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GRE Prep Club Test - If m is a negative integer and m^2 + 38
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Updated on: 27 Dec 2017, 15:40
Updated on: 27 Dec 2017, 15:40
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Question Stats:
40% (01:31) correct
60% (01:01) wrong based on 5 sessions
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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
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
Re: GRE Prep Club Test - If m is a negative integer and m^2 + 38
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21 Jan 2017, 03:31
21 Jan 2017, 03:31
1
Expert Reply
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.
\(m^3 + 380 = 381m\) 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.
gmatclubot
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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