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01 Mar 2012, 14:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (01:48) correct
26%
(01:52)
wrong
based on 122
sessions
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The ratio of women to children at a certain party is 2 to 5 and the ratio of children to men is 3 to 4. If there are more than 13 and less then 20 women at the party, what is the number of men at the party?
A. 30
B. 45
C. 60
D. 75
E. 90
A. 30
B. 45
C. 60
D. 75
E. 90
01 Mar 2012, 16:29
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NYC5648
Given: \(\frac{W}{C}=\frac{2}{5}\) and \(\frac{C}{M}=\frac{3}{4}\). Equate C's: \(\frac{W}{C}=\frac{2}{5}=\frac{6}{15}\) and \(\frac{C}{M}=\frac{3}{4}=\frac{15}{20}\) --> \(\frac{W}{\frac{C}{M}}=\frac{6}{\frac{15}{20}}\).
So, from \(\frac{W}{\frac{C}{M}}=\frac{6}{\frac{15}{20}}\) # of women, W, is a multiple of 6 and since it's given that \(13<w<20\) then \(w=18\) (the only multiple of 6 in this range). If \(W=18=3*6\) then \(M=3*20=60\).
Hope it's clear.
General Discussion
01 Mar 2012, 14:27
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When you have two different ratios, but one group appears in both ratios, you have to tranform both ratios in a way that lets you compare the ratios. You do this by finding the common denominator of both ratios, with the group that appears in both ratios in the denominator. So:
First write the ratio of men to childrean with childrean in the denominator->4:3
Now find a common denominator of both ratios, which is 15 in this case. Then you have the ratio of women to childrean as 6:15 and the ratio of men to childrean as 20:15
No combine all to get W:M:C as 6:20:15
If the number of women has to be between 13 and 20, 18 is the only option. So you multiply the combined ratio with 3 and get 60 men as your answer.
First write the ratio of men to childrean with childrean in the denominator->4:3
Now find a common denominator of both ratios, which is 15 in this case. Then you have the ratio of women to childrean as 6:15 and the ratio of men to childrean as 20:15
No combine all to get W:M:C as 6:20:15
If the number of women has to be between 13 and 20, 18 is the only option. So you multiply the combined ratio with 3 and get 60 men as your answer.
