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Some of the people in Town X are left-handed, some are tall

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Some of the people in Town X are left-handed, some are tall  [#permalink]

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New post 27 Jan 2012, 03:20
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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

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Re: Some of the people in Town X are left-handed, some are tall  [#permalink]

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New post 27 Jan 2012, 03:37
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boomtangboy wrote:
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


{Total in X}={left-handed in X}+{tall in X}-{both in X}+{neither in X};
{Total in Y}=3*{left-handed in X}+3*{tall in X}-3*{both in X}+0;

As the total number of people in Town X is four times as many as in the total number of people in Town Y (I think it's the intended meaning), then:

{left-handed in X}+{tall in X}-{both in X}+{neither in X}=4(3*{left-handed in X}+3*{tall in X}-3*{both in X}) --> {neither in X}=11({left-handed in X}+{tall in X}-{both in X}) --> hence {neither in X} (the number of people in Town X who are neither left-handed nor tall) must be a multiple of 11. The only answer which is multiple of 11 is 143=13*11.

Answer: D.

Hope it's clear.
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Re: Some of the people in Town X are left-handed, some are tall  [#permalink]

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New post 19 Jul 2012, 06:47
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Hi,

I love drawing venn diagrams, but in this question it won't help much other than providing a visual information about the question.
In the following diagram:
For town X,
a = Number of left handed people
b = Number of tall people
c = Number of both tall & left handed.
d = Neither

For town Y,
3a = Number of left handed people
3b = Number of tall people
3c = Number of both tall & left handed.
Attachment:
venn..jpg
venn..jpg [ 18.86 KiB | Viewed 8987 times ]


Now, (a+b-c)+x = 4(3a+3b-3c)
or x = 11(a+b-c)
thus, we should look for the multiple of 11 in the answer. ( (a+b-c) would be a positive quantity.)

Answer (D)

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Re: Some of the people in Town X are left-handed, some are tall  [#permalink]

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New post 25 Sep 2019, 05:53
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Re: Some of the people in Town X are left-handed, some are tall   [#permalink] 25 Sep 2019, 05:53
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