Quantitative Aptitude

Data Sufficiency 1

Quantitative Aptitude Exercise Mode

Data Sufficiency 1

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Directions to Solve

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.

Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.

Give answer(E) if the data in both Statements I and II together are necessary to answer the question.

Question 1

How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?

I. A can fill the tank in 16 minutes.

II. B can empty the full tank in 8 minutes.

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
Correct Answer: Option E

 I. A's 1 minute's filling work = 1
16

II. B's 1 minute's filling work = 1
8

(A + B)'s 1 minute's emptying work 

 =1-1=1
81616


Tank will be emptied in 16 minutes.

Thus, both I and II are necessary to answer the question.

Correct answer is (E).

Question 2

How much time will the leak take to empty the full cistern?

I. The cistern is normally filled in 9 hours.

II. It takes one hour more than the usual time to fill the cistern because of la leak in the bottom.

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
Correct Answer: Option E

Part of cistern filled without leak in 1 hour = 1
9

II. Time taken to fill the cistern in presence of leak = 10 hours.

Net filling in 1 hour = 1
10

Work done by leak in 1 hour = 1 - 1 = 1
9 10 90

Leak will empty the full cistern in 90 hours.

Clearly, both I and II are necessary to answer the question.

Correct answer is (E).

Question 3

Two taps A and B, when opened together, can fill a tank in 6 hours. How long will it take for the pipe A alone to fill the tank?

I. B alone takes 5 hours more than A to fill the tank.

II.The ratio of the time taken by A to that taken by B to fill the tank is 2 : 3.

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
Correct Answer: Option C

(A + B)'s 1 hour filling work = 1/6.

I. Suppose A takes x hours to fill the tank.

Then, B takes (X + 5) hours to fill the tank.

(A's 1 hour work) +(B's 1 hour work)
= (A + B)'s 1 hour work.

1+1=1
x(x + 5) 6

(x + 5) + x=1
x(x + 5)6


 x2 - 5x  = 12x +30

 x2 - 7x  - 30 = 0

 x2 - 10x + 3x  - 30 = 0

 x (x -10) + 3 (x - 10) = 0

 (x - 10)(x + 3) = 0

 x = 10.    [neglecting x = -3]

So, A alone takes 10 hours to fill the tank.

II. Suppose A takes 2x hours and B takes 3x hours to fill the tank. Then,

1+1=1
2x3x  6

1+1  1/ x =  1
23 6


<=> x = 5.

So, A alone takes (2 X 5) = 10 hours to fill the tank.

Thus, each one of I and II gives the answer.

 Correct answer is (C).