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05 Dec 2009, 10:27
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
61% (03:08) correct
39%
(03:12)
wrong
based on 431
sessions
History
Date
Time
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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
(A) 23
(B) 39
(C) 72
(D) 143
(E) 199
24 Feb 2012, 15:39
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Bullet
Yes, correct answer is indeed D.
Given:
{X} ={Left} + {Tall} - {Both} + {Neither}
{Y} = 3*{Left} + 3*{Tall} - 3*{Both}
{Left} + {Tall} - {Both} + {Neither} = 4*(3*{Left} + 3*{Tall} - 3*{Both})
{Neither} = 11*({Left} + {Tall} - {Both}), which means that # of people in Town X 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: D.
05 Dec 2009, 10:32
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Let A = Left Handed, B = Tall and C = Both of left handed and Tall, D= neither
Two overlapping sets problem, therefore
Total = G1+ G2 - Both + neither
Town X
total = A+B+C+D
Town Y
= 3A+3B+3C + 0
as Town X 4 times greater.
4(3A+3B+3C) = A+B+C+D
after simplifying D = 11(A+B+C)
as D is the only multiple of 11 so to me it look like an answer.
Comments please
Two overlapping sets problem, therefore
Total = G1+ G2 - Both + neither
Town X
total = A+B+C+D
Town Y
= 3A+3B+3C + 0
as Town X 4 times greater.
4(3A+3B+3C) = A+B+C+D
after simplifying D = 11(A+B+C)
as D is the only multiple of 11 so to me it look like an answer.
Comments please
