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# m + 2n = 10 and m is 50% of n

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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m + 2n = 10 and m is 50% of n [#permalink]  20 May 2018, 16:59
Expert's post
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Question Stats:

50% (00:27) correct 50% (01:09) wrong based on 18 sessions
m + 2n = 10 and m is 50% of n

 Quantity A Quantity B $$m^2$$ $$n$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Manager
Joined: 26 Jan 2018
Posts: 176
Followers: 0

Kudos [?]: 105 [0], given: 3

Re: m + 2n = 10 and m is 50% of n [#permalink]  23 May 2018, 09:35
m=n/2

m + 2n = 10

n/2+2n = 10

2.5n = 10

n=4

m + 2n = 10

m+8=10
m=2

m^2 = n =4
Hence C
GRE Instructor
Joined: 10 Apr 2015
Posts: 1407
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Kudos [?]: 1337 [0], given: 8

Re: m + 2n = 10 and m is 50% of n [#permalink]  23 May 2018, 09:41
Expert's post
sandy wrote:
m + 2n = 10 and m is 50% of n

 Quantity A Quantity B $$m^2$$ $$n$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

This is a system of equations question in disguise

Given: m + 2n = 10

We're also told that m is 50% of n, which we can rewrite as m = 0.5n

So, we have the system....
m + 2n = 10
m = 0.5n
...which we can solve for m and n

If m = 0.5n, we can take m + 2n = 10 and replace m with 0.5n to get: 0.5n + 2n = 10
Simplify: 2.5n = 10
Solve: n = 4

Since n = 4 AND since m = 0.5n, we can conclude that m = 0.5(4) = 2

So, the solution to our system of equations is n = 4 and m = 2

So, our quantities become:
Quantity A: 2²
Quantity B: 4

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: m + 2n = 10 and m is 50% of n   [#permalink] 23 May 2018, 09:41
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