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Time and Work - General Aptitude

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.
Q1:

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

ANS:E - Both I and II are necessary to answer

 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.  Correct answer is (E).