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# if y is an integer and y=|x| +x, is y = 0? 1. x<0 2. y

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if y is an integer and y=|x| +x, is y = 0? 1. x<0 2. y [#permalink]

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06 Aug 2007, 00:13
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if y is an integer and y=|x| +x, is y = 0?

1. x<0

2. y <1

Last edited by Balvinder on 06 Aug 2007, 01:40, edited 1 time in total.
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06 Aug 2007, 00:26
I think A is sufficient.

If x < 0... Then x + (-x) = 0

If y < 1... It need not be zero. If x = 1/4.... y = 1/2. So insufficient
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06 Aug 2007, 01:37
y is zero is |x| and x cancel out. So either x is zero, or x is negative.

St1:
Sufficient. Tells us x is negative.

St2:
Insufficient. If x = 1/4, then y = 1/2 (< 1 but not = 0). If x = 0, then y = 0 (<1 and = 0)

Ans A
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06 Aug 2007, 07:34
Ans: A

y = |x| + x
gives us y = 0 or y = 2x.

* Sen.1: x < 0 always gives y = 0
* Sen.2: y < 1, limits the value of x to zero or negative number. Because any x that is not 1/2 or whole will break the equation, since y is always supposed to be an integer. Which we already know from Sen.1. So this is unsufficient.
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06 Aug 2007, 08:58
Balvinder wrote:
if y is an integer and y=|x| +x, is y = 0?

1. x<0

2. y <1

Both are sufficient independently.

1. x < 0 , then |x| + x is zero as they cancel out

2. y < 1: Y being an integer limits the possible values to 0 or -ve numbers. It is impossible to generate a negative number using the equation |x| +x which means the only possible value for y is 0.
Re: gmat prep DS   [#permalink] 06 Aug 2007, 08:58
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