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# If y is an integer and y = absolute value X + x, is y = 0?

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Manager
Joined: 06 Nov 2008
Posts: 53
If y is an integer and y = absolute value X + x, is y = 0? [#permalink]

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14 Nov 2008, 10:33
If y is an integer and y = absolute value X + x, is y = 0?
(1) x < 0
(2) y < 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Manager
Joined: 23 Jul 2008
Posts: 189

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15 Nov 2008, 12:14
jallenmorris wrote:
haichao wrote:
If y is an integer and y = |x| + x, is y = 0?
(1) x < 0 sufficient
(2) y < 1sufficient

If x is negative and we are adding the absolute value of x with the value of x, then this sum will always = 0.

pick numbers

x = -1
y = |-1| + -1
y = 1 - 1 = 0

x = -2
y = |-2| + -2
y = 2 - 2 = 0

The answer is yes and always yes.

(2) Sufficient because we can answer the question "Yes, y is = to 0, and it is always = 0 when y < 1. We're told in the stem that y is an integer, so we cannot think about fractions. Integers less than y are 0 and negative integers. So can y = a negative integer at all? No. if y = |x| + x, we're either going to have a postive value for x, such as 3. y = |3| + 3; y = 6. or 0, because if x = 0; y = |0| + 0...'nuff said. Or if x is a negative number. x = -3; y = |-3| + -3; y = 3 -3 = 0. Y can NEVER be negative, so this is sufficient to answer the question definitively one way or the other.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Nice explanation. Thanks I had picked A Before I saw this one. you guys are really gr8 helping me out in correcting my silly errors
VP
Joined: 05 Jul 2008
Posts: 1367

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15 Nov 2008, 12:40
Got D.

B makes us feel that its not telling any thing about X. but given that y is an integer and less than 1. it can only have 0 value. because, if x is +ve , y will have values > 1 and if x lies between 0 and 0.5 y will have values that are not integer. If X is -ve y is anyways 0. so y has to be 0

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: x and y--26   [#permalink] 15 Nov 2008, 12:40
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# If y is an integer and y = absolute value X + x, is y = 0?

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