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

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
The sum of the wages earned by Rachel, Robin and Richard in a week is  [#permalink]

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19 Aug 2015, 00:11
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:36) correct 38% (03:52) wrong based on 51 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

Kudos for a correct solution.

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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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19 Aug 2015, 02:56
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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04 Jan 2018, 15:17
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. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The sum of the wages earned by Rachel, Robin and Richard in a week is &nbs [#permalink] 04 Jan 2018, 15:17
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