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

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AAPL: Moderator; Posts: 2695; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Wed May 29, 2019 4:54 am

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Veritas Prep

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. $3\frac{P}{2}$

B. $17\frac{P}{10}$

C. $19\frac{P}{10}$

D. $21\frac{P}{10}$

E. $11\frac{P}{5}$

OA D

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Source: Beat The GMAT — Problem Solving | Wed May 29, 2019 4:54 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed May 29, 2019 5:25 am

AAPL wrote:Veritas Prep

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. $3\frac{P}{2}$

B. $17\frac{P}{10}$

C. $19\frac{P}{10}$

D. $21\frac{P}{10}$

E. $11\frac{P}{5}$

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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swerve: Legendary Member; Posts: 2571; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu May 30, 2019 5:35 pm

Let $P=100$, thus $J=200$, last year.

So this year $P = 120$ (20% increase), and $J = 160$ (20% decrease). Price paid this year by customer $= 120+160 = 280$.

But after 25% discount, price $=$ 75% of 280 $= \frac{3}{4} \cdot 280 = 210$.

So we have to look for an option where if we put $P=100$, we should get an answer as '210'.

Hence, __D__ is the correct answer.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sat Jun 01, 2019 5:19 am

AAPL wrote:Veritas Prep

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. $3\frac{P}{2}$

B. $17\frac{P}{10}$

C. $19\frac{P}{10}$

D. $21\frac{P}{10}$

E. $11\frac{P}{5}$

OA D

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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Head of GMAT Instruction
[email protected]

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