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The number of stamps

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The number of stamps

by ssuarezo » Wed Jun 16, 2010 5:40 pm
The number of stamps that Kaye and albert had was inthe ratio of 5:3, After Kaye gave albert 10 of her stamps, the ratio of the number of stamps that Kaye had to the number Albert had was 7:5. As a result of the gift, Kaye had how many more stamps than albert?

20
30
40
60
90

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Silvia
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by amising6 » Wed Jun 16, 2010 5:45 pm
let the total number of stamp be X
so kay had 5x stamps
alberto had 3x stamp
after kay gave 10 stamp to alberto
now kay has 5x-10 stamp
alberto has 3x+10 stamp
so we know 5x-10/3x+10=7/5
solving we get x as 30


case 1)kaye had how many more stamps than Alberto before the transaction of stamps took place
i.e kay had 5*30=150
albert had 3*30=90
kay had 60 stamps more


case 2)kaye had how many more stamps than Alberto after the stamp transaction took place
kaye had (5x-10) - (3x+10)=40 stamps more
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by ssuarezo » Wed Jun 16, 2010 7:26 pm
amising6 wrote:let the total number of stamp be X
so kay had 5x stamps
alberto had 3x stamp
after kay gave 10 stamp to alberto
now kay has 5x-10 stamp
alberto has 3x+10 stamp
so we know 5x-10/3x+10=7/5
solving we get x as 30


case 1)kaye had how many more stamps than Alberto before the transaction of stamps took place
i.e kay had 5*30=150
albert had 3*30=90
kay had 60 stamps more


case 2)kaye had how many more stamps than Alberto after the stamp transaction took place
kaye had (5x-10) - (3x+10)=40 stamps more
I dont know why I get complicated when timer is on, looking for shortcuts in the middle of the exam, takes me nowhere.
Thanks again for your time Amising6, I know it's very early in India.
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by amising6 » Wed Jun 16, 2010 7:37 pm
what i beleive that if you know the concept you can do whatever problem given in stipulated time
so our task should be to know d concept and try to do it fast
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by selango » Wed Jun 16, 2010 11:26 pm
K/A=5/3--A

K-10/A+10=7/5 --B

5K-50=7A+70

15K-150=21A+210

From equation A,

3K=5A -->15K=25A

-->25A-150=21A+210-->A=90 &K=150

After Kay gave alberto 10 stamps,A=100,K=140

-->Kay had 40 more stamps than alberto
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by GMATGuruNY » Thu Jun 17, 2010 1:45 am
For anyone who struggles with ratios, this problem 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!

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.
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by ssuarezo » Thu Jun 17, 2010 8:55 am
GMATGuruNY wrote:For anyone who struggles with ratios, this problem 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!

Since the answer choices are all multiples of 10, we should try multiples of 10 until we find the combination that works:
Thanks Guru in NY:
Actually, I first tried your approach. Having 7, 5, 3, I started with multiples of 7*5, then some multiples of 5*3, and I lost time. I missed the point u mention here: Answers are in multiples of 10.
Thanks !
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by GMATGuruNY » Thu Jun 17, 2010 9:29 am
My pleasure.

A word of advice:

ALWAYS look at the answer choices.

Ever hear of the song "Look to the Rainbow"? When taking the GMAT, look to the answers. They often will guide you down the right path.
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by ssuarezo » Fri Jun 18, 2010 9:06 am
GMATGuruNY wrote:My pleasure.

A word of advice:

ALWAYS look at the answer choices.

Ever hear of the song "Look to the Rainbow"? When taking the GMAT, look to the answers. They often will guide you down the right path.
Never heard the song, but I'm going to download it now ...
Thanks for your good advice Guru !!
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by outreach » Fri Jun 18, 2010 10:21 am
kaye=k
albet=a


k/a=5/3 => k=5a/3

(k-10)/(a+10)=7/5
solving and substitute value of k we will get a =90 and k=150

after Kaye gave albert 10 of her stamps
a =100 and k=140

so answer is C
ssuarezo wrote:The number of stamps that Kaye and albert had was inthe ratio of 5:3, After Kaye gave albert 10 of her stamps, the ratio of the number of stamps that Kaye had to the number Albert had was 7:5. As a result of the gift, Kaye had how many more stamps than albert?

20
30
40
60
90

Thnks
Silvia
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