUMINUM is MUINIMULA

\ Code for ALUMINIUM is NTJMJLVKB.

Hence, [2].

78 . For decoding, we have to fi rs t reverse the word

FKDZUBFOT i.e., TOFBUZDKF.

\ Decode for FKDZUBFOT is SPECTACLE.

Hence, [5].

79 . For decoding, we have to fi rs t reverse the word

IRJEHMJJ i.e., JJMHEJRI.

\ Decode for IRJEHMJJ is KINGFISH. Hence, [4].

80. Reversed word of ELECTRICAL is LACIRTCELE

\ Code for ELECTRICAL is MZDHSSDDMD.

Hence, [3].

SECTION - III

81. [1] is neither stated nor implied in the passage. [2]

is irrelevant to the point in question. Refer to the

very first line of the passage – ‘We are tempted

to assume that technological progress is the real

progress’ . Hence, [3 ].

82. Though all the options are accepted truths, only [1]

is stated in the passage. Hence, [1].

83. [2], [3] and [4] are neither stated nor implied. [1]

will result from positive use of technology. Only [5]

sums up the porrible effect of misuse of technology

by th e eastern people. Hence , [5 ].

84. At first glance all options seem probable. But inactuality B contradicts a part of the passage, which

highlights the fact that science and technology don’t

lead to ‘all progress’. A is categorically stated in

the passage. C is implied too. Hence, [2].

85. [2] and [4] are antonymous to ‘tabooed’. All the

other options seem probable. But when we look at

the complete sentence – ‘They are not to be tabooed

but tamed and ass igned their proper place’, [1] and

[3] can be eliminated. ‘Forbidden’ fits best contextually.

Hence, [5].

86. ‘Jeopardized’, ‘imperiled’ and ‘endangered’ all mean

to be likely to cause harm or damage to something

or someone, which mean the same as ‘threatened’.

Hence, [4].

87. Use of the auxiliary verb ‘will be’ is the correct usage

for a simple future tense. [1] uses the wrong tense

form. [2] implies a possibility and [4] implies a

compulsion which are not indicated by the stem

sentence. Hence, [3].

88. ‘East’ is the name of specific direction. Thus, a proper

noun. Hence, [1].

89. ‘Enchanted’, ‘thrilled’ and ‘excited’ connote fascination.

‘Bored’ is the lack of fascination. Hence, [1].

9 0. ‘ Su cc es s fu l ly ’ is t h e a dve rb f or m o f su c ce s s.Hence, [2].

91. ‘Miscellaneous’ is the correct spelling. Hence, [5].

92. ‘Repentance’ is the correct spelling. Hence, [3].

93 . ‘Occasional ly ’ is the righ t way to spell it .

Hence, [1].

94. ‘Traverse’ means ‘to travel through’. ‘Cross’ is closest

in meaning. Hence, [4].

9 5. ‘ Fu ro r e’ m ea n s a n ex ci te d o r an gr y re a ct io n.

‘Excitement’ is the closest in meaning. Hence, [5].

96. ‘Verbose’ means ‘long-winded’ or using more words

than are required. Hence, [3].

97. ‘Brawl’ means a fight or a dispute. Hence, [5].

98. ‘Bemuse’ means to bewilder or confuse. Hence, [4].

99. There is a conjunction error in part [2]. The sentence

implies a contradiction, so we need ‘but’ in place

of ‘and’. The correct sentence should read: His wife

died last year but he can seem to manage without

her. Hence, [2].

100. The superlative degree is not required in part [1].

Since a comparison is implied, we require the

comparative degree. The correct sentence should be:

What is worse is, this distortion can’t be corrected

by eith er con tact lens or glasses. Hen ce, [1 ].

101. There is an article error in part [1]. In the sentence

we are not referring to any particular unemployed

pers on in the U.S., hen ce we do not need the definite

article ‘the’. The correct sentence should read: Inthe U.S, an unemployed person even in the lowest

rung would survive on the unemployment dole granted

by th e gover nment . Hen ce, [1] .

