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M31-15

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Bunuel
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M31-15 [#permalink] New post   09 Jun 2015, 08:12
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Question Stats:

54% (01:30) correct 46% (01:36) wrong based on 199 sessions
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If \(x\) is an integer, and \(121 < x^2 \leq 361\), what 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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E
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Bunuel
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Re M31-15 [#permalink] New post   09 Jun 2015, 08:12
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Official Solution:


If \(x\) is an integer, and \(121 < x^2 \leq 361\), what is the sum of all possible values of \(x\)?


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


Since \(x\) is squared, for every positive value of \(x\), there will be a corresponding negative value with the same magnitude. Therefore, the sum of all possible values of \(x\) will be 0.


Answer: E
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Re: M31-15 [#permalink] New post   28 May 2016, 00:43
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Nice trap!
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sajib2126
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Re: M31-15 [#permalink] 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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Re: M31-15 [#permalink] 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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Aman8686
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Re: M31-15 [#permalink] 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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Re: M31-15 [#permalink] 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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Re: M31-15 [#permalink] 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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Re: M31-15 [#permalink] New post   29 May 2019, 02:46
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Damn. I got stung by failing to consider the negatives in this question!
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Re: M31-15 [#permalink] New post   04 Mar 2020, 07:54
LevanKhukhunashvili wrote:
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


Note that x is SMALLER OR EQUAL to |19|!
so positive values actually include 19: 12, 13, 14, 15, 16, 17, 18, 19
Sum = 124
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Re: M31-15 [#permalink] New post   09 Jun 2021, 18:27
I think that this is a fantastic high-quality question & I agree with the explanation.
Thank you Bunuel.
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Re: M31-15 [#permalink] New post   12 Aug 2023, 02:06
I think this is a high-quality question and I agree with explanation.
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Re: M31-15 [#permalink] New post   12 Aug 2023, 06:00
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M31-15 [#permalink] New post   15 Aug 2023, 07:38
I think this an extremely well crafted question and urges us to never forget the properties of the square roots.
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Re M31-15 [#permalink] New post   10 Sep 2023, 11:07
I think this is a high-quality question and I agree with explanation. what a trap!
x is only given as an integer, so both positive and negative are okay.
I am so easily trapped OMG
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Re M31-15 [#permalink]
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