soumya1989 wrote:

Level 170 question

If x is an integer, and \(169 < x^2 < 324\), which of the following is the sum of all values of x?

(A) 61

(B) 62

(C) 75

(D) 93

(E) None of the above.

We are given that 169 < x^2 < 324. That is, 13 < |x| < 18. If x is positive, x = 14, 15, 16, 17. If x is negative, x = -14, -15, -16, -17. We see that for every positive value of x, the opposite (or negative) is also a possibility. Thus, the sum of all values of x will be zero.

Answer: E

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