102. The expression ‘huge and even increasing’ is incorrect

in part [3]. the correct sentence should read: The

posit ion here is that the numb er of those willing to



NMAT

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ANSWER KEY

SECTION-I

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

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

21-3 22-4 23-5 24-4 25-1 26-3 27-1 28-1 29-4 30-5

31-1 32-3 33-5 34-2 35-5 36-1 37-5 38-2 39-4 40-5

SECTION-II

41-3 42-4 43-5 44-1 45-2 46-2 47-5 48-2 49-2 50-1

51-5 52-4 53-2 54-5 55-4 56-1 57-3 58-2 59-2 60-2

61-4 62-2 63-5 64-2 65-1 66-1 67-3 68-5 69-5 70-1

71-2 72-5 73-2 74-5 75-3 76-5 77-2 78-5 79-4 80-3

SECTION-III

81-3 82-1 83-5 84-2 85-5 86-4 87-3 88-1 89-1 90-2

91-5 92-3 93-1 94-4 95-5 96-3 97-5 98-4 99-2 100-1

101 -1 102-3 103-3 104 -5 105 -2 106 -2 107 -3 108 -1 109-3 110 -2

111 -5 112 -1 113-1 114 -4 115 -3 116-2 117 -4 118 -2 119-1 120 -4

111. The passage makes a reference to all the options.

Refer to sentences 5 to 9. Hence, [5].

112. From the passage, we can infer that the savings rate

has a direct impact on the mutual funds industry.The passage also states that in India most people

lack expertise as far as investment decisions are

concerned. So if [1] were true, the mutual funds industry

would have benefited the most and that too at a

continuous pace. [3] and [4] would be immaterial if

there were inadequate number of investors. [2] would

not affect the industry in a major way. Hence, [1].

113. The author of the passage states specific facts about

the scenario in the mutual funds industry. He also

mentions the investor’s psyche in detail. The use

of the pronoun ‘we’ indicates that the author is quite

involved in the topic he is discussing. These

information point to the fact that the author could

probably be an inves tment con sul tant. Hence, [1 ].

114. The relation is that of part-whole. Just as ‘verse’

is part of a ‘poem’, similarly ‘cell’ is part of an

‘organism’. Hence, [4].

115. Just as an ‘obese’ person is ‘heavy’ (fat), similarly,

an ‘anorexic’ person is ‘light’ (thin). Hence, [3].

116. ‘Formidable’ means daunting or terrifying. Its opposite

would be ‘pleasing’ Hence, [2].

117 . ‘Cumbersome’ means complicated or unwieldy. ‘Easy’ is

the appropriate antonym. Hence, [4].

118. ‘Disperse’ means to scatter or spread widely. ‘Assemble’

is an antonym of ‘disperse’. Hence, [2].

119. ‘Venial’ means not seriously wrong and can be pardoned.

‘Unpardonable’ is an antonym of ‘venial’. Hence, [1].

120. ‘Unscrupulousness’ means ‘dishonesty’ or beingunprincipled. ‘Sincerity’ is its antonym. Hence, [4].

provid e all k inds of low grad e and even menial services

is a huge and ever increasing army . Hence, [3].

103. The error is in part [3].The use of the determiner

‘a’ in part [2] implies tha t the following nouns should be singular . The correct sen tence should read: The

need of the hour is neither panic nor inaction upon

seeing this tiger, but a collective and sus tai ned act ion

together with the government . Hence, [3].

104. [1], [3] and [4] do not fit in the first blank. Between

[2] and [5], the latter is a better fit because to ‘ensure’

something means the facility would definitely be

provid ed. Moreover, ‘envis ioned ’ fits the firs t blan k

perfect ly. Hen ce, [5] .

105. [1] can be negated immediately because ‘unfulfilled’

does not fit in the context. Among [2], [3] and [4],

only ‘beyond’ is the appropriate preposition that can

be used with ‘go’. Hence, [2 ].

106. ‘Forever’ and ‘alike’ do not fit in correctly. ‘Manacle’

which means ‘handcuff’ is negative and inappropriate.Only [2] has words that fit in the context. Hence, [2].

107. [2] and [4] are wrongly matched. ‘Heavy’ gives us

the clue that ‘lugging’ would fit in the first blank.

‘Lugging’ means carrying something with great

difficulty because it is heavy. Hence, [3].

108. [4] is inappropriate, and ‘engraved’ and attached do

not fit with deeply. ‘Deeply embedded’ is the correct

expression. Hence, [1].

109. From the passage, it is clear that ‘sunrise industry’

refers to an industry that shows definite promise for

the future. The figures that the author mentions also

point to th is idea. Hen ce, [3 ].

110. The first sentence of the passage points out to this

fact. The higher the savings rate in the country the bett er for the mutual funds indust ry in the coun try.

Hence, [2].

nmat-mock-paper-answers

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