1. 

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 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).