M31-15

Question

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

Bunuel · Accepted Answer

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

Linhbiz · Answer

Nice trap!

sajib2126 · Answer

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 ?

Bunuel · Answer

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.

Aman8686 · Answer

I got this wrong in my test and wrong again in my second pass. A perfect question to test mental agility!

AashiS · Answer

If the question asked- Positive values of x, then what would be the answer??

Thanks!

LevanKhukhunashvili · Answer

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

dcummins · Answer

Damn. I got stung by failing to consider the negatives in this question!

OhMy · Answer

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

kaladin123 · Answer

I think that this is a fantastic high-quality question & I agree with the explanation. 
Thank you  Bunuel .

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

kop18 · Answer

I think this an extremely well crafted question and urges us to never forget the properties of the square roots.

BaoN. · Answer

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

Vikramaditya00 · Answer

I think this is a  high-quality  question and I agree with explanation. Amazing trap it was fun

rj123rox · Answer

I think this is a  high-quality  question and I agree with explanation. Question is tricky
should be in difficult category in my opinion

VeeB · Answer

A subtle trap is what makes this question a gem! I totally missed the negative values and fell right into option B. correct answer is E

Posted from my mobile device

Sujithz001 · Answer

I think this is a  high-quality  question and I agree with explanation. Superb question!  Bunuel

A basic yet, crucial learning. Please keep such questions coming.

Thanks a lot!

phmahi1997 · Answer

I like the solution - it’s helpful. What a trap, Lol!

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