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X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y

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Joined: 21 Aug 2013
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X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y  [#permalink]

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13 Jan 2019, 21:13
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45% (medium)

Question Stats:

58% (00:23) correct 42% (00:53) wrong based on 26 sessions

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X and Y are real numbers. Is X*Y negative?

(1) (X+Y)^2 > 0

(2) X = Y
Manager
Joined: 09 Mar 2018
Posts: 242
Location: India
X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y  [#permalink]

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Updated on: 14 Jan 2019, 09:07
amanvermagmat wrote:
X and Y are real numbers. Is X*Y negative?

(1) (X+Y)^2 > 0

(2) X = Y

IMO B

(1) (X+Y)^2 > 0
X & Y can take any value, X*Y can be -ive or not

(2)X=Y
This will always be > 0, for +ive and -ive values, and = 0 for x=y=0

Edit -> *Correcting after Bunnel's input*

If x and y are equal, x^2 will never be less than 0

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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 13 Jan 2019, 21:27.
Last edited by KanishkM on 14 Jan 2019, 09:07, edited 2 times in total.
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Re: X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y  [#permalink]

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14 Jan 2019, 00:39
KanishkM wrote:
amanvermagmat wrote:
X and Y are real numbers. Is X*Y negative?

(1) (X+Y)^2 > 0

(2) X = Y

IMO B

(1) (X+Y)^2 > 0
X & Y can take any value, X*Y can be -ive or not

(2)X=Y
This will always be > 0, for +ive and -ive values.

x and y both can be 0. it is stated that x and y are real numbers. real number includes 0 too. in this case, xy yields 0, which is nither positive not negative.
Manager
Joined: 09 Mar 2018
Posts: 242
Location: India
Re: X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y  [#permalink]

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14 Jan 2019, 03:08
selim wrote:
KanishkM wrote:
amanvermagmat wrote:
X and Y are real numbers. Is X*Y negative?

(1) (X+Y)^2 > 0

(2) X = Y

IMO B

(1) (X+Y)^2 > 0
X & Y can take any value, X*Y can be -ive or not

(2)X=Y
This will always be > 0, for +ive and -ive values.

x and y both can be 0. it is stated that x and y are real numbers. real number includes 0 too. in this case, xy yields 0, which is nither positive not negative.

You are right, i missed out that.

_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Math Expert
Joined: 02 Sep 2009
Posts: 52343
Re: X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y  [#permalink]

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14 Jan 2019, 03:25
1
KanishkM wrote:
selim wrote:
KanishkM wrote:
X and Y are real numbers. Is X*Y negative?

(1) (X+Y)^2 > 0

(2) X = Y

IMO B

(1) (X+Y)^2 > 0
X & Y can take any value, X*Y can be -ive or not

(2)X=Y
This will always be > 0, for +ive and -ive values.

x and y both can be 0. it is stated that x and y are real numbers. real number includes 0 too. in this case, xy yields 0, which is nither positive not negative.

You are right, i missed out that.

No, the answer is still B. The question asks whether xy < 0. From (2) the question becomes: is x^2 < 0? The answer to this question is always NO, because the square of a number cannot be negative.
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Joined: 13 Jan 2018
Posts: 181
Location: India
GMAT 1: 580 Q47 V23
GPA: 4
Re: X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y  [#permalink]

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14 Jan 2019, 04:10
X and Y are real numbers. Is X*Y negative?

(1) $$(X+Y)^2$$ > 0

Let X = -1 and Y = 2, then asnwer is YES

Let X = -2 and Y = -3, then answer is NO

INSUFFICIENT

(2) X = Y

If X is positive then Y is positive, If X is negative then Y is also negative.

In either case, X*Y is positive and answer to the question is NO.

SUFFICIENT

OPTION: B
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Chaitanya

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Re: X and Y are real numbers. Is X*Y negative? (1) (X+Y)^2 > 0 (2) X = Y &nbs [#permalink] 14 Jan 2019, 04:10
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