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by guerrero » Mon May 13, 2013 11:35 am
According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%

oA D
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by Brent@GMATPrepNow » Mon May 13, 2013 11:46 am
guerrero wrote:According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%

oA D
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

This can be considered a weighted averages question or a type of mixture question. If you're interested, we have a free video on this topic: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

For these questions, we can say: (proportion of group A)(average of group A) + (proportion of group B)(average of group B) = average of both groups combined.

Now plug in the values: (3/5)(70) + (2/5)(x) = 62
Simplify: 210/5 + 2x/5 = 62
Multiply both sides by 5: 210 + 2x = 320
2x = 110
x = 55

Answer = D

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by GMATGuruNY » Mon May 13, 2013 2:44 pm
guerrero wrote:According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%
Let A = 300 people and B = 200 people.
Total happy in A+B = .64(300+200) = 320.
Total happy in A = .7(300) = 210.
Thus, total happy in B = (total happy in A+B) - (total happy in A) = 320 - 210 = 110.
Thus, percentage happy in B = 110/200 * 100 = 55.

The correct answer is D.
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by sairakarim07 » Tue May 14, 2013 12:24 am
guerrero wrote:According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%

oA D

3/2 = 64-x/70-64[weighted average]
x = 55
ANS D
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