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Time and Work – Data Sufficiency 1

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.
1.
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

Answer: Option A

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 – 5/7 = 2/7 .
2/7 work was carried by A.

II. is irrelevant.

Correct answer is (A).


2.
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

Answer: Option E

Explanation:

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

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

Correct answer is (E).

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