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GRE Math Challenge #73-If the cube of n is 180

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GMAT Club Legend
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GRE Math Challenge #73-If the cube of n is 180 [#permalink] New post 03 May 2015, 01:26
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Question Stats:

100% (01:21) correct 0% (00:00) wrong based on 4 sessions
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
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #73-If the cube of n is 180 [#permalink] New post 01 Jun 2016, 07:33
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n^3-n^2=n^2(n-1)=n*n*n-1 = 180 the only way 180 can be written that way is 5*6*6 , Hence n = 6
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Re: GRE Math Challenge #73-If the cube of n is 180 [#permalink] New post 01 Jun 2016, 14:59
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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 get: n³ = n² + 180
Rearrange to get: n³ - n² = 180
Factor to get: n²(n - 1) = 180
Or... (n)(n)(n - 1) = 180

Test the answer choices to get....
n = 6
[Reveal] Spoiler:
E


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Brent
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Re: GRE Math Challenge #73-If the cube of n is 180 [#permalink] New post 09 May 2018, 15:00
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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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Re: GRE Math Challenge #73-If the cube of n is 180   [#permalink] 09 May 2018, 15:00
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