data sufficiency (ds)_ simple equation, partnership, tnw

[Aptitude] Data Sufficiency (DS): Simple Equation, Partnership, TnW

DS Case: Simple Equation1.Rule#1 Remember to Forget2.Rule#2: Dont calculate exact value3.DS Case: Square roots4.DS case: Partnership5.DS Case: Time and Work6.

DS Case: Simple Equation

C=a+b, what is the value of C?

I. a=5

II. b=3

Answer choice:

A. Question can be answered using statement i alone.

B. Question can be answered using statement ii alone

C. Question can be answered using statement 1 and 2 together but not using anystatement alone.

D. Question cannot be answered even after using statement 1 and 2 together.

First, What is the DS question?

Weve to find the value of C?

Nope, The DS question is can we find the value of C?

In Data sufficiency(DS) question, we are not interested in finding the actual value ofsomething but we are interested in finding whether we can get an exact value usinggiven statements or not?

As usual make a table

Mrunal [Aptitude] Data Sufficiency (DS): Simple Equation, Partnership,... http://mrunal.org/2012/05/aptitude-data-sufficiency-ds-simple.html/print/

1 of 11 7/28/2014 2:02 PM

Statement Given Thought processExact Answerpossible?

Question C=a+b

I need must know the value of a andb

to find the value of cNot yet!

I a=5

C=5+b.

But b can be any number.No

II b=3

C=a+3.

But a can be any number.No

Combine

I & II

a=5,

b=3C=5+3=8. Yes

Rule#1 Remember to Forget

Each statement row I and II has to be checked individually, and you must assumeyou dont know the other statement.For example, when you calculated Statement #1s row, you got the a=5. So inyour brain, now you know that a=5.But when you start with Statement #2s row, you must not use a=5. And takeonly b=3. Because statement II gave only that much information.Only when doing the third row (Combine I&II), you can use what you learnedfrom both statements ie. a=5 and b=3

Rule#2: Dont calculate exact value

you dont have to find the exact answer.

For example, in third row, (combine I &II), you got that since a=5 and b=3 so c=5+3.STOP.

No need to calculate 5+3=8. Because you know youll get an exact answer.

What if a=21233213 and b=345349550.

Again, no need to actually calculate a+b, because it is obvious youll get an exact valuefor c


2 of 11 7/28/2014 2:02 PM

In data sufficiency, we dont have to find actual answers, but only check whether it ispossible to get exact answer or not. So dont waste time in doing addition of21233213+345349550

Final Answer: (C) Question can be answered using statement 1 and 2 together but notusing any statement alone.

DS Case: Square roots

C=a+b, what is the value of C?

I. a2=25

II. b2=9

Answer choice:

A. Question can be answered using statement i alone.

B. Question can be answered using statement ii alone

C. Question can be answered using statement 1 and 2 together but not using anystatement alone.

D. Question cannot be answered even after using statement 1 and 2 together.

Same procedure


Question C=a+b

I must know the exact valuesof

a and b to find exact value ofc.

Not yet!

I

a2=25

a=(+/-5)

C=(+/- 5)+b.

But b can be any number.No

II

b2=9

b=(+/-3)

C=(+/-3) +b.

But a can be any number.No


3 of 11 7/28/2014 2:02 PM

Combine I &II

a=(+/-5)

b=(+/-3)

Multiple answers!

Refer s(1+2)calcNo

Important: square roots

a2=25 that does not mean a=5.

Because 5 x 5 =25

but (-5) x (-5) = also 25.

So a can be either (-5) or (+5)

Similarly for statement # II. b=(+/- 3)

When we combine them both we get four possible answers

S(1+2)calc

All possible values of c

Case a b C=a+b

1 5 3 8

2 5 -3 2

3 -5 3 -2

4 -5 -3 -8

As you can see we get four possible values of c. so exact answer is not possible evenafter combining the information from statement I and II.

Although, in actual exam you dont have to do the majoori of doing second tablecontaining all possible values of c. because you know youll get multiple values ofc, since a=(+/-5).

Remember Rule #2: Dont Calculate Exact Value! Because That is waste of time.

Therefore final answer: (D) Question cannot be answered even after using statement 1and 2 together.

Now Im using some questions from Indiabix.com for Data Sufficiency. Hope theydont sue me for copyright violation :D


4 of 11 7/28/2014 2:02 PM

DS case: Partnership

Ravi, Gagan and Nitin are running a business firm in partnership. What is Gagans sharein the profit earned by them?

I. Ravi, Gagan and Nitin invested the amounts in the ratio of 2 : 4 : 7.

II. Nitins share in the profit is Rs. 8750.

A. I alone sufficient while II alone not sufficient to answer

B. II alone sufficient while I alone not sufficient to answer

C. Either I or II alone sufficient to answer

D. Both I and II are not sufficient to answer

E. Both I and II are necessary to answer

What is the question?

What is Gagans share in the profit earned by them?

NO! the DS question is can we find exact value of Gagans share?

Make the table

Statement Given Thought process.ExactAnswerpossible?

Question

Ravi, Gagan and Nitin arerunning a business firm inpartnership. Seeking Gagansprofit share.

I could solve if only Iknew the ratio of theirinvestment and totalinvestment.

Or ratio of their profitand total profit.

Not yet!

I

R:G:N=2:4:7

So according to Componendo,

Gagans share

=4/ (2+4+7) x total profit

But we dont knowwhat is total profit!

