Last year, the price of a jar of peanut butter at a certain

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Last year, the price of a jar of peanut butter at a certain

by BTGmoderatorDC » Tue Apr 09, 2019 1:23 am

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Last year, the price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P. This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20%. If a customer purchases one jar of peanut butter and one jar of jelly this year and receives a 25% discount, which of the following represents the amount that he paid, in terms of P?

A. 3P/2

B. 17P/10

C. 19P/10

D. 21P/10

E. 11P/5

OA D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Apr 09, 2019 1:23 am

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by GMATGuruNY » Tue Apr 09, 2019 2:26 am

BTGmoderatorDC wrote:Last year, the price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P. This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20%. If a customer purchases one jar of peanut butter and one jar of jelly this year and receives a 25% discount, which of the following represents the amount that he paid, in terms of P?

A. 3P/2

B. 17P/10

C. 19P/10

D. 21P/10

E. 11P/5

The price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P.
Let P = 10 and J = 20

This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20%
New P = 10 + (20% of 10) = 10 + 2 = 12
New J = 20 - (20% of 20) = 20 - 4 = 16

A customer purchases one jar of peanut butter and one jar of jelly this year and receives a 25% discount.
Before the discount:
New P + New J = 12 + 16 = 28
After the discount:
28 - (25% of 28) = 28 - 7 = 21

Which of the following represents the amount that he paid, in terms of P?
The correct answer must yield $21 when P=10.
Only D works:
21P/10 = (21*10)/10 = 21.

The correct answer is D.

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by Scott@TargetTestPrep » Wed Apr 10, 2019 4:51 pm

BTGmoderatorDC wrote:Last year, the price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P. This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20%. If a customer purchases one jar of peanut butter and one jar of jelly this year and receives a 25% discount, which of the following represents the amount that he paid, in terms of P?

A. 3P/2

B. 17P/10

C. 19P/10

D. 21P/10

E. 11P/5

OA D

Source: Veritas Prep

We are given that last year, the price of a jar of peanut butter at a certain store was P dollars, and the price of a jar of jelly at the same store was J dollars, where J = 2P.

This year the peanut butter price increased by 20%, so the new price is 1.2P.

Since the price of jelly decreased by 20%, the new price is 0.8J = 0.8(2P) = 1.6P.

Thus, the regular price of one jar of peanut butter and one jar of jelly is 1.2P + 1.6P = 2.8P.

Thus, at a 25% discount, the price is 0.75(2.8P) = 2.1P = 21P/10

Answer: D

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