# DS Case: Simple Equation

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

I. a=5

II. b=3

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 any statement alone.

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

First, What is the DS question?

We’ve 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 of something but we are interested in finding “whether we can get an exact value using given statements or not?”

As usual make a table

 Statement Given Thought process Exact Answer possible? Question C=a+b I need must know the value of a and b to find the value of c Not 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=3 C=5+3=8. Yes

# Rule#1 Remember to Forget

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

# Rule#2: Don’t calculate exact value

you don’t 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 you’ll get an exact answer.

What if a=21233213 and b=345349550.

Again, no need to actually calculate a+b, because it is obvious you’ll get an exact value for “c”

In data sufficiency, we don’t have to find actual answers, but only check whether it is possible to get exact answer or not. So don’t waste time in doing addition of 21233213+345349550

Final Answer: (C) Question can be answered using statement 1 and 2 together but not using any statement alone.

# DS Case: Square roots

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

I. a2=25

II. b2=9

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 any statement alone.

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

## Same procedure

 Statement Given Thought process Exact Answer possible? Question C=a+b I must know the exact values of a and b to find exact value of c. 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 Combine I & II a=(+/-5) b=(+/- 3) Multiple answers! Refer “s(1+2)calc” No

## 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 even after combining the information from statement I and II.

Although, in actual exam you don’t have to do the majoori of doing second table containing all possible values of “c”. because you know you’ll get multiple values of “c”, since a=(+/-5).

Remember Rule #2: Don’t Calculate Exact Value! Because That is waste of time.

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

Now I’m using some questions from Indiabix.com for Data Sufficiency. Hope they don’t sue me for copyright violation :D

# DS case: Partnership

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

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

II. Nitin’s 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 Gagan’s share in the profit earned by them?

NO! the DS question is “can we find exact value of Gagan’s share?”

Make the table

 Statement Given Thought process. Exact Answer possible? Question Ravi, Gagan and Nitin are running a business firm in partnership. Seeking Gagan’s profit share. I could solve if only I knew the ratio of their investment and total investment. Or ratio of their profit and total profit. Not yet! I R:G:N=2:4:7 So according to Componendo, Gagan’s share =4/ (2+4+7) x total profit =4/13th of total profit But we don’t know what is total profit! No II Nitin’s share in the profit is Rs. 8750. But we don’t know total profit. We also don’t know what is the ratio of R:G:N? No Combine I & II eq1) From S1, we can infer Nitin’s share in profit = 7/13th of total profit. (same componendo)eq2) From s2, we know Nitin got Rs.8750. Because (eq1)=(eq2) you can get total profit. And from total profit, you can find Gagan’s share using Statement I*** YES!

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

***Notice I haven’t wasted my precious time in actually doing the calculation. Because we were never required to find actual profit share of Gagan. We had to find only whether is it possible to calculate exact value of Gagan’s share or not?

However for the sake of clarity, I’m completing the calculation from the (***) cell. But you don’t have to waste your time doing this, in actual exam.

## Unnecessary but for conceptual clarity

Eq1= eq2

7/13th of total profit = Nitin’s 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 Gagan’s share in profit =4/13th of total profit

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

=(4 x 8750) /7

=4 x 1250

=Rs.5000.

So we got an “Exact value” for Gagan’s share in profit (Rs.5000/-).

But we could only come upto this point only after combing the information from statement 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.

A. I only

B. II and III only

C. III only

D. I and III only

E. Any one of the three

Make sure you’ve 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?”

 Statement Given Thought process Exact Answer possible? Question Find # of Men needed to finish the job in t=10 days. i.e. how many “S” For STD, I know t=10 I only need to know value of “D” Then I can find “s” Not yet. I 20% of the work can be completed by 8 workers in 8 days. Refer S1calc Yes. II 20 workers can complete the work in 16 days. Refer S2calc Yes III One-eighth of the work can be completed 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 64×5)

So the total work is “64x5m” and we’ve to do this in t=10 days. Make a new column. Suppose we need “F” number of men. So their speed is Fm

 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 you’ll get exact value. So DS answer for Statement 1 is “YES”) but still for the sake of clarity

Speed x time = distance

Fm x 10 =64x5m

F= (64×5m)/ 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,

We’ve to cover the same distance in 10 days. So we’ll need “F” men

Make a new column

 20 men “F” men Speed 20m Fm Time 16 10 Distance 20m x 16 20m x 16

It’s obvious you’ll get an exact value of “F” by running STD formula on last column. No need to waste time in exact calculation.

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, I’m 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=(8×40) / (m x10)

F=32 men needed.

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.

## Mrunal recommends

Books: UPSC Prelims Books: UPSC Mains Books: Maths /Reasoning

## 6 Comments on “[Aptitude] Data Sufficiency (DS): Simple Equation, Partnership, TnW”

1. What is the option C in DS PARTNERSHIP QUESTION……I MEAN IN WCH SITUATION IT WILL BE D ANS…..

2. COULD YOU PLEASE DO A QUICK RECAP FOR GRAPHS,IT WILL BE VERY HELPFUL.
THANKS.

3. in the square root wala question it is not mentioned that c takes a unique value…..so it can be answered using values of a and b……. c can take multiple values

4. didt we

5. In partnership qusetion answer shall be D as we are not sure whether the profits are shared on the basis on investment amount or investment time.

6. W/5 ,8Men,8 days
Total work W=40 days
1man=320 days
therefore
W/[x*(W/320)]=10
x=32