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

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boomtangboy
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Some of the people in Town X are left-handed, some are tall [#permalink] 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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D
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Re: Some of the people in Town X are left-handed, some are tall [#permalink] 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] 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 19823 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] New post   21 Oct 2019, 05:21
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 = A + B - both + neither
X = T + L - both + neither
Y = 3T + 3L - 3both
X = 4Y
4(3T + 3L - 3both)=T + L - both + neither
12T+12L-12both=T+L-both+neither
11T+11L-11both=neither
neither=11(T+L-both)

Answer (D)
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Re: Some of the people in Town X are left-handed, some are tall [#permalink] New post   21 Oct 2019, 18:13
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If the total number of people in Town X is four times greater than the total number of people in Town Y.

I have a doubt here.
When we say x is four times greater than y.
then the equation is x = y+4y

But when we says that four times of Y.
Then the equation is x= 4y .

Please tell me my mistake to clear this doubt so that I can avert further mistakes in word problems.
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Some of the people in Town X are left-handed, some are tall [#permalink] New post   22 Oct 2019, 04:41
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gvij2017 wrote:
If the total number of people in Town X is four times greater than the total number of people in Town Y.

I have a doubt here.
When we say x is four times greater than y.
then the equation is x = y+4y

But when we says that four times of Y.
Then the equation is x= 4y .

Please tell me my mistake to clear this doubt so that I can avert further mistakes in word problems.


https://gmatclub.com/forum/0-1-is-how-m ... 80239.html
https://gmatclub.com/forum/at-a-certain ... 85632.html

X is 4 times greater than Y: X=4Y
X is 4 times as many as Y: X=4Y
X is 4 times as much as Y: X=4Y
X is 4 times of Y: X=4Y

Think of it like this, if x=2 and y=1… then:
y is half of x
x is twice as many/much as y
x is two times greater than y
x is two times/twice of y
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Re: Some of the people in Town X are left-handed, some are tall [#permalink] New post   23 Oct 2019, 15:56
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Thanks!

I appreciate your explanation.
So can you tell me how will you word x= y+4y?

exc4libur wrote:
gvij2017 wrote:
If the total number of people in Town X is four times greater than the total number of people in Town Y.

I have a doubt here.
When we say x is four times greater than y.
then the equation is x = y+4y

But when we says that four times of Y.
Then the equation is x= 4y .

Please tell me my mistake to clear this doubt so that I can avert further mistakes in word problems.


https://gmatclub.com/forum/0-1-is-how-m ... 80239.html
https://gmatclub.com/forum/at-a-certain ... 85632.html

X is 4 times greater than Y: X=4Y
X is 4 times as many as Y: X=4Y
X is 4 times as much as Y: X=4Y
X is 4 times of Y: X=4Y

Think of it like this, if x=2 and y=1… then:
y is half of x
x is twice as many/much as y
x is two times greater than y
x is two times/twice of y
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Some of the people in Town X are left-handed, some are tall [#permalink] New post   24 Oct 2019, 04:41
gvij2017 wrote:
Thanks!

I appreciate your explanation.
So can you tell me how will you word x= y+4y?


x is 5 times greater than y: x=5y=y+4y
x is 4 times more than y: x=y+4y
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Re: Some of the people in Town X are left-handed, some are tall [#permalink] New post   10 Mar 2022, 07:56
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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


Answer: Option D

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Re: Some of the people in Town X are left-handed, some are tall [#permalink] New post   13 Jul 2022, 06:55
Hi Bunuel
is there any difference between the two highlighted parts below?
I thought 4 times greater = 5 times.
Bunuel wrote:
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] New post   08 Feb 2023, 02:02
I believe 4 times greater means; y = x+4x
I thing wording of the question is somewhat misleading.

Please help @bunnel chetan2u
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Re: Some of the people in Town X are left-handed, some are tall [#permalink] New post   08 Feb 2023, 03:36
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jim441 wrote:
I believe 4 times greater means; y = x+4x
I thing wording of the question is somewhat misleading.

Please help @bunnel chetan2u


Agree that it's confusing but check below:

Merriam Webster's Dictionary of English Usage:

    The argument in this case is that times more (or times larger, times stronger, times brighter, etc.) is ambiguous, so that "He has five times more money than you" can be misunderstood as meaning "He has six times as much money as you." It is, in fact, possible to misunderstand times more in this way, but it takes a good deal of effort. If you have $100, five times that is $500, which means that "five times more than $100" can mean (the commentators claim) "$500 more than $100," which equals "$600," which equals "six times as much as $100." The commentators regard this as a serious ambiguity, and they advise you to avoid it by always saying "times as much" instead of "times more." Here again, it seems that they are paying homage to mathematics at the expense of language. The fact is that "five times more" and "five times as much" are idiomatic phrases which have - and are understood to have - exactly the same meaning.

    The "ambiguity" of times more is imaginary: in the world of actual speech and writing, the meaning of times more is clear and unequivocal. It is an idiom that has existed in our language for more than four centuries, and there is no real reason to avoid its use.

More on this here.

Also, check the following posts by Ianstewart:

IanStewart wrote:
ethanhunt007 wrote:
Hi, I have an issue with the phrase "greater than"

If I say X is twice of Y, then it should mean --> X = 2Y
If I say X is two times greater than Y, shouldn't it mean --> X = 3Y


There seems to be some confusion about this earlier in this thread. The phrase "X is 2 times greater than Y" simply means that X = 2Y. It's understandable that this might seem confusing, because if instead we say "X is 200% greater than Y" we definitely mean that X = 3Y, but this all boils down to idiomatic usage in English. If you think of smaller numbers, it might be clear this is how the phrase is used in the language (there's a reason you've never heard anyone say "X is 1 times greater than Y" to mean that X is twice as big as Y), and it's also what the dictionary says, as quoted at this link:

https://mathforum.org/library/drmath/view/61774.html


IanStewart wrote:
ethanhunt007 wrote:
Hi, I have an issue with the phrase "greater than"

If I say X is twice of Y, then it should mean --> X = 2Y
If I say X is two times greater than Y, shouldn't it mean --> X = 3Y


There seems to be some confusion about this earlier in this thread. The phrase "X is 2 times greater than Y" simply means that X = 2Y. It's understandable that this might seem confusing, because if instead we say "X is 200% greater than Y" we definitely mean that X = 3Y, but this all boils down to idiomatic usage in English. If you think of smaller numbers, it might be clear this is how the phrase is used in the language (there's a reason you've never heard anyone say "X is 1 times greater than Y" to mean that X is twice as big as Y), and it's also what the dictionary says, as quoted at this link:

https://mathforum.org/library/drmath/view/61774.html


To summarize, I think the actual wording on the GMAT will always use "times as many" (at least in quant section), so you should not worry about it.
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Re: Some of the people in Town X are left-handed, some are tall [#permalink] New post   01 Apr 2024, 02:59
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Re: Some of the people in Town X are left-handed, some are tall [#permalink]
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