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PS - Proportions

by karthikpandian19 » Sun Jun 10, 2012 6:32 pm
Gavin and Sheryl were each given d dollars to spend during a vacation. Though
they left on the same day, Sheryl decided to return 4 days sooner than Gavin,
and Gavin spent 14 days on vacation. If Sheryl gave Gavin k dollars of her allowance
so ance that they would have had the same total amount to spend per day of
vacation, what was the dollar amount, in terms of k, that Sheryl was given in
advance?
6k
8k
9k
10k
12k
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by eagleeye » Sun Jun 10, 2012 7:50 pm
The correct answer should be 6k. Let me explain:

We are told that Gavin spent 14 days and Sheryl 4 less than that hence Sheryl spent 10 days.
They both had the same money d to start , but Sheryl gave k dollars to Gavin, hence
Sheryl has d-k dollars and Gavin has d+k dollars. We are told that per day money spent is the same, so
(d-k)/10 = (d+k)/14 => 4d=24k => d=6k.

Let me know if this helps :)
Last edited by eagleeye on Sun Jun 10, 2012 8:18 pm, edited 1 time in total.
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by GMATGuruNY » Sun Jun 10, 2012 8:14 pm
karthikpandian19 wrote:Gavin and Sheryl were each given d dollars to spend during a vacation. Though
they left on the same day, Sheryl decided to return 4 days sooner than Gavin,
and Gavin spent 14 days on vacation. If Sheryl gave Gavin k dollars of her allowance
so ance that they would have had the same total amount to spend per day of
vacation, what was the dollar amount, in terms of k, that Sheryl was given in
advance?
6k
8k
9k
10k
12k
Let each person's amount per day = 1.
Total for Gavin over 14 days = 14*1 = 14.
Total for Sheryl over 10 days = 10*1 = 10.
Total amount given in advance = 14+10 = 24.
d = amount each were given in advance = 24/2 = 12.
Since Sheryl was given 12 but used only 10, amount she gave Gavin = k = 12-10 = 2.

The question asks for the value of d=12. This is our target.
Now we plug k=2 into the answers to see which yields our target of 12.
Only answer choice A works:
6k = 6*2 = 12.

The correct answer is A.
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by karthikpandian19 » Sun Jun 10, 2012 9:22 pm
OA is A
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Karthik
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