In Smithtown, the ratio of right-handed people to left-handed people i

Question

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%

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

bluesquare · Accepted Answer

Let's say total people = 20
Right handed people =  \frac{3}{4}*20=15 
Left handed people =  \frac{1}{4}*20=5 
Men =  \frac{3}{5}*20=12 
Women =  \frac{2}{5}*20=8

Maximizing Right handed men means that all the men are right handed -> 3 left handed women so the left handed women is  \frac{5}{20} = \frac{1}{4}

or algebraically:
Let's say total people = X
Right handed people =  \frac{3}{4}X 
Left handed people =  \frac{1}{4}X 
Men =  \frac{3}{5}X 
Women =  \frac{2}{5}X 
 \frac{3}{5}<\frac{3}{4}  so all men must be right handed. Therefore all left handed people must be women -> Left handed people (women) =  \frac{1}{4}X

aniketmunshi · Answer

RH: LH is 3:1, (Given). let's consider 30:10 (easier numbers for calculations as compared to 1 and 3)
Thus, total no. of people is 40
Men:Women is 3:2,(Given)
No. of men=3/5 of 40, i.e 24, thus No. of women is 16.

Let's put into a matrix
Refer attached Matrix 1

To maximize, RH Men, let us assume all the 24 Men are RH. Thus refilling the matrix,
Refer attached Matrix 2.

Now, we can get any ratio/percentage from here.
from the question, % LH women is (10/40)*100 , i.e 25%, option C!!

scribbling such a matrix does not consume much time.

Cheers!
Aniket

chetan2u · Answer

looking at the ratio we can take total number of people=20..
***rh lh
m 12 3 15
w 0  5  5
**12 8 20

ans 5/20 or 25% C

KS15 · Answer

Let the Total number of people =100
Then, No of Men=60 and No. of women=40
Also, number of right handers=75 and number of left handers=25

Now, in order to maximize the no of right handed men, all men need to be right handed i.e =60
Therefore, no of right handed women=75-60=15
Number of left handed women=40-15=25
Answer=25/100=25% C

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION: We can create a double-set matrix to solve this problem: 2015-06-15_1405.png There is an unstated constraint that we can only have an integer number of people, since it is impossible to have a partial person. Thus, both x and y are integers. Moreover, the total number of people must be both a multiple of 4 and of 5 in order for the given ratios to be possible. From this constraint, there are two ways to solve. Algebraic Solution Since the question specifies that the number of right-handed men be as large as possible, we can assume that all the men are right-handed, and of course that means that none of the men are lefthanded. Because each column in a double set matrix must total, we can also fill in the number of lefthanded women (the group we are interested in): 2015-06-15_1405_001.png Thus, left-handed women represent y/(4y) = 25% of the total population. Smart Number Solution Since the total number of people in Smithtown must be a multiple of 20, let's set our total to 20 and determine the subtotals of men, women, left- and right-handed based on the ratios given in the problem: 2015-06-15_1406.png To maximize the number of right-handed men, we assign all the men to the “right-handed men” cell and fill in the remaining cells: 2015-06-15_1406_001.png Therefore, left-handed women represent 5/20 = 1/4 = 25% of the population. The correct answer is C.

tarunsng · Answer

because this is percentage question. lets take 100 as a total
the ratio of Right-Handed people to Left-hanged people(3:1) can be written as 75:25. making the total 100
same way ratio of Men to Women(3:2) can be written as 60:40. again making the total 100
fill all this information in double-matrix table
Now because we want to maximize the number of right-handed men. fill 0 for left-handed men.
because 0+25=25. 25% of women are left-handed

mvictor · Answer

I used the double matrix approach...

law258 · Answer

This was a fun problem!

I looked at the ratios given and set up a population of 20 (because it would allow for nice clean numbers when dealing with the ratios)

20 people --> 3/5 are men (M) & 2/5 are women (W) --> 12M & 8 W

Further --> 3/4 indiv R.H. & 1/4 indiv L.H. --> 15 R.H. & 5 L.H.

If we're maximizing the number of men who are right handed, that means that all men are right handed, leaving us with 3 R.H. and 5 L.H. to give out to women. Thus, 5/20 will be left handed women.

Abhishek009 · Answer

3 + 1 = 4 and 3 +2 = 5 , LCM of 4 & 5 = 20

So, Let the no of people in the town be 20

Rh = 15 ; Lh = 5

M = 12 ; W = 8

Maximizing Rh Men = 12 Right handed men and 3 right handed women 5 left handed women...

So, Percentage of left handed women = 5/20*100 => 25%
 
Hence, answer will be (C) 25%

ScottTargetTestPrep · Answer

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

Adarsh_24 · Answer

how do you arrive at the conclusion that the right to left ratio should remain same?
I know now that you won't get a clear answer unless that's the case.

but, I spent quite some time to reach that conclusion. Is there something obvious in question stem that I'm missing?

bumpbot · Answer

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In Smithtown, the ratio of right-handed people to left-handed people i

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