BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Stamps

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Fri Jul 16, 2010 1:27 am

Stamps

by RikaMueller » Sun Nov 28, 2010 2:13 am
The number of stamps that Kayle and Alberto had were in a ratio of 5:3. After Kayle gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number that Alberto had was 7:5. As a result of this gift. Kayle had how many more stamps than Alberto?

20
30
40
60
90

Pls clarify.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 am
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Sun Nov 28, 2010 3:06 am
1) Express the old ratio as a fraction. transition from "ratio of stamps" to real number of stamps, so that you can make the change (+10/-10).

ratio is 5:3, so real numbers are 5x:3x, or 5x/3x expressed as a fraction.

2) Make the change in numerator and denominator:
Kayle gave 10 stamps, so her new quantitiy is 5x-10
Alberto got 10 stamps, so his new quantity is 3x+10

fraction is now 5x-10 / 3x+10

3) the new ratio is 7:5, so the fraction must equal the new ratio: 5x-10/3x+10 = 7/5.
Solve for x:
5(5x-10) = 7(3x+10)
25x-50 = 21x+70
4x = 120
x=30.

4) Don't choose B! what is x? it is the multiplier, needed in the transition from ratio to real number. Originally, Kayle and Alberto had 5x and 3x stamps, or 5*30=150 and 3*30=90 stamps respectively. After the change, they have 140 (10 stamps less) and 100 (10 stamps more) respectively, so as a result of this gift, Kayle has 40 more stamps. Answer is C.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Nov 28, 2010 3:32 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 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
For anyone who struggles with setting up equations, 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

Now 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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 332
Joined: Tue Feb 09, 2010 3:50 pm
Thanked: 41 times
Followed by:7 members
GMAT Score:720

by rishab1988 » Sun Nov 28, 2010 4:16 am
Let the no of stamp Kayle initially has =K
Let the ...Alberto has =A

Then K/A =5/3

or 3K-5A =0 (1)

After Kayle 10 of her stamps,she has = K-10 stamps
Alberto,after receiving those stamps,has = A+10 stamps

(K-10)/(A+10) = 7/5

5K-50 = 7A+70
5K-7A =120 (2)

From 1 and 2

A =90 and K =150 [ i'm not showing that.If you don'e get it,just pm me ]

NOW the QUESTION IS " WHAT IS (K-10)-(A+10)=?"

(140)-(100)=40

Therefore C
Top
Post new topic Post Reply
• Page 1 of 1