Problem Solving

In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT

M7MBA wrote:In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT

Good question to use a judiciously chosen assumed number of people. 3 to 1 implies 4 people, 3 to 2 implies 5. The least common denominator of these is 20.

So 20 people. 3 to 1 means 3/4, 1/4 and 3 to 2 means 3/5 and 2/5.

So RHP = 3/4*20 =15 and LHP therefore 5.

Likewise Men =3/5*20 = 12, so Women =8.

To maximize the numbe of right handed men, we should assume that all men, 12, are right handed. This leaves 15-12 = 3 right handed people who must be women.

Since we made all men right handed, the 5 left handed people must also be women.

Therefore, the percent of people who are left handed women is 5/20 = [spoiler]25%, C[/spoiler]