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16 Sep 2014, 01:28
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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. \(None \ of \ the \ above\)
A. \(-21\)
B. \(-20\)
C. \(-19\)
D. \(-1\)
E. \(None \ of \ the \ above\)
16 Sep 2014, 01:28
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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. \(None \ of \ the \ above\)
To simplify the equation \(m^3 + 380 = 380m + m\), we can rearrange the terms such that the ones involving 380 are on one side.
\(m^3-m= 380m-380\).
Then, we can factor it:
\(m(m+1)(m-1)=380(m-1)\).
Since \(m\) is a negative integer, we know that \(m-1\neq{0}\), so we can safely divide both sides of the equation by it to get \(m(m+1)=380\).
Hence, we have that 380 is the product of two consecutive negative integers \(m\) and \(m+1\). By trial and error it's easy to find that \(380=-20*(-19)\), therefore, \(m=-20\).
Answer: B
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. \(None \ of \ the \ above\)
To simplify the equation \(m^3 + 380 = 380m + m\), we can rearrange the terms such that the ones involving 380 are on one side.
\(m^3-m= 380m-380\).
Then, we can factor it:
\(m(m+1)(m-1)=380(m-1)\).
Since \(m\) is a negative integer, we know that \(m-1\neq{0}\), so we can safely divide both sides of the equation by it to get \(m(m+1)=380\).
Hence, we have that 380 is the product of two consecutive negative integers \(m\) and \(m+1\). By trial and error it's easy to find that \(380=-20*(-19)\), therefore, \(m=-20\).
Answer: B
shasadou
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
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Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
25 Dec 2015, 01:41
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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
-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
