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56% (01:32) correct 44% (01:28) wrong based on 63 sessions
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Re M28-14 [#permalink]
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 16 Sep 2014, 01:28
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Re: M28-14 [#permalink]
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20 Oct 2014, 22:44
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?
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Re: M28-14 [#permalink]
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21 Oct 2014, 01:10
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Re: M28-14 [#permalink]
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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
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Re: M28-14 [#permalink]
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29 Aug 2016, 05:14
Hi Bunuel,
if this is the product of two consecutive negative integers,then isnt m=-19 instead of -20?(m+1=-20)
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Re: M28-14 [#permalink]
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29 Aug 2016, 05:26
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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 \(m^3 + 380 = 381m\).
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 What do you think Bunuel?
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Re: M28-14 [#permalink]
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17 Jun 2017, 10:50
MikeMighty wrote: 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 \(m^3 + 380 = 381m\).
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 What do you think Bunuel? Yes, you can use plug-in method to solve this question.
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Re: M28-14 [#permalink]
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18 Jun 2017, 06:56
MikeMighty wrote: 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 answerWhat do you think Bunuel? Hi Mike, 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 Case 2:Negative ( Positive equal to 381 - 381) = 0 .......Incorrect D) -1 This will give you case 1......Eliminate D C ) -19 m^2 = 381...So it is case 2.....Eliminate C B) -20 -20 ( 400 -381)= -20 * 19 = -380.........Correct Answer B
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Re: M28-14 [#permalink]
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03 Jul 2017, 22:55
hi brunel could you pls clear how to elaborate:
m3−m = m(m+1)(m−1)
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Re: M28-14 [#permalink]
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03 Jul 2017, 23:11
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Re: M28-14 [#permalink]
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28 Sep 2017, 08:04
Is this approach correct?
Divide both side by M
m^2+ 380/m=381
Then plug in numbers and check.
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Re: M28-14 [#permalink]
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28 Sep 2017, 08:06
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I did this a bit differently though not sure if that was fluke or not -
On the Right side we have -
381m = which would clearly be a multiple of m
On the left we have-
\(m^3\) + 380. Now \(m^3\) is clearly a multiple of m too so 380 must be a multiple of m too.
Now test for are -20, -19 and -1.
-1 and -19 dont work when used in the equation.
-20 works. Hence B.
Is this the right approach?
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Re: M28-14 [#permalink]
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18 Mar 2018, 03:11
Bunuel wrote: 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. \(None \ of \ the \ above\) HI Bunuel, \(m^3 + 380 = 381m\) ==> \(m^3-381m=-380\) \(m(m^2-381)=-380\)==> m=-380 or \((m^2-381)=-380\) How to proceed further?
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NandishSS wrote: Bunuel wrote: 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. \(None \ of \ the \ above\) HI Bunuel, \(m^3 + 380 = 381m\) ==> \(m^3-381m=-380\) \(m(m^2-381)=-380\)==> m=-380 or \((m^2-381)=-380\) How to proceed further? HI GMATPrepNow / Brent Can you pls help me with above query?
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Re: M28-14 [#permalink]
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30 Mar 2018, 08:06
NandishSS wrote: NandishSS wrote: Bunuel wrote: 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. \(None \ of \ the \ above\) HI Bunuel, \(m^3 + 380 = 381m\) ==> \(m^3-381m=-380\) \(m(m^2-381)=-380\)==> m=-380 or \((m^2-381)=-380\) How to proceed further? HI GMATPrepNow / Brent Can you pls help me with above query? This can be solved with some TRICKY factoring. Given: m³ - 381m + 380 = 0 Rewrite -381m as -m - 380m to get: m³ - m - 380m + 380 = 0 Factor IN PARTS to get: m(m² - 1) - 380(m - 1) = 0 Factor m² - 1 to get: m(m+1)( m-1) - 380( m-1) = 0 Collect "like" terms to get: (m-1)[ m(m+1) - 380] = 0 Simplify: (m-1)(m² + m - 380) = 0 Factor to get: (m-1)(m+20)(m-19) = 0 So, the possible m-values are 1, -20 and 19 The question tells us that m is NEGATIVE So, m must equal -20 Answer: B Cheers, Brent
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