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# M31-15

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Math Expert
Joined: 02 Sep 2009
Posts: 52902

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09 Jun 2015, 07:12
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

51% (02:48) correct 49% (01:05) wrong based on 72 sessions

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If $$x$$ is an integer, and $$121 < x^2 \leq 361$$, which of the following is the sum of all possible values of $$x$$?

A. 135
B. 124
C. 116
D. 105
E. None of the above

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Joined: 02 Sep 2009
Posts: 52902

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09 Jun 2015, 07:12
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Official Solution:

If $$x$$ is an integer, and $$121 < x^2 \leq 361$$, which of the following is the sum of all possible values of $$x$$?

A. 135
B. 124
C. 116
D. 105
E. None of the above

Notice that since $$x$$ is squared, then for every positive value of $$x$$ there will be its negative pair with the same magnitude. So, the sum of all possible values of $$x$$ will be 0.

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Joined: 08 Jul 2015
Posts: 56
GPA: 3.8
WE: Project Management (Energy and Utilities)

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27 May 2016, 23:43
Nice trap!
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This alone: justice in thought, goodness in action, speech that cannot deceive, and a disposition glad of whatever comes, welcoming it as necessary, as familiar, as flowing from the same source and fountain as yourself. (Marcus Aurelius)

Intern
Joined: 02 Sep 2016
Posts: 10

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08 Sep 2016, 04:06
i didnt understand the question. can you elaborate it a bit more?
Math Expert
Joined: 02 Sep 2009
Posts: 52902

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08 Sep 2016, 04:10
manchitkapoor wrote:
i didnt understand the question. can you elaborate it a bit more?

Check alternative solutions here: if-x-is-an-integer-and-121-x-2-361-which-of-the-following-is-198509.html
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Joined: 26 Jul 2014
Posts: 12
Schools: Kellogg PT '17

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17 Nov 2016, 18:25
Hi, bunnel, can we deduce from the question " x is greater or equal to -19 and less or equal +19 and x is greater than 11 or less then -11 ", meaning 19 >=x>11, In that case sum of x will be 105.
Please explain why we can deduce from two different range of values to a common range of value for x ?
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Joined: 02 Sep 2009
Posts: 52902

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17 Nov 2016, 20:46
1
sajib2126 wrote:
Hi, bunnel, can we deduce from the question " x is greater or equal to -19 and less or equal +19 and x is greater than 11 or less then -11 ", meaning 19 >=x>11, In that case sum of x will be 105.
Please explain why we can deduce from two different range of values to a common range of value for x ?

Not sure I completely follow what you wrote there but anyway the ranges of x are:

-19 <= x < -11 and 11 < x < = 19:

x = +/- 19;
x = +/- 18;
...
x = +/- 12.
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Joined: 22 Aug 2017
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21 Nov 2017, 06:18
Hello can you please tell me where I am wrong

I didn't took negative values because in GMAT sqrt(n) is only a positive value. For example sqrt(4) is only 2 and not both -2 and 2
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Posts: 52902

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21 Nov 2017, 06:23
Raphire wrote:
Hello can you please tell me where I am wrong

I didn't took negative values because in GMAT sqrt(n) is only a positive value. For example sqrt(4) is only 2 and not both -2 and 2

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt[4]{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.
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02 Feb 2018, 19:28
Please explain my doubt: If you read the question carefully, it's written as "sum of all positive values of x" - Then we should not take negative values in my view.
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02 Feb 2018, 23:10
1
shubhamag17 wrote:
Please explain my doubt: If you read the question carefully, it's written as "sum of all positive values of x" - Then we should not take negative values in my view.

Which of the following is the sum of all POSSIBLE values of x? NOT "positive values of x"?
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29 Jun 2018, 03:45
I got this wrong in my test and wrong again in my second pass. A perfect question to test mental agility!
Intern
Joined: 24 Jun 2018
Posts: 27
Location: India

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06 Oct 2018, 03:37
If the question asked- Positive values of x, then what would be the answer??

Thanks!
Re: M31-15   [#permalink] 06 Oct 2018, 03:37
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# M31-15

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