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Anna and Carol buy CDs and tapes at a music store that sells

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Anna and Carol buy CDs and tapes at a music store that sells

by AAPL » Thu Apr 05, 2018 12:23 pm

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Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $50.00 on four CDs and five tapes, how much does one tape cost?

A. $5.00
B. $6.25
C. $12.00
D. $25.00
E. $100.00

The OA is A.

I get the solution to this PS question as follows,

$$CD \Rightarrow C$$
$$Tapes \Rightarrow T$$
Carol: $$4C + 5T = 50$$
Anna: $$12C + 5T = 100$$
$$12C - 4C = 50 \Rightarrow 8C = 50 \Rightarrow C = 6.25$$
$$4C + 5T = 50 \Rightarrow 25+5T=50 \Rightarrow 5T=25 \Rightarrow T=5$$
Option A.

Has anyone another approach to solve this PS question? Thanks!
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by Sionainn@PrincetonReview » Thu Apr 05, 2018 1:23 pm
This is a great one for plugging in the answers and ballparking.

We know Carol spends a total of $50 four 4 CDs and 5 tapes. Some of these answer choices are too big. There is no way that a single tape can cost $100 when she spends a total of $50, so eliminate E. If Carol only bought 5 tapes, the cost would be $10 each but since she buys 5 tapes and 4 CDs, a tape must cost less than $10. Eliminate C and D.

Then work with the remaining answer to see which on works. Since $5 is a simpler number, try A first (when working with numeric answer choices only one answer can work, so once you find one that works you can stop. So start with the easier number).

If the tapes are $5 each, then Carol spends $25 on tapes and $25 on CDs. Since she buys 4 CDs, each one would cost $6.25.

Now see if these values fit with the information we have for Anna. Anna purchases 12 CDs (12*$6.25 = $75) and 5 tapes (5*$5 = $25). This gives a total of $100. This is twice as much as Carol spends so all of the info fits together and the answer is A.

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BA - Stanford University, MPP - Harvard University
Instructor, tutor for The Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

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by Jeff@TargetTestPrep » Sat Jul 14, 2018 9:13 am
AAPL wrote:Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $50.00 on four CDs and five tapes, how much does one tape cost?

A. $5.00
B. $6.25
C. $12.00
D. $25.00
E. $100.00

Let c denote the price of one CD and t denote the price of one tape (both in dollars).

We can create the following equation for Carol's expenditure:

4c + 5t = 50

We can create the following equation for Anna's expenditure:

12c + 5t = 100

Subtracting the first equation from the second, we have:

8c = 50

c = 50/8 = 6.25

Thus:

4(6.25) + 5t = 50

5t = 25

t = 5

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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