ratio of stamps

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LevelOne
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Topic: ratio of stamps
PostSat Jul 04, 2009 12:57 pm Reply with quote
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 Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

20
30
40
60
90

Simple enough? I tried to set up a ratio but it didn't work... Sad

5x-10/3x = 7/5
then I solved for x and got x=12.5, which didn't do any good to get to the right answer. Can you shed some light, please?
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ssmiles08
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PostSat Jul 04, 2009 1:12 pm Reply with quote
LevelOne wrote:
5x-10/3x = 7/5
then I solved for x and got x=12.5, which didn't do any good to get to the right answer. Can you shed some light, please?
your equation is wrong.

when Kaye is giving 10 away, Alberto is gaining 10.

so your equation should be (5x-10)/(3x+10) = 7/5

25x - 50 = 21x + 70

4x = 120

x = 30

Kaye had 5x = 150 stamps.
Alberto had 3x = 90 stamps.

150 - 10 = 140
90 + 10 = 100

140 - 100 = 40

IMO C.
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kaulnikhil
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PostSat Jul 04, 2009 1:14 pm Reply with quote
before any stamps were transfered
K/A = 5/3=5x/3x
after the transfer of stamps
K/A =5x-10/3x+10 = 7/5
25x-50=21x+70
4x=120
x=30

therefore K has 5x30-10 = 150-10 =140
A has 3x30 +10 = 100
ans =40
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jba05d
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PostSat Jul 04, 2009 1:20 pm Reply with quote
You must reflect the additional 10 stamps that Alberta received from Kayne in the denominator of your ratio. The correct formula is as follows

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

Solving for x,

25X - 50 = 21x + 70

4x = 12-

x = 30

Therefore, Kayne originally had 150 stamps and now, after giving 10 stamps to Alberta, has 140 stamps. Alberta originally had 90 stamps and now, after receiving 10 stamps from Kayne, has 100 stamps. Therefore, Kayne has 40 more stamps that Alberta. The correct answer is (C).
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ghacker
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PostSat Jul 04, 2009 4:32 pm Reply with quote
This is a simple problem
It can be solved with out using any equations , by using logic only( with the help of the given answers)

Observe the following

the answers are given and they are all integers and multiples of 10

We also know that the total number of stamps is a constant

so it must be divisible by 8 and by 12 or its a multiple of 24

and we know that the difference can only take the following values( as per the given answers) - 40, 50,60,80,110

So the number of stamps must be 240 (ratio : > 5:3 or 150:90 or after the revision 140 : 100)

Hence the difference is 40
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LevelOne
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PostSat Jul 04, 2009 10:39 pm Reply with quote
thanks a lot, all. I totally understand it now.
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Mayur Sand
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PostSun Jul 05, 2009 7:45 pm Reply with quote
i have a doubt in 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 Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

Since question says the ratio tht Alberto had and not the actual ration b/w Kate and Alberto how can you equate

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

i guess question was wrong . Please explain if iam missing something
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aj5105
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PostSun Jul 05, 2009 9:00 pm Reply with quote
(From GMAT Prep test 1)

Below is the right question.

The number of stamps that Kaye and Alberto had were in the ratio of 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?


Mayur Sand wrote:
i have a doubt in 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 Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

Since question says the ratio tht Alberto had and not the actual ration b/w Kate and Alberto how can you equate

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

i guess question was wrong . Please explain if iam missing something
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