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# M31-15

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Math Expert
Joined: 02 Sep 2009
Posts: 58464

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09 Jun 2015, 08:12
1
6
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Difficulty:

65% (hard)

Question Stats:

51% (01:36) correct 49% (01:41) wrong based on 53 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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09 Jun 2015, 08:12
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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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28 May 2016, 00:43
Nice trap!
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08 Sep 2016, 05:06
i didnt understand the question. can you elaborate it a bit more?
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08 Sep 2016, 05:10
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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17 Nov 2016, 19:25
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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17 Nov 2016, 21:46
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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21 Nov 2017, 07:18
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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21 Nov 2017, 07:23
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, 20:28
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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03 Feb 2018, 00:10
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, 04:45
I got this wrong in my test and wrong again in my second pass. A perfect question to test mental agility!
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06 Oct 2018, 04:37
If the question asked- Positive values of x, then what would be the answer??

Thanks!
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14 Mar 2019, 06:48
AashiS wrote:
If the question asked- Positive values of x, then what would be the answer??

Thanks!

If the question asked sum of POSITIVE values of x:

From the stem we know:
x is an integer
11<x<19

The possible values are 12, 13, 14, 15, 16, 17, 18

Sum=15*7=105
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29 May 2019, 02:46
Damn. I got stung by failing to consider the negatives in this question!
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Re: M31-15   [#permalink] 29 May 2019, 02:46
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# M31-15

Moderators: chetan2u, Bunuel