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The number of stamps that Kaye and Alberto had were in ratio [#permalink]

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05 Nov 2006, 16:07

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The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

The number of stamps that Kaye and Alberto had wer in the ration 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?
20
30
40
60
90

I know how to do these, and yet I keep getting the wrong answer on this one...
_________________

Let Kaye have x stamps alberto have x:y = 5:3 and after giving 10 stamps x-10:y+10 = 7:5
Put x =5y/3 in the eq above and solve to get value of y as 90 and then x=5y/3=150.
After giving 10 x=140 and y=100.
Thus kaye has 40 more stamps then alberto

The number of stamps that Kaye and Alberto had wer in the ration 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?
20
30
40
60
90

Can any one post the solution to solve this using random numbers? Since the ratio is 5: 3

And lets say I choose the total stamps to be 15... Then Kaye might have 15/5 = 3 stamps and Alberto might have 15/3 = 5 stamps ...but 3/5 is not 5:3? What am I doing wrong here?Can someone please help

Can any one post the solution to solve this using random numbers? Since the ratio is 5: 3

And lets say I choose the total stamps to be 15... Then Kaye might have 15/5 = 3 stamps and Alberto might have 15/3 = 5 stamps ...but 3/5 is not 5:3? What am I doing wrong here?Can someone please help

im sure u r following Manhattan gmat... they always ask u to pick smart numbers..

15 is not a smart number..U just cant pick it and reduce 10 from it and have a rati of 7 the current ratio is 5:3 and after giving away 10 .. the ratio becomes 7:5 picking numbers satisfying this is condition is tough unless ur very good at multiplication and see numbers very easily. It took me 15 seconds to guess 5:3 shud be 150:90 so its better that u follow the std method;

Can any one post the solution to solve this using random numbers? Since the ratio is 5: 3

And lets say I choose the total stamps to be 15... Then Kaye might have 15/5 = 3 stamps and Alberto might have 15/3 = 5 stamps ...but 3/5 is not 5:3? What am I doing wrong here?Can someone please help

im sure u r following Manhattan gmat... they always ask u to pick smart numbers..

15 is not a smart number..U just cant pick it and reduce 10 from it and have a rati of 7 the current ratio is 5:3 and after giving away 10 .. the ratio becomes 7:5 picking numbers satisfying this is condition is tough unless ur very good at multiplication and see numbers very easily. It took me 15 seconds to guess 5:3 shud be 150:90 so its better that u follow the std method;

5x-10/3x+10 = 7/5 , X = 30

Yes, I was referring to smart numbers ..Looks like its difficult to solve this using smart numbers?

Yes, I was referring to smart numbers ..Looks like its difficult to solve this using smart numbers?

I would strongly suggest that you should stick to the method of solving which is quite straight forward as shown by yezz above. You may not be able to put your finger on the right numbers for a long time so its a gamble. Nevertheless, if you do insist on using numbers to figure out, pick numbers smartly (I don't know what you mean by smart numbers except LCM/HCF is some cases and 100 in percentages.)

Let me explain what I mean by 'picking numbers smartly' I see that the given ratio is 5:3 So actual numbers could be K-10 and A-6. If K gives 10 to A, ratio becomes 0:16. K has less than A but we need K to retain more than A so that the ratio is 7:5. Actual numbers could be K-50 and A-30. If K gives 10 to A, ratio becomes 40:40 i.e. 1:1. The ratio has increased from before. Both have equal numbers. If the common multiplier chosen is less than 10, K will have less than A. If the common multiplier chosen is more than 10, K will retain more than A. So we need to go higher up. Actual numbers could be K-100 and A-60. If K gives 10 to A, ratio becomes 9:7. Still less than 7:5. So we need to go further up Actual numbers could be K-150 and A-90. If K gives 10 to A, ratio becomes 7:5. There is a logic you are following to reach to the answer. Say, if I had jumped to K-200, A-120 directly, the new ratio would be 19:13 which is greater than 7:5 so I would try and find something in between K-100 and K-200. But using this approach, I am hoping that the multiplier will be an easy round number. Though it is true in most cases for GMAT, I would still not use this approach considering that the alternative standard method is quick and clean.
_________________

The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of 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

Given: \(\frac{K}{A}=\frac{5x}{3x}\) (where \(x\) is a positive integer) and \(\frac{5x-10}{3x+10}=\frac{7}{5}\) --> \(x=30\) --> \(K=150\) and \(A=90\).