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by GMATGuruNY » Tue May 09, 2017 8:28 am
Hmna wrote:If x^2 -7x=144 , and y and n are integers such that y^n=x , which of the following CANNOT be a value for y

A)-9
B)16
C)4
D)-3
x² - 7x - 144 = 0
(x-16)(x+9) = 0
x=16 or x=-9.

Since y^n = x, y^n = 16 or y^n = -9.
Options for y: -9, 16, 4, -3.
The option in red is not possible.
There is no positive integer n such that (-3)^n = 16 or (-3)^n = -9.

The correct answer is D.
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by Matt@VeritasPrep » Thu May 11, 2017 8:47 pm
x² - 7x = 144

x² - 7x - 144 = 0

(x + 9) * (x - 16) = 0

So x = -9 or x = 16.

If y = -9 and n = 1, then x = -9: cross out (A).

If y = 16 and n = 1, then x = 16: cross out (B).

If y = 4 and n = 2, then x = 16: cross out (C).

By process of elimination, (D) is the right answer.
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