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The sum of the wages earned by Rachel, Robin and Richard in a week is

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The sum of the wages earned by Rachel, Robin and Richard in a week is [#permalink]

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New post 19 Aug 2015, 01:11
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Question Stats:

63% (02:02) correct 38% (03:05) wrong based on 48 sessions

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The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. It is also known that 4 times Rachel's wage is equal to 6 times Robin's wage and 8 times Richard's wage. How much is Rachel's wage more than that of Robin?

A. $300
B. $400
C. $600
D. $800
E. $1200



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Re: The sum of the wages earned by Rachel, Robin and Richard in a week is [#permalink]

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New post 19 Aug 2015, 03:56
Bunuel wrote:
The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. It is also known that 4 times Rachel's wage is equal to 6 times Robin's wage and 8 times Richard's wage. How much is Rachel's wage more than that of Robin?

A. $300
B. $400
C. $600
D. $800
E. $1200



Kudos for a correct solution.



Rachel=\(R_1\)
Robin=\(R_2\)
Richard = \(R_3\)
Let T = total of the above 3.

Given, \(4*R_1 = 6*R_2=8*R_3\) ----> T/4 + T/6+T/8 = 2600 --->13T/24=2600---> T=4800

Thus, \(R_1\) - \(R_2\) = T/4-T/6 = 1200-800 = 400. B is the correct answer.
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Re: The sum of the wages earned by Rachel, Robin and Richard in a week is [#permalink]

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New post 04 Jan 2018, 16:17
Hi All,

One of the quirky aspects to this question is that all 3 names start with an "R" (which is is something the GMAT writers would rarely do). As such, I'm going to create 3 new variables to represent the wages that each person earned:

A = Rachel's wage
B = Robin's wage
C = Richard' wage

With the given information, we can create the following two equations:
A + B + C = 2600
4A = 6B = 8C

The second equation can be converted into a ratio; since we know that 4A = 6B = 8C, we can TEST VALUES and define the relationship among the three variables:

The 3 variables in this equation could be:
C=3, B=4 and A=6

Thus, we know that the ratio of A:B:C = 6:4:3... meaning that for every 3 dollars Richard earns, Robin earns 4 dollars and Rachel earns 6 dollars. Thus, the TOTAL wages must be a multiple of 13.... which they are ($2600). By extension, the ratio tells us that...
Rachel earned $1200
Robin earned $800
Richard earned $600

Thus Rachel earned $400 more than Robin.

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Re: The sum of the wages earned by Rachel, Robin and Richard in a week is   [#permalink] 04 Jan 2018, 16:17
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