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# x and y are both non-zero integers. Are x and y both less than

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Senior Manager
Joined: 19 Oct 2018
Posts: 499
Location: India
x and y are both non-zero integers. Are x and y both less than  [#permalink]

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21 May 2019, 03:41
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x and y are both non-zero integers. Are x and y both less than zero?

1. $$\sqrt{x}*\sqrt{y}$$ ≠ $$\sqrt{xy}$$
2. |x|*y=|y|*x
Manager
Joined: 12 Jan 2019
Posts: 217
Re: x and y are both non-zero integers. Are x and y both less than  [#permalink]

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22 May 2019, 07:26
nick1816 wrote:
x and y are both non-zero integers. Are x and y both less than zero?

1. $$\sqrt{x}*\sqrt{y}$$ ≠ $$\sqrt{xy}$$
2. |x|*y=|y|*x

if only one is negative, using option 1, we can not say if it is equal or not ie we can neither say that it is equal nor that it is unequal. So I think A should be the answer.

BTW what is the source of the question ? and what is official solution?
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Joined: 24 Jun 2008
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Re: x and y are both non-zero integers. Are x and y both less than  [#permalink]

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22 May 2019, 09:21
The question doesn't really make sense, because as soon as they write √x in Statement 1, they are presupposing that x is not negative, since that expression is nonsense if x is negative, or at least it is on the GMAT, since the GMAT never tests "imaginary numbers". So just by virtue of the fact that they write √x and √y in Statement 1, neither x nor y can be negative, but if that's the case, Statement 1 cannot be true, since (√x)(√y) = √(xy) is always true if x and y are zero or greater.

So since this question only makes sense if you consider imaginary numbers, which are out of the scope of the GMAT, it's potentially a confusing question to study.
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Senior Manager
Joined: 19 Oct 2018
Posts: 499
Location: India
Re: x and y are both non-zero integers. Are x and y both less than  [#permalink]

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22 May 2019, 09:28
I tried to make this question by myself and did a blunder. Now i know where i went wrong. Next time i'll take care of these things.
IanStewart wrote:
The question doesn't really make sense, because as soon as they write √x in Statement 1, they are presupposing that x is not negative, since that expression is nonsense if x is negative, or at least it is on the GMAT, since the GMAT never tests "imaginary numbers". So just by virtue of the fact that they write √x and √y in Statement 1, neither x nor y can be negative, but if that's the case, Statement 1 cannot be true, since (√x)(√y) = √(xy) is always true if x and y are zero or greater.

So since this question only makes sense if you consider imaginary numbers, which are out of the scope of the GMAT, it's potentially a confusing question to study.
Re: x and y are both non-zero integers. Are x and y both less than   [#permalink] 22 May 2019, 09:28
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