Some of the people in Town V 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 V, three times as many people are tall as are tall in Town V, three times as many people are both as are both in Town V, but no one is neither. If the total number of people in Town V 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 V who are neither left-handed nor tall?
Options:
A) 23 B) 39 C) 72 D) 143 E) 199
Yes, correct answer is indeed D.   {V}={Left} + {Tall} - {Both} + {Neither};   {Y} = 3*{Left} + 3*{Tall} - 3*{Both};   Since the total number of people in Town V is four times greater than the total number of people in Town Y, then:   {Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});   {Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town V who are neither left-handed nor tall must be a multiple of 11.   Only answer choice D, is a multiple of 11: 143=11*13.   Answer: 143.
<result>D</result>
Some of the people in Town V 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 V, three times as many people are tall as are tall in Town V, three times as many people are both as are both in Town V, but no one is neither. If the total number of people in Town V 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 V who are neither left-handed nor tall?