Data Sufficiency - Quant/Math - CAT 2013

The question for the day is a data sufficiency question.

In this question, there is a question statement which is followed by two statements. You have to decide whether the information provided in the two statements is sufficient for answering the question.

Mark 1

If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark 2

If the question can be answered by using either statement alone.

Mark 3

If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

Mark 4

If the question cannot be answered even by using both the statements together.

Question:

What is the value of x, if x and y are natural numbers?

1. x + y = 3
2. xy = 2

Solution:

Statement A:
The question states that x and y are natural numbers. Therefore, they should start from 1, 2, .... If x + y = 3 where x and y are natural numbers

x has to be 1 or 2 and y has to be 2 or 1

i.e.	if x = 1	y = 2	Therefore, x + y = 3
else	if x = 2	y = 1	& x + y = 3

So from statement A we cannot conclusively find the value of x. It can be either 1 or 2.

Statement B:
xy = 2       with x and y being natural numbers, x = 1 or 2 and y could be 2 or 1.

i.e.	when x = 1,	y = 2	& xy = 2 or
	when x = 2,	y = 1	& xy = 2

Statement A and Statement B
x + y = 3 & xy = 2

x can take either 1 or 2. So both the statements together are not sufficient to answer the question.

Therefore, the answer choice is (4).

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