Some of the people in Town X are left-handed, some are tall : Problem Solving (PS)

Bullet

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Joined: 17 Nov 2009

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Schools:University of Toronto, Mcgill, Queens

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

05 Dec 2009, 10:27

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61% (03:08) correct

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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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Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92698

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

24 Feb 2012, 15:39

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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

Show Spoiler

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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Bullet

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Joined: 17 Nov 2009

Posts: 21

Schools:University of Toronto, Mcgill, Queens

Re: Overlapping Sets Problem [#permalink]

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

MBAhereIcome

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Joined: 07 Aug 2011

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Re: Overlapping Sets Problem [#permalink]

24 Feb 2012, 15:22

1

Kudos

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.

pavanpuneet

Manager

Joined: 26 Dec 2011

Posts: 78

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

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.

B

acegmat1526

Intern

Joined: 20 Aug 2014

Posts: 1

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

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.

earnit

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

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

Show Spoiler

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.

L

KarishmaB

Tutor

Joined: 16 Oct 2010

Posts: 14804

Location: Pune, India

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

17 Apr 2015, 00:44

1

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Expert Reply

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

Show Spoiler

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: https://mathforum.org/library/drmath/view/52334.html
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Temurkhon

Senior Manager

Joined: 23 Jan 2013

Posts: 430

Schools: Cambridge'16

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

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

D

JonShukhrat

Senior Manager

Joined: 06 Jun 2019

Posts: 317

Location: Uzbekistan

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

24 Sep 2019, 13:41

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

Hi MartyTargetTestPrep,

Could you, please, shed some light on the interpretation of the above highlighted part of the stem?

Does it mean 4x or 5x on GMAT?

Many thanks in advance.
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MartyTargetTestPrep

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

24 Sep 2019, 19:40

1

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Expert Reply

JonShukhrat 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

Hi MartyTargetTestPrep,

Could you, please, shed some light on the interpretation of the above highlighted part of the stem?

Does it mean 4x or 5x on GMAT?

Many thanks in advance.

Ideally, it would mean 5x, but I'm not sure that every writer would agree with that interpretation.

Fortunately, I am pretty sure that such an unclear way of expressing such a relationship would not be used in an official GMAT quant question, though wording like that has appeared in the correct answer to an official Sentence Correction question.
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JonShukhrat

Senior Manager

Joined: 06 Jun 2019

Posts: 317

Location: Uzbekistan

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

25 Sep 2019, 02:22

MartyTargetTestPrep wrote:

JonShukhrat 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

Hi MartyTargetTestPrep,

Could you, please, shed some light on the interpretation of the above highlighted part of the stem?

Does it mean 4x or 5x on GMAT?

Many thanks in advance.

Ideally, it would mean 5x, but I'm not sure that every writer would agree with that interpretation.

Fortunately, I am pretty sure that such an unclear way of expressing such a relationship would not be used in an official GMAT quant question, though wording like that has appeared in the correct answer to an official Sentence Correction question.

Once again many thanks Marty!
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Re: Some of the people in Town X are left-handed, some are tall [#permalink]

25 Oct 2021, 04:38

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

Show Spoiler

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.

Hi Bunuel , Could you please elaborate on why it would be 4 times the population of X and not 5 times?

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92698

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

25 Oct 2021, 07:52

1

Kudos

Expert Reply

sam12rawat 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

Show Spoiler

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.

Hi Bunuel , Could you please elaborate on why it would be 4 times the population of X and not 5 times?

I think the following posts should clear your doubt:
https://gmatclub.com/forum/tires-r-us-h ... l#p2357023
https://gmatclub.com/forum/every-attend ... l#p2286932
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Re: Some of the people in Town X are left-handed, some are tall [#permalink]

19 Mar 2023, 21:07

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

19 Mar 2023, 21:07

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