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

Question

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

Bunuel · Accepted Answer

{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.

cyberjadugar · Answer

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 [ 18.86 KiB | Viewed 44299 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)

Regards,

exc4libur · Answer

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)

gvij2017 · Answer

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.

exc4libur · Answer

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

gvij2017 · Answer

Thanks!

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

exc4libur · Answer

x is 5 times greater than y: x=5y=y+4y
x is 4 times more than y: x=y+4y

GMATinsight · Answer

Answer: Option D

Step-by-Step Video solution by  GMATinsight

https://www.youtube.com/watch?v=FHj1cc0C4nQ

stoned · Answer

Hi  Bunuel 
is there any difference between the two highlighted parts below?
I thought 4 times greater = 5 times.

jim441 · Answer

I believe 4 times greater means; y = x+4x
I thing wording of the question is somewhat misleading.

Please help @bunnel  chetan2u

Bunuel · Answer

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:

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.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=85616 --- Harsha GMAT-Club-Forum-ttjz1rpz.png

JulietackleGMAT · Answer

I also have trouble in equaling   with  .
X=Y+4Y(the greater part )

Wadree · Answer

Let..... In town X..... 10 people are lefty......10 are tall..... 5 are both.....and some are neither we dont know......
...*****.....means both which is 5.......and ????? Means neither we dont know.....

......................|————lefty(10)—————|
------------***(5)***-------------?????????? 
|_______tall(10)______|

So......in town X are 15 people + those who are neither.....

So....in town Y......30 are lefty.....30 are tall......and 15 are both ......no one neither........****** Means both which is 15.......

......................|————lefty(30)—————|
------------**(15)***------------- total 45 people in town Y
|_______tall(30)______|

So 4 times as many ppl in town X as in town Y.....and so people in town X = 4×45 = 180
So ppl who are neither in town X are....... 180 - 15 = 165

Now..... in town X..... Total people = 180 ...... when neither = 165 .....
Total people = 12 ...... when neither = 11 .....
We cant go simplify further cuz men cant be fraction and 11 is a prime.......
So number of ppl who can be neither is a MULTIPLE OF 11.......and da only option dat checks out is ..... 143 ........

Wadree · Answer

Yes.... this indeed is a vital flaw of the question.....while it wants to mean X = 4Y ...... it says X = 5Y ...... 😭🥀💔

Bunuel · Answer

No, it's not. Please check here: https://gmatclub.com/forum/some-of-the- ... l#p3153815

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

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