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On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
07 Sep 2010, 12:59
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On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
Given: \(\frac{w}{c}=\frac{5}{2}\) --> \(w=5x\) and \(c=2x\) for some integer \(x\). Q: \(m=?\)
(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11 --> \(\frac{c}{m}=\frac{5}{11}\) --> \(c=5y\) and \(m=11y\), for some integer \(y\). Not sufficient to calculate \(m\).
(2) the number of women on the sight-seeing tour was less than 30 --> \(w<30\). Not sufficient to calculate \(m\).
(1)+(2) \(w=5x<30\) --> \(x<6\). \(c=2x\) and as \(c=5y\), \(c\) is a multiple of 5 --> \(x=5\) --> \(c=10=5y\) --> \(y=2\) --> \(m=11y=22\). Sufficient.
Answer: C.
OR: \(\frac{\frac{w}{c}}{m}=\frac{\frac{25}{10}}{22}\) --> \(\frac{w}{m}=\frac{25}{22}\) and as \(w<30\), then \(w=25\) because for other values of \(w<30\), \(m\) (and \(c\)) are not integers --> \(m=22\).
Hope it's clear.
Given: \(\frac{w}{c}=\frac{5}{2}\) --> \(w=5x\) and \(c=2x\) for some integer \(x\). Q: \(m=?\)
(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11 --> \(\frac{c}{m}=\frac{5}{11}\) --> \(c=5y\) and \(m=11y\), for some integer \(y\). Not sufficient to calculate \(m\).
(2) the number of women on the sight-seeing tour was less than 30 --> \(w<30\). Not sufficient to calculate \(m\).
(1)+(2) \(w=5x<30\) --> \(x<6\). \(c=2x\) and as \(c=5y\), \(c\) is a multiple of 5 --> \(x=5\) --> \(c=10=5y\) --> \(y=2\) --> \(m=11y=22\). Sufficient.
Answer: C.
OR: \(\frac{\frac{w}{c}}{m}=\frac{\frac{25}{10}}{22}\) --> \(\frac{w}{m}=\frac{25}{22}\) and as \(w<30\), then \(w=25\) because for other values of \(w<30\), \(m\) (and \(c\)) are not integers --> \(m=22\).
Hope it's clear.
09 Aug 2008, 01:31
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clubzzang
C.
w:c = 5:2
1) c:m = 5:11
w:c:m = 25:10:22
But this does not give us exact number of men
2) this itself does not tell anything about number of men.
Toegther, since number of women is less than 30 and since the number of ppl will always be an integer and also that
25:10:22 can not be reduced further => there will be 25 women => there will be 22 men. thus suff
