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D
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If the combined number of men and women who attended a certain conference was 65, what was the ratio of men to women at the conference?
(1) There were 35 more men than women at the conference
(2) If the number of women attending the conference increased by 5 but the number of men remained the same, then the ratio of men to women would be 5/2.
(1) There were 35 more men than women at the conference
(2) If the number of women attending the conference increased by 5 but the number of men remained the same, then the ratio of men to women would be 5/2.
03 Feb 2020, 05:27
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You might be able to tell the answer is D because we have one linear equation from the stem (m + w = 65) and each statement will give us a second linear equation clearly different from that one.
If you wanted to solve without much algebra, using Statement 1, if we remove the excess 35 men from the group, we'll have 30 people left, and the number of men and women will be equal. So we must have 15 women and adding back the 35 men, we must have 50 men. So we can find the numbers of men and women and answer the question.
Using Statement 2, if we add 5 women to the group, we'll have 70 people, and if the ratio of men to women is now 5 to 2, then 5/7 of those people will be men, so we have 50 men and 20 women in this new group, and removing the 5 additional women, 50 men and 15 women in the original group. So again we know all our numbers and can answer the question.
If you wanted to solve without much algebra, using Statement 1, if we remove the excess 35 men from the group, we'll have 30 people left, and the number of men and women will be equal. So we must have 15 women and adding back the 35 men, we must have 50 men. So we can find the numbers of men and women and answer the question.
Using Statement 2, if we add 5 women to the group, we'll have 70 people, and if the ratio of men to women is now 5 to 2, then 5/7 of those people will be men, so we have 50 men and 20 women in this new group, and removing the 5 additional women, 50 men and 15 women in the original group. So again we know all our numbers and can answer the question.
03 Feb 2020, 06:03
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cnsih1532
If the combined number of men and women who attended a certain conference was 65, what was the ratio of men to women at the conference?
(1) There were 35 more men than women at the conference
(2) If the number of women attending the conference increased by 5 but the number of men remained the same, then the ratio of men to women would be 5/2.
(1) There were 35 more men than women at the conference
(2) If the number of women attending the conference increased by 5 but the number of men remained the same, then the ratio of men to women would be 5/2.
Solution:
- • Let M and W be the total number men and women in the conference, respectively.
- o \(M + W = 65\)…(i)
Statement 1:
- • \(M -W = 35\)
- • \(2M = 100\)
- o \(M = 50\)
• \(\frac{M}{W} = \frac{50}{15} = \frac{10}{3}\)
Statement 2:
- • \(\frac{M}{(W+5)} = 5/2\)
- o \(M = 5*\frac{(W + 5)}{2}\)
- • \(5W+25 +2W = 130\)
- o \(7W = 105\)
o \(W = 15\)
• \(\frac{M}{W} = \frac{50}{15} = \frac{10}{3}\)
Note:-
There is no need to solve and find the exact answer. This has been done just to show you how to get the answer. Ideally, the moment you see that there are two unique equations and two variables, you should be able to infer that you can find the value of M and N or ratio of M and N.
