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# Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2

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Re: Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2 [#permalink]
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Bunuel wrote:
Is xy positive?

(1) $$x = y + 1$$
x=1 , y=0
xy becomes neither positive nor negative Clearly insufficient

(2) $$(x + y)^2 < (x - y)^2$$
Simplifying ,
x^2 +y^2 +2x*y < x^2 +y^2 -2x*y
=> 4xy<0
=>xy<0

Therefore IMO B
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Re: Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2 [#permalink]
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Kudos
Bunuel wrote:
Is xy positive?

(1) $$x = y + 1$$
(2) $$(x + y)^2 < (x - y)^2$$

I considered statement (2) in a different manner from what has been outlined above, perhaps because I was not writing anything down. I thought I would share, just in case others in the community could benefit. (These types of number properties questions are quite common.)

* First, neither x nor y can be 0, since either quadratic would then be the same as the other, violating the inequality.

* Second, if x is positive, y must be negative (a positive plus another positive would be greater when squared than a positive plus a negative); along the same lines, if x is negative, y must be positive (a negative plus another negative would be greater when squared than a negative plus a positive, and if both x and y were negative, the right-hand side of the inequality would be less than the left-hand side).

Putting our two realizations together, we can conclude that Statement (2) is sufficient, and the answer is (B): a positive-negative product will be negative. (We do not even have to test numbers, although we could.)

- Andrew
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Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2 [#permalink]
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Statement 1: x = y + 1 --> Clearly insufficient
Statement 2: This says x and y should be of opposite signs. Therefore sufficient

IMO B

Bunuel wrote:
Is xy positive?

(1) $$x = y + 1$$
(2) $$(x + y)^2 < (x - y)^2$$

Project DS Butler Data Sufficiency (DS3)

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Re: Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2 [#permalink]
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For xy = positive, both x and y should be of the same sign.

Statement 1 : x=y+1.
x=2, y=1 ---- Satisfies the statement and xy is positive.
x=0, y=-1 --- Satisfies the statement but xy is not positive.
Hence, insufficient.

Statement 2 : (x+y)^2<(x−y)^2
This will happen only when x and y are of different signs. Sub different values for x and y and you will agree that x and y have to be of different signs to satisfy this statement.
Hence, sufficient.
Re: Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2 [#permalink]
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