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M31-15

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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
[Reveal] Spoiler: OA

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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 27 May 2016, 23:43
Nice trap!
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New post 08 Sep 2016, 04:06
i didnt understand the question. can you elaborate it a bit more?

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New post 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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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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New post 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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New post 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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M31-15   [#permalink] 21 Nov 2017, 06:23
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