If m is an integer and m^3+380=381m, and m+m^3<0 then what is the value of m? : Crackverbal Support

If m is an integer and m^3+380=381m, and m+m^3<0 then what is the value of m? Print

Modified on: Tue, 12 Oct, 2021 at 12:16 PM

SOLUTION:

Using statement (1)

m^{3 +} 380 = 381m

=>m³-380m –m +380 = 0 or

=>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.

This implies m=1, m= -20, m=19. Hence we do not have one specific value for m.

(INSUFFICIENT)

Using statement (2)

We can have m that can be any negative integer.

(INSUFFICIENT)

Using both (1) and (2)

From m=1, m= -20, m=19, at m= -20

We have 2(- 20) + (-20)³< 0, satisfying statement (2)

At m = 1 and m= 19 we won’t have statement (2) satisfied.

Thus m= -20 by combining both.( SUFFICIENT)

Thus OPTION(C)

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If m is an integer and m^3+380=381m, and m+m^3&lt;0 then what is the value of m? Print