Prep question

[hnature0704]

Thank you

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 thenumber Kaye had to the number Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

1) 20
2) 30
3) 40
4) 60
5) 90

[selango]

Can you please check the question again?

[hnature0704]

Can you please check the question again?

Sorry, I fixed it. The new ratio should be 7:5, not 7:4. Thank you for pointing it out

[selango]

K/A=5/3

3K=5A or 3K-5A=0--Eqn1

After Kaye gave 10 stamps to Alberto

K-10/A+10=7/5

5K-50=7A+70

5K-7A=120--Eqn2

solving Eqn1 and Eqn2 we get K= 150 A= 90

After Kaye gave 10 stamps to alberto K=140,A=100

Kaye has 40 stamps more than Alberto

Pick C

[GMATGuruNY]

Thank you

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 thenumber Kaye had to the number Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

1) 20
2) 30
3) 40
4) 60
5) 90

Others likely will show you the algebraic way of solving. For anyone who struggles with the algebra, this problem also can be solved quite easily -- even efficiently -- by using the following technique:

Guess and Check

Here's the situation in the problem:

Original ratio: 5/3
Exchange: Kaye loses 10, Albert gets 10
New ratio: 7/5

Let's guess and check! The goal is to determine the one set of values that will satisfy all the conditions in the problem.

Since the answer choices are all multiples of 10, we should try multiples of 10 until we find the combination that works:

Original values: Kaye has 50, Albert has 30
After the exchange: Kaye has 40, Albert has 40
Is the new ratio 7:5? 40/40 = 1/1. Doesn't work.

Let's double everything:

Original values: Kaye has 100, Albert has 60
After the exchange: Kaye has 90, Albert has 70
Is the new ratio 7:5? 90/70 = 9/7. Doesn't work.

Let's triple everything:

Original values: Kaye has 150, Albert has 90
After the exchange: Kaye has 140, Albert has 100
Is the new ratio 7:5? 140/100 = 70/50 = 7/5. Success!

Since after the exchange Kaye has 140-100 = 40 more stamps than Albert, the correct answer is C.

[MAAJ]

Another way to do this:

5x - 10=7
3x + 10 5

Solve for X and you will get X = 30

5x = 5 (30) = 150; thus 150 - 10 = 140
3x = 3 (30) = 90; thus 90 + 10 = 100

The difference between 140-100 = 40

The answer is [spoiler](C)[/spoiler]