No


5 of 11 7/28/2014 2:02 PM

=4/13th of total profit

IINitins share in the profit is Rs.8750.

But we dont knowtotal profit.

We also dont knowwhat is the ratio ofR:G:N?

No

Combine I& II

eq1) From S1, we can infer

Nitins share in profit = 7/13th oftotal profit. (samecomponendo)eq2) From s2, weknow Nitin got Rs.8750.

Because (eq1)=(eq2)

you can get totalprofit. And from totalprofit, you can findGagans share usingStatement I***

YES!

Final answer: (E) Both I and II are necessary to answer. Question solved in less than 1minute.

***Notice I havent wasted my precious time in actually doing the calculation. Becausewe were never required to find actual profit share of Gagan. We had to find onlywhether is it possible to calculate exact value of Gagans share or not?

However for the sake of clarity, Im completing the calculation from the (***) cell. Butyou dont have to waste your time doing this, in actual exam.

Unnecessary but for conceptual clarity

Eq1= eq2

7/13th of total profit = Nitins share in profit

7/13th x total profit = 8750

Total profit = (8750/7) x 13 (no need to calculate, because this will cut in next stage)

Now Gagans share in profit =4/13th of total profit

=4/13 x {(8750/7) x 13}

=(4 x 8750) /7

=4 x 1250


6 of 11 7/28/2014 2:02 PM

=Rs.5000.

So we got an Exact value for Gagans share in profit (Rs.5000/-).

But we could only come upto this point only after combing the information fromstatement 1 and 2.

Therefore final answer is (E) Both I and II are necessary to answer.

DS Case: Time and Work

How many workers are required for completing the construction work in 10 days?

I. 20% of the work can be completed by 8 workers in 8 days.

II. 20 workers can complete the work in 16 days.

III. One-eighth of the work can be completed by 8 workers in 5 days.

Answer Choices:

A. I only

B. II and III only

C. III only

D. I and III only

E. Any one of the three

Make sure youve read the previous article on TnW: Men Women and Children

What is the DS-question here?

Number of Men needed to finish job in 10 dayS?

Nope. The DS question is can we find exact number of men needed? YES / NO?


Question

Find # of Men needed

to finish the job in t=10 days.

i.e. how many S

For STD, I knowt=10

I only need toknow value of D

Not yet.


7 of 11 7/28/2014 2:02 PM

Then I can finds

I20% of the work can becompleted by 8 workers in 8days.

Refer S1calc Yes.

II20 workers can complete thework in 16 days.

Refer S2calc Yes

IIIOne-eighth of the work can becompleted by 8 workers in 5 days

Refer S3calc Yes

S1calc

20% of the work can be completed by 8 workers in 8 days.

Assume speed of 1 man Is m.

So speed of 8 men = 8m

Usual STD approach

8 men

Speed 8m

Time 8

Distance 8mx8=64m

Run STD on last column

We get the work done by 8 men in 8 days = 64m

But 64m is only 20% of the total work

20%=1/5th of total work

64m=1/5th of total work

Total work =64x5m (no need to calculate exact value of 645)

So the total work is 64x5m and weve to do this in t=10 days. Make a new column.Suppose we need F number of men. So their speed is Fm


8 of 11 7/28/2014 2:02 PM

8 men F men

Speed 8m Fm

Time 8 10

Distance 8mx8=64m 64x5m

Run STD on last column. (by this time, you should know that youll get exact value. SoDS answer for Statement 1 is YES) but still for the sake of clarity

Speed x time = distance

Fm x 10 =64x5m

F= (645m)/ 10m

F=32 men needed.

S2Calc

Statement #2 says 20 workers can complete the work in 16 days.

20 men

Speed 20m

Time 16

Distance 20m x 16

Run STD on first column, total distance = 20m x 16,

Weve to cover the same distance in 10 days. So well need F men

Make a new column

20 men F men

Speed 20m Fm

Time 16 10

Distance 20m x 16 20m x 16

Its obvious youll get an exact value of F by running STD formula on last column.No need to waste time in exact calculation.


9 of 11 7/28/2014 2:02 PM

So DS answer for second statement =YES.

S3calc

Statement #3 says One-eighth of the work can be completed by 8 workers in 5 days

Make column, run std.

8 men

Speed 8m

Time 5

Distance 8m x5= 40m

Distance covered by 8 men in 5 days = 40m

But statement says this is only 1/8th of total work

1/8th of total work = 40m

Total work =8 x 40m

We want to cover this in 10 days only. (There is no need to calculate the exact value,this situation is same as s1calc, so DS answer is going to be Yes)

But still for clarity, Im making new column

8 men F men

Speed 8m Fm

Time 5 10

Distance 8m x5= 40m 8x40m

Run STD on last column

Speed x time = distance

Fm x 10 = 8x40m

F=(840) / (m x10)

F=32 men needed.


10 of 11 7/28/2014 2:02 PM

DS answer for statement 3: yes because exact value possible.

Final answer: since we get YES in DS for each statement 1,2,3 individually.Therefore Answer choice is E any one of the three.

URL to article: http://mrunal.org/2012/05/aptitude-data-sufficiency-ds-simple.html

Posted By Mrunal On 07/05/2012 @ 18:36 In the category Aptitude


11 of 11 7/28/2014 2:02 PM

data sufficiency (ds)_ simple equation, partnership, tnw

Documents