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# S96-02

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:50
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5
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Difficulty:

95% (hard)

Question Stats:

33% (00:57) correct 67% (01:12) wrong based on 127 sessions

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If $$x$$ and $$y$$ are integers and $$x \lt y$$, what is the value of $$x + y$$?

(1) $$x^y = 4$$

(2) $$|x| = |y|$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:50
1
Official Solution:

The question cannot be easily rephrased to incorporate the particular information given. However, of course we should take note that both variables are integers and that $$x$$ is less than $$y$$. We are looking for the value of $$x + y$$.

Statement (1): SUFFICIENT. First, we should list out all the possible scenarios in which integers $$x$$ and $$y$$ fit the equation $$x^y = 4$$.

There are three possibilities, as we can find by trial and error: $$2^2 = 4$$, $$(-2)^2 = 4$$, and $$4^1 = 4$$. However, of these possibilities, there is only one for which $$x$$ is less than $$y$$, namely $$(-2)^2 = 4$$. Thus, we can find the value of $$x + y$$, which is $$-2 + 2 = 0$$.

Statement (2): SUFFICIENT. Knowing that $$|x| = |y|$$ does not tell us the values of the integers. However, since they have the same absolute value, but $$x$$ is less than $$y$$, it must be the case that $$y$$ is a positive integer and $$x$$ is the negative of that integer. For instance, if $$y$$ is 5, then $$x$$ is -5. The sum of $$x$$ and $$y$$ must therefore be 0, no matter what.

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Joined: 19 Jul 2016
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27 Aug 2016, 04:31
I didn't understand the logic of the solution. By knowing |x| = |y|, how can we find out x+y? Also, when it is mentioned that x<y.
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27 Aug 2016, 04:41
agarwalneha1 wrote:
I didn't understand the logic of the solution. By knowing |x| = |y|, how can we find out x+y? Also, when it is mentioned that x<y.

Please read the first sentence of the question: If $$x$$ and $$y$$ are integers and $$x \lt y$$,...
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27 Aug 2016, 09:28
Bunuel wrote:
agarwalneha1 wrote:
I didn't understand the logic of the solution. By knowing |x| = |y|, how can we find out x+y? Also, when it is mentioned that x<y.

Please read the first sentence of the question: If $$x$$ and $$y$$ are integers and $$x \lt y$$,...

Thanks.. I got the point.
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Joined: 20 Jul 2016
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18 Oct 2016, 01:47
I still don't understand how the second statement in sufficient.
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18 Oct 2016, 01:53
A1996J wrote:
I still don't understand how the second statement in sufficient.

If x and y are integers and x<y, what is the value of x+y?

(1) x^y=4 --> as x and y are integers and x<y then only possible solution is (-2)^2=4 (other integer solutions for x^y=4 are: 2^2=4 and 4^1=4) --> x+y=-2+2=0. Sufficient.

(2) |x|=|y| --> as also x<y then they have opposite signs (x<0<y, so |x|=-x and|y|=y) --> -x=y --> x+y=0. Sufficient.

Hope it helps.
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15 Oct 2017, 08:33
I love this question, got it wrong because I didnt understand the logic of statement 2. Cheers
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Joined: 24 May 2018
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17 Jun 2018, 03:04
1
I think this is a high-quality question and I agree with explanation.
Re S96-02 &nbs [#permalink] 17 Jun 2018, 03:04
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# S96-02

Moderators: chetan2u, Bunuel

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