In Smithtown, the ratio of right-handed people to

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

In Smithtown, the ratio of right-handed people to

by M7MBA » Mon Apr 22, 2019 6:22 am

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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

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Source: Beat The GMAT — Problem Solving | Mon Apr 22, 2019 6:22 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Apr 22, 2019 10:00 am

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]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Apr 23, 2019 6:59 pm

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

We can let the total number of people = 60, so we have 45 right-handed people and 15 left-handed people.

We also have 36 men and 24 women.

To maximize the number of right-handed men, we have 36 right-handed men and 9 right-handed women. So we could have the remaining 15 women be left-handed, which is 15/60 = 25% of the people in Smithtown.

Answer: C

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