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The number of stamps that Kaye and Alberto had were...

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The number of stamps that Kaye and Alberto had were...

by BTGmoderatorLU » Tue Apr 03, 2018 6:28 pm
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90

The OA is C.

I get the solution in the following way,

K = Kaye
A = Alberto

K / A = 5 / 3 - - - - - - - - - (1)
(K - 10) / (A + 10) = 7 / 5 - - - - - (2)

Substitute values from 1 in 2

A = 90
K = 150

As a result of the gift, Alberto has A + 10 = 100 and Kaye has K - 10 = 140 and the difference between them is 40. Option C.

Please, can anyone explain another way to solve this PS question? Thanks!
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by Brent@GMATPrepNow » Tue Apr 03, 2018 6:32 pm
BTGmoderatorLU wrote:The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90
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
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by GMATGuruNY » Tue Apr 03, 2018 7:09 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 Jeff@TargetTestPrep » Fri Apr 06, 2018 7:55 am
BTGmoderatorLU wrote:The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90
We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information, we can create the following equation:

(5x - 10)/(3x + 10) = 7/5

5(5x - 10) = 7(3x + 10)

25x - 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) - 10 = 140 stamps, and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 - 100 = 40 more stamps than Alberto has.

Answer: C

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by swerve » Fri Apr 06, 2018 11:47 am
Another method is to use ratios:

Note that the total number of stamps is the same in both the cases.
On ratio scale, 5:3 gives 8 total stamps while 7:5 gives 12 total stamps. So total stamps must be at least LCM of 8 and 12 i.e. 24.
So in first case, Kaye had 15 stamps while Alberto had 9. After the exchange, Kaye had 14 stamps while Alberto had 10. So Kaye gave 1 stamp to Alberto. But actually, Kaye gave 10 stamps to Alberto. So actual total number of stamps is 240.
So the multiplier of 7:5 is 20 (because 12*20 = 240). Kaye had (7-5)*20 = 40 more stamps than Alberto.

Regards!
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