Bunuel wrote:

Official Solution:

If \(m\) is a negative integer and \(m^3 + 380 = 381m\), then what is the value of \(m\)?

A. \(-21\)

B. \(-20\)

C. \(-19\)

D. \(-1\)

E. \(None \ of \ the \ above\)

Given \(m^3 + 380 = 380m+m\).

Re-arrange: \(m^3-m= 380m-380\).

\(m(m+1)(m-1)=380(m-1)\). Since \(m\) is a negative integer, then \(m-1\neq{0}\) and we can safely reduce by \(m-1\) to get \(m(m+1)=380\).

So, we have that 380 is the product of two consecutive negative integers: \(380=-20*(-19)\), hence \(m=-20\).

Answer: B

Hi

BunuelI have a small conceptual doubt regarding this option.

When you say that we can safely eliminate x-1 on both sides, What does it exactly mean?

For example:

X^2=X. Here if we eliminate X on both sides, we say that X=0 is also one of the possible solutions.

Similarly, if we eliminate x-1 from this option, can we say that x-1=0 was one of the solutions of x but since x is a negative integer, X can't be negative.

I hope I have been able to convey my doubt.

Realllllu hoping for your reply on this concept. And if you can suggest some questions that test this concept, I will be really glad.

Regards

Nitesh