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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: 59634
The sum of the wages earned by Rachel, Robin and Richard in a week is  [#permalink]

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19 Aug 2015, 01:11
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Difficulty:

65% (hard)

Question Stats:

63% (02:31) correct 37% (03:40) wrong based on 54 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, 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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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. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8659 Location: United States (CA) Re: The sum of the wages earned by Rachel, Robin and Richard in a week is [#permalink] ### Show Tags 20 Oct 2019, 10:01 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.

We can create the equations:

R + B + D = 2600

and

4R = 6B

2R = 3B

2R/3 = B

and

4R = 8D

R/2 = D

Substituting into the first equation, we have:

R + 2R/3 + R/2 = 2600

Multiplying by 6, we have:

6R + 4R + 3R = 15,600

13R = 15,600

R = 1,200

So B = 800 and R - B = 1200 - 800 = 400.

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Re: The sum of the wages earned by Rachel, Robin and Richard in a week is   [#permalink] 20 Oct 2019, 10:01
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