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If y is an integer and y = |x| + x, is y = 0?

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by ahmedshafea » Mon Sep 11, 2017 12:39 pm
If y is an integer and y = |x| + x, is y = 0?

(1) x < 0
(2) y < 1


I rephrased the original question as Is x<0?
Statement 1 : SF
Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x
- X<0 or,
- 0<X<0.5
Basis this II is insufficient.. Where am I going wrong ?


Can some experts help me with this? How to come up with the correct answer?
Need thorough explanation regarding this one. Thanks
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Source: — Data Sufficiency |

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by [email protected] » Mon Sep 11, 2017 7:47 pm
Hi ahmedshafea,

We're told that Y is INTEGER and that Y = |X| + X. We're asked if Y = 0. This is a YES/NO question. Before we deal with the two Facts, we can certainly 'rewrite' the given question. Y would equal 0 under two circumstances:
-If X is ANY NEGATIVE value.
-If X is 0.

Y would NOT equal 0 if X was a positive (in this situation, Y would equal 2X). Thus, the question is ultimately asking... "Is X less than OR equal to 0?"

1) X < 0

Fact 1 clearly defines X as negative, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) Y < 1

The prompt tells us that Y is an INTEGER - and since Y cannot be negative, the only integer that's possible here is 0. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

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