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If the question statement is "m is a negative integer and m^3 + 380 = 381m", how did you derive that "given m^3 + 380 = 380m+m." Is this a typo and there is a +m missing?
If the question statement is "m is a negative integer and m^3 + 380 = 381m", how did you derive that "given m^3 + 380 = 380m+m." Is this a typo and there is a +m missing?
not having that algebraic gift i did it the following way: the stem simplifies to m(m^2-381)= -380, where we know that m is -ve therefore (m^2-381) should be +ve for the product to be a -ve number.
-1 and -19 rule out because they would leave a -ve results int he brackets and hence give +ve product which cannot be true. therefore we need to brute force options -20 and -21. start with -20 and you get the desired result
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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 \(m^3 + 380 = 381m\).
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
Great explanation as always. However, I approached it differently.
\(m^3 + 380 = 381m\)
\(m(m^2-381)=-380\) then \(m^2-380=\frac{-380}{m}\) next \(m^2=381-\frac{380}{m}\), and now we plug in the answer choices and only (C) -19 gives us the right answer
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 \(m^3 + 380 = 381m\).
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
Great explanation as always. However, I approached it differently.
\(m^3 + 380 = 381m\)
\(m(m^2-381)=-380\) then \(m^2-380=\frac{-380}{m}\) next \(m^2=381-\frac{380}{m}\), and now we plug in the answer choices and only (C) -19 gives us the right answer
Great explanation as always. However, I approached it differently.
\(m^3 + 380 = 381m\)
\(m(m^2-381)=-380\) then \(m^2-380=\frac{-380}{m}\) next \(m^2=381-\frac{380}{m}\), and now we plug in the answer choices and only (C) -19 gives us the right answer
I would like to highlight that the correct answer is B not C. The right answer is -20.
I did the same like you till a point and used other reasoning. Usign sense of numbers and memorizing some square of integers a re perfect. I will elaborate.
\(m(m^2-381)=-380\).........I need two numbers that gives -380
m^2 can't me less than or equal to 381 otherwise, it will be as follows:
Case 1:
Negative ( Positive less 381 - 381) = positive value .......Incorrect
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. \(None \ of \ the \ above\)
Similar to plug-in method, but more efficient in my opinion is to use cyclicity.
Start with choice A. -21^3 will have 1 in the units digit. So the LHS (-1 + 380) has 9 in the units digit. But the RHS (381 * -21) has 1 in the units digit, so this cant be the answer. Repeat this process for all options, and you'll see that only -20 passes the units digit test. At this point, -20 *might* be the answer, but we dont know for sure. You'll have to brute force it to confirm.
close
58% (01:25) correct 
