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

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

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

MANHATTAN GMAT OFFICIAL SOLUTION:

We can create a double-set matrix to solve this problem:
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):
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:

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:
Therefore, left-handed women represent 5/20 = 1/4 = 25% of the population.

The correct answer is C.

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

I used the double matrix approach...

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.

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%

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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