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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 05 Dec 2009, 10:27
18
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A
B
C
D
E

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  75% (hard)

Question Stats:

63% (02:53) correct 37% (03:06) wrong based on 246 sessions

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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 24 Feb 2012, 15:39
4
3
Bullet 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

I calculated OA and it looks like D but i'm not 100% sure


Yes, correct answer is indeed D.

Given:
{X}={Left} + {Tall} - {Both} + {Neither};

{Y} = 3*{Left} + 3*{Tall} - 3*{Both};

Since the total number of people in Town X 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 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.
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Re: Overlapping Sets Problem  [#permalink]

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New post 05 Dec 2009, 10:32
3
2
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
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Re: Overlapping Sets Problem  [#permalink]

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New post 24 Feb 2012, 15:22
1
Bullet wrote:
as Town X 4 times greater.
4(3A+3B+3C) = A+B+C+D
after simplifying D = 11(A+B+C)


12(A+B+C) = A+B+C+D
look at both sides now. you have 12 times A rather than 3 times A.
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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 13 Jul 2012, 02:08
I am not fine with the language with this question.. does four times greater right usage.. or should it be four times..does the same meaning is construed.
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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 01 Mar 2015, 18:55
Hi Bunnel,

I have a quick question. The question says "total number of people in Town X is four times greater than the total number of people in Town Y". Wouldn't this translate to X=5Y instead of X=4Y. Sorry if I am missing something.
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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 16 Apr 2015, 19:51
Bunuel wrote:
Bullet 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

I calculated OA and it looks like D but i'm not 100% sure


Yes, correct answer is indeed D.

Given:
{X}={Left} + {Tall} - {Both} + {Neither};

{Y} = 3*{Left} + 3*{Tall} - 3*{Both};

Since the total number of people in Town X 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 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.



I think the highlighted portion actually means: If X is the total population of Town X and Y is the total population of town Y then
X = 4Y + Y = 5Y
The Question stem states 4 times greater than Y not 4 times as much as Y.

Kindly Let me know if at all i am wrong.
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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 17 Apr 2015, 00:44
1
earnit wrote:
Bunuel wrote:
Bullet 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

I calculated OA and it looks like D but i'm not 100% sure


Yes, correct answer is indeed D.

Given:
{X}={Left} + {Tall} - {Both} + {Neither};

{Y} = 3*{Left} + 3*{Tall} - 3*{Both};

Since the total number of people in Town X 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 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.



I think the highlighted portion actually means: If X is the total population of Town X and Y is the total population of town Y then
X = 4Y + Y = 5Y
The Question stem states 4 times greater than Y not 4 times as much as Y.

Kindly Let me know if at all i am wrong.


This discussion has taken place many times before. Check out this link to understand why it will be the way Bunuel has done it: http://mathforum.org/library/drmath/view/52334.html
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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 17 Apr 2015, 04:42
w+x+y+z=12w+12x+12y

z=11w+11x+11y

z=11(w+x+z)

it should be multiple of 11

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

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Re: Some of the people in Town X are left-handed, some are tall &nbs [#permalink] 03 Dec 2017, 02:54
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