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.
The sum of the wages earned by Rachel...
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can create the equations: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.
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
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews