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Question on ratios

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by stephkhaira » Mon Aug 26, 2013 6:36 pm
The number of stamps Kyle had and the number of stamps Amy had were in a ratio of 5:3 respectively. After Kyle gave Amy 10 stamps, the ratio changed to 7:5. As a result of the gift, Kyle had how many more stams than Amy?

20
30
40
60
90


[spoiler]ans: 40[/spoiler]
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by Uva@90 » Mon Aug 26, 2013 7:33 pm
stephkhaira wrote:The number of stamps Kyle had and the number of stamps Amy had were in a ratio of 5:3 respectively. After Kyle gave Amy 10 stamps, the ratio changed to 7:5. As a result of the gift, Kyle had how many more stams than Amy?

20
30
40
60
90


[spoiler]ans: 40[/spoiler]
Hi Stephkhaira,
Let K be the number of stamps Kyle had and
A be the number of stamps Amy had.

Let X be the common multiple.

Given that K/A = 5X/3X.

After Kyle gave Amy 10 stamps, the ratio changed to 7:5

from the above statement,

K/A => 5X-10/3X+10 =7/5
Solve for X.
So X = 30..
Hence early Kyle had 5*30 = 150 and
Amy had 3*30 =90.

After Kyle given 10 stamps,
Kyle had 140 and
Amy had 100 Stamps.

So,Kyle had 40 more stamps than Amy.

Regards,
Uva.
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by GMATGuruNY » Mon Aug 26, 2013 7:57 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?

20
30
40
60
900
The answer choices imply that the values in the problem are all MULTIPLES OF 10.

Since K:A = 5:3, the following options are implied:
K=50, A=30
K=100, A=60
K=150, A=90
K=200, A=120.

After K gives away 10 stamps and A receives 10 stamps, the resulting values for K and A must be in a ratio of 7 to 5:
K=40, A=40
K=90, A=70
K=140, A=100.
We can stop here, since 140:100 = 14:10 = 7:5.

Thus, after the exchange, K-A = 140-100 = 40.

The correct answer is C.
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by Uva@90 » Mon Aug 26, 2013 8:24 pm
GMATGuruNY 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?

20
30
40
60
900
The answer choices imply that the values in the problem are all MULTIPLES OF 10.

Since K:A = 5:3, the following options are implied:
K=50, A=30
K=100, A=60
K=150, A=90
K=200, A=120.

After K gives away 10 stamps and A receives 10 stamps, the resulting values for K and A must be in a ratio of 7 to 5:
K=40, A=40
K=90, A=70
K=140, A=100.
We can stop here, since 140:100 = 14:10 = 7:5.

Thus, after the exchange, K-A = 140-100 = 40.

Mitch,
Your method is cool.

Regards,
Uva.
The correct answer is C.
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