The number of stamps that Kaye and Alberto had

Question

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

Kindly help i got D as the answer, which is wrong......

Brent@GMATPrepNow · Answer

kaudes11114 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

Brent Hanneson - Creator of GMATPrepNow.com

Matt@VeritasPrep · Answer

Here's a way that's harder to see but easier to solve.

Let's say that the total number of stamps is t.

Before the gift, Kaye has 5/8 of the stamps, or (5/8)t.

After the gift, Kaye has 7/12 of the stamps, or (7/12)t.

Since Kaye gave away 10 stamps, we know the difference is 10, so (5/8)t - (7/12)t = 10, or (1/24)t = 10.

That tells us that we have 240 stamps. Since the ratio after the gift is 7:5, Kaye has 140, Alberto has 100, and the difference is 40.

GMATGuruNY · Answer

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.

kaudes11114 · Answer

thanks everyone!

i solved the question like this

K:A = 5:3
so K has 5x stamps and A has 3x Stamps

after K gave A 10 of her stamps ratio is 7:5

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

solving this we will get x= 30

So as a result of gift K have 7x-5x=60 more stamps than A

What is wrong with this approach?

Brent@GMATPrepNow · Answer

kaudes11114 wrote:thanks everyone!

i solved the question like this

K:A = 5:3
so K has 5x stamps and A has 3x Stamps

after K gave A 10 of her stamps ratio is 7:5

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

solving this we will get x= 30

So as a result of gift K have 7x-5x=60 more stamps than A

What is wrong with this approach?

You're almost there.
x does, indeed, equal 30
However, 7x and 5x do not represent the number of stamps each has after the transaction.
The expressions (5x-10) and (3x+10) represent these values.

So, after the transaction, Kaye has (5x-10) stamps, and Alberto has (3x+10) stamps.
So, if x = 30, then Kaye has 140 stamps and Alberto has 100 stamps.
This means that Kaye has 40 more stamps that Alberto.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

kaudes11114 · Answer

Brent@GMATPrepNow wrote:kaudes11114 wrote:thanks everyone! i solved the question like this K:A = 5:3 so K has 5x stamps and A has 3x Stamps after K gave A 10 of her stamps ratio is 7:5 so (5x-10)/(3x+10)= 7/5 solving this we will get x= 30 So as a result of gift K have 7x-5x=60 more stamps than A What is wrong with this approach? You're almost there. x does, indeed, equal 30 However, 7x and 5x do not represent the number of stamps each has after the transaction. The expressions (5x-10) and (3x+10) represent these values. So, after the transaction, Kaye has (5x-10) stamps, and Alberto has (3x+10) stamps. So, if x = 30, then Kaye has 140 stamps and Alberto has 100 stamps. This means that Kaye has 40 more stamps that Alberto. Cheers, Brent Oh........ thank you Brent

GaneshMalkar · Answer

I don't know where I am going wrong... Please help me... K/A = 5/3 => 3K - 5A = 0 after exchange => K-10 / A+10 = 7/5 => 5K -7A = 120 Solving I got A = 90 and K = 150 and K - A = 60

Bill@VeritasPrep · Answer

Matt@VeritasPrep wrote:Here's a way that's harder to see but easier to solve.

Let's say that the total number of stamps is t.

Before the gift, Kaye has 5/8 of the stamps, or (5/8)t.

After the gift, Kaye has 7/12 of the stamps, or (7/12)t.

Since Kaye gave away 10 stamps, we know the difference is 10, so (5/8)t - (7/12)t = 10, or (1/24)t = 10.

That tells us that we have 240 stamps. Since the ratio after the gift is 7:5, Kaye has 140, Alberto has 100, and the difference is 40.

I went for a similar idea but different execution. The key for me is that the total number of stamps does not change. There is a transfer of stamps between Kaye and Alberto, but there are no stamps added or removed.

We start with an 8 part ratio and end with a 12 part ratio. If we have the same number of stamps in each ratio, we should be able to manipulate them to have the same number of parts.

Using the LCM of 8 and 12 (24), we can multiply the first ratio by 3 and the second ratio by 2 to give us:

Before gift: K:A = 5:3 = 15:9

After gift: K:A = 7:5 = 14:10

So Kaye gave away 10 stamps and lost 1 part of her ratio (going from 15 to 14)...each part must then be worth 10. The ending ratio has a difference of 4 parts, so Kaye must have 40 more stamps than Alberto.

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Scott@TargetTestPrep · Answer

kaudes11114 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

We are given that the number of stamps that Kaye and Alberto had were 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.

Answer: C

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