The average earning of each member of the Gates family...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

The average earning of each member of the Gates family...

by swerve » Wed Nov 29, 2017 6:05 pm

The average earning of each member of the Gates family is 20% less than the average earning of each member of the the Buffets family. The total earning of the Gates family is 20% more than the total earning of buffets family. the no. family members in the buffets family is what percent of the no.of the family members of gates:

A.66.66
B.75
C.25
D.33.33
E. 50

The OA is A.

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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Source: Beat The GMAT — Problem Solving | Wed Nov 29, 2017 6:05 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Nov 29, 2017 10:03 pm

swerve wrote:The average earning of each member of the Gates family is 20% less than the average earning of each member of the the Buffets family. The total earning of the Gates family is 20% more than the total earning of buffets family. the no. family members in the buffets family is what percent of the no.of the family members of gates:

A.66.66
B.75
C.25
D.33.33
E. 50

The OA is A.

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

Say there are g number of members in the Gates family and b number of members in the Buffet family; say average earning of a member of Buffet family = $100; thus, the average earning of Gates family = $80.

Total earning of Gates family = 80b and total earning of Buffet family = 100g

We are given that 80g - 100b = 20% of 100b =>80g - 100b = 20b => 80g = 120b => b = 23 of g => b = 66.66% of g

The correct answer: A

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 12, 2019 3:54 pm

swerve wrote:The average earning of each member of the Gates family is 20% less than the average earning of each member of the the Buffets family. The total earning of the Gates family is 20% more than the total earning of buffets family. the no. family members in the buffets family is what percent of the no.of the family members of gates:

A.66.66
B.75
C.25
D.33.33
E. 50

The OA is A.

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 let the average earning of each member of the Buffets family be 10, and thus the average earning of each member of the Gates family will then be 8. We can also let b = the number of members in Buffets family and g = the number of members in Gates family. Therefore, we can create the equation:

8g = 10b x 1.2

8g = 12b

b = 8g/12 = (2/3)g

We see that the number of members in Buffets family is â…”, or 66.66%, of the number of members in Gates family.

Answer: A

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