sandy wrote:

If the cube of n is 180 greater than the square of n, then n =

(A) 10

(B) 9

(C) 8

(D) 7

(E) 6

We can create the equation:

n^3 = 180 + n^2

n^3 - n^2 - 180 = 0

We can see that it’s not easy to factor n^3 - n^2 - 180. Therefore, we will just check the answer choices and see which one satisfies the equation. Notice the cube root of 180 is less than 6 (because 6^3 = 216), so we’ll try the answer choices in reverse. That is, we’ll try answer choice E first.

If n = 6, then 6^3 - 6^2 - 180 = 216. - 36 - 180 = 0.

We see that we’ve found our answer.

Answer: E

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