stamps

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Viper83: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon Aug 16, 2010 4:42 am

by Viper83 » Mon Jun 13, 2011 10:05 am

the number of stamps that kaye and alberto had were in the ratio 5:3. after kaye gave alberto 10 stamps the ratio that kaye had to the number 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

C

Last edited by Viper83 on Mon Jun 13, 2011 11:00 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Mon Jun 13, 2011 10:05 am

Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Mon Jun 13, 2011 10:28 am

I think there must be some typo in the question. It says "After Kaye gave Alberto 10 stamps..." and then the question asks "How many stamps did Kaye give to Alberto?" Can you verify the question / setup?

Thanks!

Ashley Newman-Owens
GMAT Instructor
Veritas Prep

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 13, 2011 10:40 am

Viper83 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) 60
E) 90

C

I've amended the question to reflect its actual wording.

Here is a way to solve the problem very quickly without having to set up any algebraic equations.

Since the original ratio is 5:3, and 5+3 = 8, Kaye starts with 5/8 of the stamps.
Since the final ratio is 7:5, and 7+5 = 12, Kaye finishes with 7/12 of the stamps.
Since all the answer choices are multiples of 10, and Kaye starts with 5/8 of the stamps and finishes with 7/12 of the stamps, the total number of stamps must be a multiple of 8, 10 and 12.

The LCM (lowest common multiple) of 8, 10 and 12 = 120.

Let stamps = 120.
Start: Kaye has (5/8)*120 = 75, Albert has 120-75 = 45.
Finish: Kaye has (7/12)*120 = 70, Albert has 120-70 = 50.
Number of stamps Kaye gives Alberto = 75-70 = 5.

Since Kaye needs to give Alberto twice as many stamps, the total number of stamps -- in fact, ALL the values above -- must double.

Finish doubled: Kaye has 2*70 = 140 stamps, Albert has 2*50 = 100 stamps.
Difference between Kaye and Alberto = 140-100 = 40.

The correct answer is C.

Here are all the values when doubled:
Let stamps = 240.
Start: Kaye has (5/8)*240 = 150, Albert has 240-150 = 90.
Finish: Kaye has (7/12)*240 = 140, Albert has 240-140 = 100.
Number of stamps Kaye gives Alberto = 150-140 = 10.
Success!
Difference between Kaye and Alberto at the finish = 140-100 = 40.

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Mon Jun 13, 2011 10:48 am

Hi,
Let the number of stamps with Kaye and Alberto be 5x and 3x
After Kaye gave 10 stamps to Alberto, they will be having (5x-10) and (3x+10). Given that this ratio is 7:5
So, (5x-10)/(3x+10) = 7/5 =>25x-50 = 21x+70 => x=30.
Difference = (5x-10)-(3x+10)= 2x-20 = 2(30)-20 = 40
Hence, C

Cheers!

Things are not what they appear to be... nor are they otherwise

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Viper83: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon Aug 16, 2010 4:42 am

by Viper83 » Mon Jun 13, 2011 11:15 am

Sorry about the typo...it is fixed now.

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