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Sarah receives 10z coins in addition to what she already...

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by AAPL » Mon Nov 20, 2017 7:29 am
Sarah receives 10z coins in addition to what she already had. She now has 5y+1 times as many coins as she had originally. In terms of y and z, how many did Sarah have originally?

A. 10z(5y + 1)
B. (5y+1)/10z
C. 2z/y
D. 10/(5y + 1)
E. 10/(5y + 10)

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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by DavidG@VeritasPrep » Mon Nov 20, 2017 8:14 am
AAPL wrote:Sarah receives 10z coins in addition to what she already had. She now has 5y+1 times as many coins as she had originally. In terms of y and z, how many did Sarah have originally?

A. 10z(5y + 1)
B. (5y+1)/10z
C. 2z/y
D. 10/(5y + 1)
E. 10/(5y + 10)

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
We could try some easy numbers. Say y = 1. That means that after she receives more coins, she'll have 5*1 + 1 = 6 times as many coins as she had originally.

Let's say she started with 1 coin. Then we know she'll end up with 1*6 = 6 coins, meaning she must have received 5 more coins. If she received 5 more coins, then z = 1/2, so that 10*(1/2).= 5.

To summarize:
- she starts with 1 coin
- z = 1/2
- y = 1

We want the number of coins Sara had initially, or 1. So the correct answer will give us a value of 1 when we plug '1/2' in for z and '1' in place of y. Only C works, as 2*(1/2)/1 = 1
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by DavidG@VeritasPrep » Mon Nov 20, 2017 8:17 am
AAPL wrote:Sarah receives 10z coins in addition to what she already had. She now has 5y+1 times as many coins as she had originally. In terms of y and z, how many did Sarah have originally?

A. 10z(5y + 1)
B. (5y+1)/10z
C. 2z/y
D. 10/(5y + 1)
E. 10/(5y + 10)

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
And there's always good old-fashioned algebra. Say she starts with T coins. After she receives 10z more, she'll have T + 10z. And we know that her new number of coins (T + 10z) is '5y +1' times the old value of coins, T. Algebraically, we'd get

(T + 10z) = (5y + 1)(T)
T + 10z = 5yT + T
10z = 5yT
10z/5y = T
2z/y = T
The answer is C
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by Brent@GMATPrepNow » Mon Nov 20, 2017 8:51 am
David has demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, you can watch the following video:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933

Afterwards, here are some more questions to practice with:
- https://www.beatthegmat.com/what-mistake ... 76293.html
- https://www.beatthegmat.com/car-dealer-s ... 74136.html
- https://www.beatthegmat.com/ps-rate-times-t276107.html
- https://www.beatthegmat.com/to-find-the- ... 73338.html
- https://www.beatthegmat.com/y-dollars-fr ... 73031.html
- https://www.beatthegmat.com/meters-in-x- ... 73854.html
- https://www.beatthegmat.com/a-better-exp ... 79396.html


Cheers,
Brent


Here are some more questions to practice with:
- https://www.beatthegmat.com/what-mistake ... 76293.html
- https://www.beatthegmat.com/car-dealer-s ... 74136.html
- https://www.beatthegmat.com/ps-rate-times-t276107.html
- https://www.beatthegmat.com/to-find-the- ... 73338.html
- https://www.beatthegmat.com/y-dollars-fr ... 73031.html
- https://www.beatthegmat.com/meters-in-x- ... 73854.html
- https://www.beatthegmat.com/a-better-exp ... 79396.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Thu Oct 17, 2019 7:23 pm
AAPL wrote:Sarah receives 10z coins in addition to what she already had. She now has 5y+1 times as many coins as she had originally. In terms of y and z, how many did Sarah have originally?

A. 10z(5y + 1)
B. (5y+1)/10z
C. 2z/y
D. 10/(5y + 1)
E. 10/(5y + 10)

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
We can let n = the number of coins Sarah had originally.

n + 10z = (5y + 1)n

n + 10z = 5yn + n

10z = 5yn

n = 10z/(5y) = 2z/y

Answer: C

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