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Ratio from GMAT prep

by jkelk » Mon Mar 12, 2012 3:12 am
The no. of stamps that Kaye & Albert had were in the ratio 5:3. After Kaye gave Albert 10 of her stamps, the ratio of the no. of stamps kaye had to the the no. Albert had was 7:5. As a result of this gift, Kaye had how many more stamps than Albert?

A. 20
B. 30
C. 40
D. 60
E. 90
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by killer1387 » Mon Mar 12, 2012 3:21 am
K/A=5/3
(K-10)/(A+10)=7/5

A=90; K=150
AFTER GIFT DIFFERENCE=140-100=40

HENCE C
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by GMATGuruNY » Mon Mar 12, 2012 3:52 am
The no. of stamps that Kaye & Albert had were in the ratio 5:3. After Kaye gave Albert 10 of her stamps, the ratio of the no. of stamps kaye had to the the no. Albert had was 7:5. As a result of this gift, Kaye had how many more stamps than Albert?

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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by Anurag@Gurome » Mon Mar 12, 2012 5:22 am
jkelk wrote:The no. of stamps that Kaye & Albert had were in the ratio 5:3. After Kaye gave Albert 10 of her stamps, the ratio of the no. of stamps kaye had to the the no. Albert had was 7:5. As a result of this gift, Kaye had how many more stamps than Albert?

A. 20
B. 30
C. 40
D. 60
E. 90
Let the number of stamps that Kaye had = 5x
and the number of stamps that Albert had = 3x
When Kaye gave Albert 10 of her stamps, Kaye had 5x - 10 stamps and Albert had 3x + 10 stamps.
Then (5x - 10) : (3x + 10) = 7 : 5
5(5x - 10) = 7(3x + 10)
25x - 50 = 21x + 70
4x = 120
x = 30
Now Kaye had (5 * 30) - 10 = 150 - 10 = 140 stamps
and Albert had (3 * 30) + 10 = 90 + 10 = 100 stamps

Therefore, Kaye had 140 - 100 = 40 more stamps than Albert.

The correct answer is C.
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