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# If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0

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Math Expert
Joined: 02 Sep 2009
Posts: 58344
If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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01 Nov 2018, 00:17
1
3
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Difficulty:

15% (low)

Question Stats:

78% (00:51) correct 22% (00:54) wrong based on 84 sessions

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If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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01 Nov 2018, 01:25
Bunuel wrote:
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Question: is x = y?

Statement 1: |x| = |y|

@y=2, x may be 2 or -2 hence
NOT SUFFICIENT

Statement 2: xy > 0

i.e. signs of both x and y are same because their product is positive but their absolute values may be same or different hence
NOT SUFFICIENT

Combining the two statements

Statement 1 states that absolute values of x and y are same
Statement 2 says that signs of x and y are same
i.e. x = y
SUFFICIENT

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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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01 Nov 2018, 01:38
1
From statement 1:

|x| = |y|.
Squaring on both sides,
x^2 = y^2
x^2-y^2 = 0
(x+y)(x-y) = 0
x = y or x = -y.
Insufficient.

From statement 2:

xy>0
Either x and y both are positive or both negative.
No extra info.
Insufficient.

Combining both:

x and y are both positive.
hence x = y.

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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0  [#permalink]

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01 Nov 2018, 10:35
If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Stmnt 1= both x & y can be + or - hence not sufficient
stmnt 2= again x& y can be of same sign so not suffcient

combining 1 & 2 suffices the given relation hence C is correct
Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0   [#permalink] 01 Nov 2018, 10:35
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