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The sum of the wages earned by Rachel...

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by swerve » Mon Nov 20, 2017 6:03 am
The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. Is is also known that 4 times Rachel's wages 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.

The OA is B.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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by [email protected] » Mon Nov 20, 2017 3:03 pm
Hi swerve,

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: B

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Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Thu Oct 17, 2019 7:20 pm
swerve wrote:The sum of the wages earned by Rachel, Robin and Richard in a week is $2600. Is is also known that 4 times Rachel's wages 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.

The OA is B.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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.

Answer: B

Scott Woodbury-Stewart
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[email protected]

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