After writing that sets document, here's a problem for you

Question

After writing that sets document, here's a problem for you to try out. :-D 

Some of the people in Town X are left-handed, some are tall, some are both, and some are neither.
In Town Y, three times as many people are left-handed as are left-handed in Town X, three times as many people are tall as are tall in Town X, three times as many people are both as are both in Town X, but no one is neither. 
If the total number of people in Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?

(A) 23
(B) 39
(C) 72
(D) 143
(E) 199

MA · Answer

(D) 143. Explanation later.

prep_gmat · Answer

Is it four times greater or four times as many?.

ywilfred · Answer

Hi, I meant 4 times as many, as in, if Town x = a, then Town y = 4a :-D

MA · Answer

ywilfred, is it x=3y or y = 3x? i think it should be x=3y.

kapslock · Answer

(D) 143.

If L = n(Left handed), T = n(Tall), LT = n(Left handed and Tall) and N = n(nither tall nor left handed), then
 
X = L + T + LT + N
Y = 3L + 3T + 3LT

Also, X = 4Y
or L + T + LT + N = 12 L + 12 T + 12LT
or N = 11(L + T + LT)

Thus N is a multiple of 11, and there's only D that satisfies that.

ywilfred · Answer

Let's put it this way:
If the total number of people in Town X is 4 times greater than the total number of people in Town Y, then if Town X has 40 people, then Town Y has 10 people.

kapslock · Answer

YWilfred, can you now post the OA?

Thanks.

ywilfred · Answer

The answer is 143, just as you worked it out to be. nice job.

After writing that sets document, here's a problem for you

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