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# If x > 0, is x > y? (1) |x - y| > |y| (2) |x - y| = 3

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
If x > 0, is x > y? (1) |x - y| > |y| (2) |x - y| = 3  [#permalink]

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09 Dec 2019, 00:35
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Difficulty:

65% (hard)

Question Stats:

59% (02:07) correct 41% (02:04) wrong based on 45 sessions

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If $$x > 0$$, is $$x > y$$?

(1) $$|x - y| > |y|$$
(2) $$|x - y| = 3$$

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If x > 0, is x > y? (1) |x - y| > |y| (2) |x - y| = 3  [#permalink]

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09 Dec 2019, 04:16
If x > 0, is x > y?

STATEMENT (1) |x - y| > |y|
squaring both sides we get,
x^2+y^2-2xy > y^2
x^2-2xy > 0
x(x-2y) > 0
(x-2y) > 0 (since x>0 )

x>2y and x positive value
any value of y will always be less than x

is x > y? --YES
SUFFICIENT

STATEMENT (2) |x - y| = 3

suppose x = 5, y = 2
then x>y
is x > y? --answer is YES

if x = 2 , y = 5 then |x - y| = 3
is x > y? --NO

INSUFFICIENT

A is the answer
If x > 0, is x > y? (1) |x - y| > |y| (2) |x - y| = 3   [#permalink] 09 Dec 2019, 04:16
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# If x > 0, is x > y? (1) |x - y| > |y| (2) |x - y| = 3

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