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S96-02

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S96-02  [#permalink]

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New post 16 Sep 2014, 01:50
1
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

30% (01:27) correct 70% (01:25) wrong based on 116 sessions

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Re S96-02  [#permalink]

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New post 16 Sep 2014, 01:50
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.


Answer: D
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Re: S96-02  [#permalink]

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New post 27 Aug 2016, 05:31
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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New post 27 Aug 2016, 05:41
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New post 27 Aug 2016, 10:28
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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New post 18 Oct 2016, 02:47
I still don't understand how the second statement in sufficient.
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New post 18 Oct 2016, 02:53
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.

Answer: D.

Hope it helps.
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New post 15 Oct 2017, 09:33
I love this question, got it wrong because I didnt understand the logic of statement 2. Cheers
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New post 17 Jun 2018, 04:04
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I think this is a high-quality question and I agree with explanation.
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S96-02  [#permalink]

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New post 02 Aug 2019, 23:52
I think this is a high-quality question and I agree with explanation. interesting ques, though got it wrong(chose option A) but learned a point.
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S96-02   [#permalink] 02 Aug 2019, 23:52
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