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

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

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New post 31 Oct 2018, 23:17
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (00:44) correct 20% (00:59) wrong based on 54 sessions

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

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New post 01 Nov 2018, 00:25
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

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

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New post 01 Nov 2018, 00:38
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.

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

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New post 01 Nov 2018, 09:35
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
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Re: If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0 &nbs [#permalink] 01 Nov 2018, 09:35
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