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If M is an integer, what is the value of m?

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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Aug 05, 2015 10:50 am
Uva@90 wrote:If M is an integer, what is the value of m?

1) m^3 + 380 = 381m
2) m + m^3 < 0
Statement 1:
m³ - 381m + 380 = 0

m³ - m - 380m + 380 = 0

m(m² - 1) - 380(m - 1) = 0

m(m+1)(m-1) - 380(m-1) = 0

(m-1) [ m(m+1) - 380 ] = 0

(m-1)(m² + m - 380) = 0

(m-1)(m+20)(m-19) = 0.

Options for m:
m=1, m=-20, m=19.
INSUFFICIENT.

Statement 2:
Here, m can be any negative integer.
INSUFFICIENT.

Statements combined:
Of the 3 options for m implied by statement 1, only m=-20 also satisfies statement 2.
Thus, m=-20.
SUFFICIENT.

The correct answer is C.
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