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by kartikc11 » Sun Jun 22, 2014 11:28 pm
I sense this is easy, but I didn't get it done on time
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Source: — Problem Solving |

by Brent@GMATPrepNow » Mon Jun 23, 2014 12:03 am
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. 6O
E. 9O
One option is to solve the question using TWO VARIABLES.
Let K = # of stamps K had after the exchange
Let A = # of stamps A had after the exchange
This means that K+10 = # of stamps K had before the exchange
This means that A-10 = # of stamps A had before the exchange

Note: Our goal is to find the value of K-A

The number of stamps that K and A (originally) had were in the ratio 5:3
So, (K+10)/(A-10) = 5/3
We want a prettier equation, so let's cross multiply to get 3(K+10) = 5(A-10)
Expand: 3K + 30 = 5A - 50
Rearrange: 3K - 5A = -80

After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5
So, K/A = 7/5
We want a prettier equation, so let's cross multiply to get 5K = 7A
Rearrange to get: 5K - 7A = 0

At this point we have two equations:
5K - 7A = 0
3K - 5A = -80

Our goal is to find the value of K - A.
IMPORTANT: We need not solve for the individual values of K and A. This is great, because something nice happens when we subtract the blue equation from the red equation.
We get: 2K - 2A = 80
Now divide both sides by 2 to get: K - A = 40

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by kartikc11 » Mon Jun 23, 2014 12:18 am
wonderful!!! thank you
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by GMATGuruNY » Mon Jun 23, 2014 1:40 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
Since all of the answer choices are multiples of 10, and Kaye and Albert exchange 10 stamps, the number of stamps for each is almost certainly a MULTIPLE OF 10.

Before the exchange of 10 stamps, K:A = 5:3, implying the following options:
K=50, A=30
K=100, A=60
K=150, A=90
K=200, A=120.

After Kaye give Albert 10 stamps, check which option yields the required 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 of 10 stamps, K-A = 140-100 = 40.

The correct answer is C.
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