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14 Dec 2010, 22:03
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
52% (01:20) correct
48%
(01:11)
wrong
based on 1299
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If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1
(1) x < 0
(2) y < 1
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
14 Dec 2010, 22:39
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Each of (1) and (2) are sufficient to answer the question. Thus the answer should be "D".
From(1), any value of X<0, whether it's integer or fraction will lead to Y = 0 because the mode function will result in positive value and positive value added to same negative value will result in Zero.
From (2), We can have Y as negative Integer ( -1,-2....) if and only if the Right hand side of equation is different. It's just adding the same X and it can't lead to the negative value.
Yes it can definitely lead to the Zero.
Thus Answer should be D.
You can plug and play certain values ( numbers ) in order to verify the above.
From(1), any value of X<0, whether it's integer or fraction will lead to Y = 0 because the mode function will result in positive value and positive value added to same negative value will result in Zero.
From (2), We can have Y as negative Integer ( -1,-2....) if and only if the Right hand side of equation is different. It's just adding the same X and it can't lead to the negative value.
Yes it can definitely lead to the Zero.
Thus Answer should be D.
You can plug and play certain values ( numbers ) in order to verify the above.
15 Dec 2010, 01:50
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If y is an integer and y = |x| + x, is y = 0?
Notice that from \(y=|x|+x\) it follows that y cannot be negative:
If \(x>0\), then \(y=x+x=2x=2*positive=positive\);
If \(x\leq{0}\) (when x is negative or zero) then \(y=-x+x=0\).
(1) \(x<0\) --> \(y=|x|+x=-x+x=0\). Sufficient.
(2) \(y<1\). We found out above that y cannot be negative and we are given that y is an integer, hence \(y=0\). Sufficient.
Answer: D.
Also discussed in Inequality and absolute value questions from my collection: https://gmatclub.com/forum/inequality-an ... 86939.html
Hope it's clear.
Notice that from \(y=|x|+x\) it follows that y cannot be negative:
If \(x>0\), then \(y=x+x=2x=2*positive=positive\);
If \(x\leq{0}\) (when x is negative or zero) then \(y=-x+x=0\).
(1) \(x<0\) --> \(y=|x|+x=-x+x=0\). Sufficient.
(2) \(y<1\). We found out above that y cannot be negative and we are given that y is an integer, hence \(y=0\). Sufficient.
Answer: D.
Also discussed in Inequality and absolute value questions from my collection: https://gmatclub.com/forum/inequality-an ... 86939.html
Hope it's clear.
