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# GRE Prep Club Test - If m is a negative integer and m^2 + 38

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GRE Prep Club Test - If m is a negative integer and m^2 + 38 [#permalink]  02 Jan 2017, 07:18
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Need help how the below questions is solved... How do you get M^3 from M^2 in the original equation as stated in the explanation that -20 is the answer...

If m is a negative integer and $$m^2 + 380 = 381m$$, then what is the value of m

(A) -21
(B) -20
(C) 19
(D) -1
(E) none of the above
[Reveal] Spoiler: OA

Last edited by Carcass on 27 Dec 2017, 15:40, edited 3 times in total.
Edited by Carcass
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Re: GRE Prep Club Test - If m is a negative integer and m^2 + 38 [#permalink]  21 Jan 2017, 03:31
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The equation $$m^2 + 380 = 381m$$ does not satisfy m=-20, the equation $$m^3 + 380 = 381m$$ does.

$$m^3 + 380 = 381m$$ or

$$m^3 + 380 = 380m + m$$ or

rearranging

$$m^3 - m = 380m -380$$

$$m(m^2 - 1) = 380(m -1)$$

now $$(m^2 - 1)$$ can be rewritten as $$(m+1)(m-1)$$.

$$m(m + 1)(m - 1) = 380(m -1)$$ since m is a negative integer we can cancel out m-1 terms from both sides.

so $$m(m+1)=380$$ .

Clearly m = -20 the only possible answer.
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Sandy
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Re: GRE Prep Club Test - If m is a negative integer and m^2 + 38   [#permalink] 21 Jan 2017, 03:31
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