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The number or stamps (GMAT Prep 1)

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The number or stamps (GMAT Prep 1)

by alex.gellatly » Sun Jul 15, 2012 12:27 am
The number of stamps that Kaye and Alberto had were in the ration 5:3, respectively. After Kaye Gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

20
30
40
60
90

Thanks
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by Anurag@Gurome » Sun Jul 15, 2012 12:34 am
alex.gellatly wrote:The number of stamps that Kaye and Alberto had were in the ration 5:3, respectively. After Kaye Gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?
Let us assume that now Kaye has 7x stamps and Alberto has 5x stamps.
Hence, Kaye has 2x stamps more than Alberto.

Before the gift, Kaye had (7x + 10) stamps and Alberto had (5x - 10) stamps.
So, (7x + 10)/(5x - 10) = 5/3
--> 3(7x + 10) = 5(5x - 10)
--> (21x + 30) = (25x - 50)
--> 4x = 80
--> 2x = 40

The correct answer is C.
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by GMATGuruNY » Sun Jul 15, 2012 2:46 am
alex.gellatly wrote:The number of stamps that Kaye and Alberto had were in the ration 5:3, respectively. After Kaye Gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

20
30
40
60
90

Thanks
We can plug in the answer choices, which represent K-A after the gift.

Answer choice C: K-A = 40.
The ratio after the gift (7:5) must yield a difference of 40:
K:A = 7:5 = 70:50 = 140:100, implying that K=140 and A=100.
Thus, before the exchange of 10 stamps, K = 140+10 = 150 and A = 100-10 = 90.
150:90 = 5:3.
Success!

The correct answer is C.
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