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 Post subject: GRE Ratio (Select One)
PostPosted: Wed May 02, 2012 5:07 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
A company is creating a recipe for a bean dish. The ratio of white beans to red beans is 6:5 and the ratio of red beans to black beans is 2:1. What is the ratio of white beans to black beans?

A. 12:1
B. 12:2
C. 12:3
D. 12:5
E. 12:9


The correct answer is (D). The "connector" of the two ratios is red beans, so we change each ratio so that each has the same proportion number of red beans in it. Multiply the first ratio by 2 to get 12:10. Then multiply the second ratio by 5 to get 10:5. The two ratios are now 12:10 (white to red) and 10:5 (red to black), and they can now be combined into one 3-way ratio 12:10:5, which is the ratio of white to red to black. Thus, the ratio of white to black beans is 12:5, choice (D).
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What is the criteria to use 2 and 5 ? May I use a different number, for instance 6 and 6?


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 Post subject: Re: t.3, s.4, qt.19: ratio.
PostPosted: Wed May 02, 2012 5:24 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
What is the criteria to use 2 and 5 ? May I use a different number, for instance 6 and 6?
We have two proportions with a common "participant" (red beans):
6 : 5 (white beans : red beans)
2 : 1 (red beans : black beans)
The both proportions are to the lowest terms.

In order to make one proportion out of these two we need to have the same proportion number of red beans in the both proportions. Such number is the common multiple of 2 and 5. It's better to take the LEAST common multiple, so the new proportion will also be to the lowest terms.

The LCM of 2 and 5 is 10. So we multiply the first proportion by 10/5 = 2 to get 12 : 10.
We multiply the second proportion by 10/2 = 5 to get 10 : 5.

Now we can combine the proportions: 12 : 10 : 5.

If we didn't choose the LEAST common multiple, but just a common multiple, e.g. 20, then the combined proportion would not be to the lowest terms: 24 : 20 : 10.

So now you can answer your question
Quote:
…, for instance 6 and 6?
No, because the common "participant" would not have the same proportion number.
36 : 30
12 : 6
So we would not be able to combine them.

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Here is the problem to practice:
Combine the two proportions into one with the lowest terms:
5 : 6 (oranges : bananas)
10 : 7 (bananas : pineapples)


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