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Number of stamps

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by dreamv » Sat Jan 14, 2012 10:59 pm
The number of stamps that Kaye and Alberto had were in the ratio 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 ?

A.20
B.30
C.40
D.60
E.90
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Source: — Problem Solving |

by Anurag@Gurome » Sat Jan 14, 2012 11:09 pm
dreamv wrote:The number of stamps that Kaye and Alberto had were in the ratio 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 Kaye and Alberto now have 7x and 5x stamps respectively. Hence, now Kaye has 2x more stamps than Alberto.

Now, before Kaye gave Alberto 10 stamps, Kaye had (7x + 10) stamps and Alberto had (5x - 10).

So, (7x + 10)/(5x - 10) = 5/3
--> (21x + 30) = (25x - 50)
--> 4x = 80
--> 2x = 40

The correct answer is C.
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by ArunangsuSahu » Sat Jan 14, 2012 11:13 pm
(5x-10):(3x+10)=7/5
x=30
Ka has (140-100)=40 more
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by ronnie1985 » Sun Jan 15, 2012 8:38 pm
K:A = (5x-10):(3x+10) = 7:5.
Solve for x to get x = 30. K = 5x-10 = 140, A = 3x+10 = 100,Diff = 40
(C)
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by GMATGuruNY » Sun Jan 15, 2012 10:11 pm
dreamv wrote:The number of stamps that Kaye and Alberto had were in the ratio 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 ?

A.20
B.30
C.40
D.60
E.90
We can plug in the answer choices, which represent K-A after the gift.

Answer choice C: K-A = 40.
Since after the gift K:A = 7:5 = 70:50 = 140:100, K=140 and A=100.
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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