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GMAT PREP RATIO ??

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GMAT PREP RATIO ??

by dferm » Thu Apr 24, 2008 5:22 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 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

Please Explain.....
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by simplyjat » Thu Apr 24, 2008 9:14 am
Let Kaye have K stamps and Alberto have A stamps
Initially
K/A = 5/3 => 3K = 5A ...1

After the transfer,
(K-10)/(A+10) = 7/5 => 5K - 50 = 7A + 70 ...2

Solve 1 & 2 to get the desired values of A & K
simplyjat
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by AleksandrM » Thu Apr 24, 2008 9:34 am
You will have 150 - 90 = 60.
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by dferm » Thu Apr 24, 2008 10:59 am
What's the answer....


Alexander you are incorrect.
Simplyjat what is the answer...
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by Sunny22uk » Thu Apr 24, 2008 1:08 pm
is the answer 40?
The reason for this answer is that the questions is asking about present and we should subtract 10 from 150 and add 10 to 90
What say?
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by dferm » Thu Apr 24, 2008 2:15 pm
The answer is 40 but WHY????
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by AleksandrM » Thu Apr 24, 2008 5:26 pm
Sorry dferm, I was at work when I solved this problem, and had to finish up my lunch break. Here is the whole story .

5/3 = K/A ------> 5A = 3K [1]

K - 10/A + 10 = 7/5 -------> 7A + 70 = 5K - 50 [2]

Take equation 1 and convert it into:

A = 3K/5

Then, plug it into your first equation:

7(3K/5) + 70 = 5K - 50

21K/5 - 5K = -120

4 1/5K - 5K = -120

-4/5K = -120

K = 150 [this number is the total for K before the trade took place]

Plug this number into the second equation:

7A + 70 = 5(150) - 50

7A = 750 - 120

7A = 630

A = 90 [once again, this is the number for A before the trade took place]

NOW:

150 - 10/90 + 10 = 7/5 IS TRUE

Therefore: 140 - 100 = 40 more stamps.

Hope this helps.
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by luvaduva » Thu Apr 24, 2008 7:12 pm
Another Easy way is the following:

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

**see bottom if this is confusing**

25x - 50 = 21x +70

4x = 120

x = 30

Kaye initially had 5(30) = 150 and Alberto had 3(30) = 90
After the exchange...150-10 = 140 and 90 + 10 = 100, 140-100 = 40



The ratio 5/3 means that Kaye's and Alberto's cards are governed initially by this. So, initially they could have had 10 cards and 6 cards, respectively or 500 and 300 cards, respectively.

The amount of cards that Kaye and Alberto have initially can then be expressed as 5x/3x.
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by AleksandrM » Fri Apr 25, 2008 9:26 am
luvaduva, that is great. I didn't see that right away. This certainly saves two steps and time!!! I will try to apply this method in the future.
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by II » Sat Apr 26, 2008 4:50 pm
what level question would you say this is ? 500-600 or 600-700 ?
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backsolving too

by resilient » Sun Apr 27, 2008 12:46 am
with the unknown multiplier concept in mind, it is easy to backsolve this question also. I am really biased and love to backsolve. BUt simply starting from 10 (no), 20 (no) but 30 does work and force an answer.
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by AleksandrM » Sun Apr 27, 2008 7:54 am
II, in reply to your question, I would say that this is about a 600 to 630 level question. It is not that difficult, but it requires you to take several steps in arriving at the solution. In this case, you have to take at least two steps, and up to four. But, I am certainly no pro in this guessing game.

Also, if you are curious, I asked a similar question about the OG. You can find the thread here:

https://www.beatthegmat.com/difficulty-o ... html#40700
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by Sunny22uk » Sun Apr 27, 2008 7:26 pm
This question is another example of why we should go back to the question and always check our answers.
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Ratio

by 480ocean » Mon Jan 19, 2009 3:20 pm
Resilient posted that this problem is easy to back solve with the unknown multiplier concept. Can someone explain?
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