If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2
OA:D
Source:Math Revolution
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If y =|x|- x, is y> 0?
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Statement 1:NandishSS wrote:If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2
Since y = |x| - x, we get:
y = |negative| - (negative) = positive + positive = positive.
Thus, y > 0.
SUFFICIENT.
Statement 2:
Since y > 2, it must be true that y > 0.
SUFFICIENT.
The correct answer is D.
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Hi NandishSS,
This question can be solved with Number Properties or by TESTing VALUES.
We're told that Y = |X| - X. We're asked if Y is greater than 0. This is a YES/NO question.
1) X < 0
IF...
X = -1
Y = |-1| - (-1) = 2 and the answer to the question is YES.
Notice how the math 'works' here: the absolute value of a negative (which is POSITIVE) minus a negative (which creates another POSITIVE)... means that Y will ALWAYS be positive when X is negative. Thus, the answer to the question would ALWAYS be YES.
Fact 1 is SUFFICIENT.
2) Y > 2
If Y is greater than 2, then the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question can be solved with Number Properties or by TESTing VALUES.
We're told that Y = |X| - X. We're asked if Y is greater than 0. This is a YES/NO question.
1) X < 0
IF...
X = -1
Y = |-1| - (-1) = 2 and the answer to the question is YES.
Notice how the math 'works' here: the absolute value of a negative (which is POSITIVE) minus a negative (which creates another POSITIVE)... means that Y will ALWAYS be positive when X is negative. Thus, the answer to the question would ALWAYS be YES.
Fact 1 is SUFFICIENT.
2) Y > 2
If Y is greater than 2, then the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Jay@ManhattanReview
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Hi Nandish,NandishSS wrote:If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2
OA:D
Source:Math Revolution
y =|x|- x can rewritten as:
1. y =|x| - |x|, if x is positive
=> y = 0
=> y is not less than 0.
2. y =|x| - x = 0, if x = 0
=> y = 0
=> y is not less than 0.
3. y =|x| + |x|, if x is negative
=> y = 2*|x| = a positive quantity
=> y > 0.
Let us see each statement one by one.
S1: x < 0 => x is negative. This is case 3 scenerio. Suffcient.
S2: y > 2 itself answers the question. A number greater than 2 means that the number is greater than 0. Sufficient.
Answer: D
Hope this helps!
-Jay
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