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Source: — Problem Solving |

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by [email protected] » Mon Sep 07, 2015 9:14 am
Hi anant03,

Here's a discussion on this question:

https://www.beatthegmat.com/the-number-o ... 74676.html

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by Brent@GMATPrepNow » Mon Sep 07, 2015 9:37 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
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by Matt@VeritasPrep » Tue Sep 08, 2015 2:12 am
An approach I like:

Before the gift, Kaye had 5/8 of the stamps.

After the gift, Kaye had 7/12 of the stamps. So the difference between Kaye and Alberto = (7/12)s - (5/12)s, or (2/12)s, or (1/6)s. Hence we need to solve for s, then the answer will be (1/6)s.

Let's say there are s stamps. We now know that (5/8)s - 10 = (7/12)s.

Solving that equation gives us s = 240. We want (1/6)s, so the answer is 40.

To me this is a little quicker and cleaner than the system of equations proposed above.
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by anant03 » Tue Sep 15, 2015 1:03 am
Brent@GMATPrepNow 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. 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
Hi Brent ,

Whats wrong with my approach.

first K:A = 5:3

so K=5A/3

after giving 10 stamps the ratio would be

K-10:A+10 = 7:5

put the value of K in the above equation

will A = 90 and K =150.

Please advise and correct me if I took in a wrong way.

Thanks
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by Brent@GMATPrepNow » Tue Sep 15, 2015 5:29 am
anant03 wrote:
Brent@GMATPrepNow 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. 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
Hi Brent ,

Whats wrong with my approach.

first K:A = 5:3

so K=5A/3

after giving 10 stamps the ratio would be

K-10:A+10 = 7:5

put the value of K in the above equation

will A = 90 and K =150.

Please advise and correct me if I took in a wrong way.

Thanks
To see what went wrong, you need to show what you actually did when you write put the value of K in the above equation

Cheers,
Brent
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by anant03 » Fri Sep 18, 2015 7:03 am
Hi ,

Let K:A=5:3 .......(|)

by solving this we get K = 5A/3

and after giving 10 stamps the ratio would be

K-10:A+10 = 7:5 .....(||)

if I put the vale of K from equation | to equation || then we get

A=90

and if I put the value of A in in equation | then we get K = 150

please correct me.

Thanks..
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by Brent@GMATPrepNow » Fri Sep 18, 2015 7:30 am
anant03 wrote:Hi ,

Let K:A=5:3 .......(|)

by solving this we get K = 5A/3

and after giving 10 stamps the ratio would be

K-10:A+10 = 7:5 .....(||)

if I put the vale of K from equation | to equation || then we get

A=90

and if I put the value of A in in equation | then we get K = 150

please correct me.

Thanks..
Here's the problem. You have determined how many stamps each person had BEFORE the exchange (K = 150 and A = 90)
The question refers to the number of stamps AFTER the exchange.
Kaye: 150 - 10 = 140
Alberto: 90 + 10 = 100

Their difference = 140 - 100 = 40
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