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Director  Joined: 16 May 2014
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GRE Math Challenge #58-m^3 + 380 = 381m [#permalink]
Expert's post 00:00

Question Stats: 62% (00:39) correct 37% (01:01) wrong based on 16 sessions
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
[Reveal] Spoiler: OA

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If you find this post helpful, please press the kudos button to let me know !  GRE Instructor Joined: 10 Apr 2015
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Re: GRE Math Challenge #58 [#permalink]
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Expert's post
soumya1989 wrote:
If m is a negative integer and m³ + 380 = 381m, then what is the value of m?
A. -21
B. -20
C. -19
D. -1
E. None of the above

Here's one approach:

Given: m³ + 380 = 381m
Rearrange to get m's on one side to get: m³ - 381m = -380
Factor to get: m(m² - 381) = -380

At this point, it's probably easiest to just PLUG IN the answer choices.
HOWEVER, I'm going to skip answer choice A since 21 is NOT a factor of 380, and we already know that -380 = m(m² - 381), which means m must be a factor of 380

Plug -20 into the equation to get: (-20)[(-20)² - 381] = -380
Evaluate: (-20)[400 - 381] = -380
Then...: (-20) = -380
Works!!

[Reveal] Spoiler:
B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails

Manager Joined: 17 Feb 2015
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Re: GRE Math Challenge #58 [#permalink]
what about C  Manager Joined: 17 Feb 2015
Posts: 107
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Re: GRE Math Challenge #58 [#permalink]
GreenlightTestPrep wrote:
soumya1989 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

Here's my approach:

Upon scanning the answer choices (ALWAYS scan the answer choices before performing any work!), I see answer choice D (m = -1) and it looks like a legitimate answer.
So, let's try it:
(-1)^3 + 380 = 381(-1)
-1 + 380 = -381
NOPE - looked good though! What if we try m = 1?
Let's try
(1)^3 + 380 = 381(1)
1 + 380 = 381
PERFECT!!!
m = 1.

[Reveal] Spoiler:
E

Cheers,
Brent Intern Joined: 19 Aug 2015
Posts: 1
Followers: 0

Kudos [?]: 1  , given: 0

Re: GRE Math Challenge #58 [#permalink]
1
KUDOS
Intern Joined: 25 Dec 2016
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Kudos [?]: 6 , given: 9

Re: GRE Math Challenge #58-m^3 + 380 = 381m [#permalink] Director Joined: 03 Sep 2017
Posts: 521
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Re: GRE Math Challenge #58 [#permalink]
2
KUDOS
GreenlightTestPrep wrote:
soumya1989 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

Here's my approach:

Upon scanning the answer choices (ALWAYS scan the answer choices before performing any work!), I see answer choice D (m = -1) and it looks like a legitimate answer.
So, let's try it:
(-1)^3 + 380 = 381(-1)
-1 + 380 = -381
NOPE - looked good though! What if we try m = 1?
Let's try
(1)^3 + 380 = 381(1)
1 + 380 = 381
PERFECT!!!
m = 1.

[Reveal] Spoiler:
E

Cheers,
Brent

1 can even be an answer since a third degree equation has three answers. However, since also -20 is a solution and it is among the choices, the answer should be C! If there wouldn't be -20, then E could have worked. But not in this case! GRE Instructor Joined: 10 Apr 2015
Posts: 1541
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Re: GRE Math Challenge #58 [#permalink]
1
KUDOS
Expert's post
GRE wrote:

You're absolutely right!
I've edited my response accordingly.

Thanks!

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails GRE Instructor Joined: 10 Apr 2015
Posts: 1541
Followers: 56

Kudos [?]: 1466  , given: 8

Re: GRE Math Challenge #58 [#permalink]
2
KUDOS
Expert's post
IlCreatore wrote:

1 can even be an answer since a third degree equation has three answers. However, since also -20 is a solution and it is among the choices, the answer should be C! If there wouldn't be -20, then E could have worked. But not in this case!

You're right - my mistake!
I've fixed my response.

Cheers and thanks,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Re: GRE Math Challenge #58   [#permalink] 27 Sep 2017, 07:49
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