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M31-15

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M31-15  [#permalink]

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New post 09 Jun 2015, 08:12
1
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:36) correct 49% (01:41) wrong based on 53 sessions

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New post 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.


Answer: E
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New post 28 May 2016, 00:43
Nice trap!
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New post 08 Sep 2016, 05:06
i didnt understand the question. can you elaborate it a bit more?
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New post 08 Sep 2016, 05:10
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New post 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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New post 17 Nov 2016, 21:46
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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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Re: M31-15  [#permalink]

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New post 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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New post 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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New post 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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New post 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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New post 06 Oct 2018, 04:37
If the question asked- Positive values of x, then what would be the answer??

Thanks!
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New post 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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New post 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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