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# Data Sufficiency Quiz For Upcoming Exams

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.
 A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the work was carried out by A? I. A completed the job alone after A and B worked together for 5 days. II. Part of the work done by A could have been done by B and C together in 6 days.
 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

Explanation:

 B’s 1 day’s work = 1 20
 (A+ B)’s 1 day’s work = 1 7
 I. (A + B)’s 5 day’s work = 5 7
 Remaining work = 1 – 5 = 2 . 7 7
 2 work was carried by A. 7

II. is irrelevant.

 How long will Machine Y, working alone, take to produce x candles? I. Machine X produces x candles in 5 minutes. II. Machine X and Machine Y working at the same time produce x candles in 2 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

Explanation:

 I. gives, Machine X produces x candles in 1 min. 5
 II. gives, Machine X and Y produce x candles in 1 min. 2
 From I and II, Y produces x – x = 3x candles in 1 min. 2 5 10
 3x candles are produced by Y in 1 min. 10
 x candles will be produced by Y in 10 x x min = 10 min. 3x 3

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

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.
In how many days can 10 women finish a work?
I. 10 men can complete the work in 6 days.
II.
 10 men and 10 women together can complete the work in 3 3 days 7
III. If 10 men work for 3 days and thereafter 10 women replace them, the remaining work in completed in 4 days.
 A. Any two of the three B. I and II only C. II and III only D. I and III only E. None of these

Explanation:

I. (10 x 6) men can complete the work in 1 day.

 1 man’s 1 day’s work = 1 60
 II. 10 x 24 men + 10 x 24 women can complete the work in 1 day. 7 7
 240 men’s 1 day work + 240 women’s 1 day work = 1. 7 7
 240 x 1 + 240 women’s 1 day’s work = 1. 7 60 7
 240 women’s 1 day’s work = 1 – 4 = 3 7 7 7
 10 women’s 1 day’s work = 3 x 7 x 10 = 1 7 240 8

So, 10 women can finish the work in 8 days.

III. (10 men’s work for 3 days) + (10 women’s work for 4 days) = 1

(10 x 3) men’s 1 day’s work + (10 x 4) women’s 1 day’s work = 1

30 men’s 1 day’s work + 40 women’s 1 day’s work = 1

Thus, I and III will give us the answer.

And, II and III will give us the answer.

 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

Explanation:

 I. 20 work can be completed by (8 x 8) workers in 1 day. 100

Whole work can be completed by (8 x 8 x 5) workers in 1 day.

 = 8 x 8 x 5 workers in 10 days = 32 workers in 10 days. 10

II. (20 x 16) workers can finish it in 1 day.

 (20 x 16) workers can finish it in 10 days. 10

32 workers can finish it in 10 days.

 III. 1 work can be completed by (8 x 5) workers in 1 day. 8

Whole work can be completed by (8 x 5 x 8) workers in 1 day.

 = 8 x 5 x 8 workers in 10 days = 32 workers in 10 days. 10

Any one of the three gives the answer.

 8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work? I. 19 men and 12 women together can complete the work in 18 days. II. 16 men can complete two-third of the work in 16 days. III. In 1 day, the work done by three men in equal to the work done by four women.
 A. I only B. II only C. III only D. I or II or III E. II or III only

Explanation:

Clearly, I only gives the answer.

Similarly, II only gives the answer.

And, III only gives the answer.

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A. 20 days
B.
 22 1 days 2
C. 25 days
D. 30 days

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

 If difference of time is 60 days, B takes 3 x 60 = 90 days. 2

So, A takes 30 days to do the work.

 A’s 1 day’s work = 1 30
 B’s 1 day’s work = 1 90
 (A + B)’s 1 day’s work = 1 + 1 = 4 = 2 30 90 90 45
 A and B together can do the work in 45 = 22 1 days. 2 2
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
 A. Rs. 375 B. Rs. 400 C. Rs. 600 D. Rs. 800

Explanation:

 C’s 1 day’s work = 1 – 1 + 1 = 1 – 7 = 1 . 3 6 8 3 24 24
 A’s wages : B’s wages : C’s wages = 1 : 1 : 1 = 4 : 3 : 1. 6 8 24
 C’s share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400.
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
 A. 4 days B. 5 days C. 6 days D. 7 days

Explanation:

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

 Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2
 Solving these two equations, we get : x = 1 and y = 1 . 100 200
 (15 men + 20 boy)’s 1 day’s work = 15 + 20 = 1 . 100 200 4

15 men and 20 boys can do the work in 4 days.

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
 A. 8 hours B. 10 hours C. 12 hours D. 24 hours

Explanation:

 A’s 1 hour’s work = 1 ; 4
 (B + C)’s 1 hour’s work = 1 ; 3
 (A + C)’s 1 hour’s work = 1 . 2
 (A + B + C)’s 1 hour’s work = 1 + 1 = 7 . 4 3 12
 B’s 1 hour’s work = 7 – 1 = 1 . 12 2 12

B alone will take 12 hours to do the work.

A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
 A. 23 days B. 37 days C. 37 D. 40 days

Explanation:

 Whole work is done by A in 20 x 5 = 25 days. 4
 Now, 1 – 4 i.e., 1 work is done by A and B in 3 days. 5 5

Whole work will be done by A and B in (3 x 5) = 15 days.

 A’s 1 day’s work = 1 , (A + B)’s 1 day’s work = 1 . 25 15
 B’s 1 day’s work = 1 – 1 = 4 = 2 . 15 25 150 75
 So, B alone would do the work in 75 = 37 1 days. 2 2