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In Smithtown, the ratio of right-handed people to left-handed people i

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In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 09 Jun 2015, 02:06
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In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%

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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 10 Jun 2015, 00:37
2
3
Let's say total people = 20
Right handed people = \(\frac{3}{4}*20=15\)
Left handed people = \(\frac{1}{4}*20=5\)
Men = \(\frac{3}{5}*20=12\)
Women = \(\frac{2}{5}*20=8\)

Maximizing Right handed men means that all the men are right handed -> 3 left handed women so the left handed women is \(\frac{5}{20} = \frac{1}{4}\)

or algebraically:
Let's say total people = X
Right handed people = \(\frac{3}{4}X\)
Left handed people = \(\frac{1}{4}X\)
Men = \(\frac{3}{5}X\)
Women = \(\frac{2}{5}X\)
\(\frac{3}{5}<\frac{3}{4}\) so all men must be right handed. Therefore all left handed people must be women -> Left handed people (women) = \(\frac{1}{4}X\)
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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 09 Jun 2015, 02:14
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Bunuel wrote:
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%


looking at the ratio we can take total number of people=20..
***rh lh
m 12 3 15
w 0 5 5
**12 8 20

ans 5/20 or 25% C
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In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 13 Jun 2015, 07:31
2
RH: LH is 3:1, (Given). let's consider 30:10 (easier numbers for calculations as compared to 1 and 3)
Thus, total no. of people is 40
Men:Women is 3:2,(Given)
No. of men=3/5 of 40, i.e 24, thus No. of women is 16.

Let's put into a matrix
Refer attached Matrix 1

To maximize, RH Men, let us assume all the 24 Men are RH. Thus refilling the matrix,
Refer attached Matrix 2.

Now, we can get any ratio/percentage from here.
from the question, % LH women is (10/40)*100 , i.e 25%, option C!!

scribbling such a matrix does not consume much time.






Cheers!
Aniket
Attachments

File comment: Matrix 1
matrix 1.png
matrix 1.png [ 2.21 KiB | Viewed 4167 times ]

File comment: Matrix 2
matrix 2.png
matrix 2.png [ 2.67 KiB | Viewed 4169 times ]

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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 13 Jun 2015, 09:04
2
1
Bunuel wrote:
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%


Let the Total number of people =100
Then, No of Men=60 and No. of women=40
Also, number of right handers=75 and number of left handers=25

Now, in order to maximize the no of right handed men, all men need to be right handed i.e =60
Therefore, no of right handed women=75-60=15
Number of left handed women=40-15=25
Answer=25/100=25% C
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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 15 Jun 2015, 02:08
2
Bunuel wrote:
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%


MANHATTAN GMAT OFFICIAL SOLUTION:

We can create a double-set matrix to solve this problem:
Attachment:
2015-06-15_1405.png
2015-06-15_1405.png [ 24.83 KiB | Viewed 4091 times ]

There is an unstated constraint that we can only have an integer number of people, since it is impossible to have a partial person. Thus, both x and y are integers. Moreover, the total number of people must be both a multiple of 4 and of 5 in order for the given ratios to be possible. From this constraint, there are two ways to solve.

Algebraic Solution
Since the question specifies that the number of right-handed men be as large as possible, we can assume that all the men are right-handed, and of course that means that none of the men are lefthanded.

Because each column in a double set matrix must total, we can also fill in the number of lefthanded women (the group we are interested in):
Attachment:
2015-06-15_1405_001.png
2015-06-15_1405_001.png [ 19.48 KiB | Viewed 4089 times ]

Thus, left-handed women represent y/(4y) = 25% of the total population.

Smart Number Solution
Since the total number of people in Smithtown must be a multiple of 20, let's set our total to 20 and determine the subtotals of men, women, left- and right-handed based on the ratios given in the problem:
Attachment:
2015-06-15_1406.png
2015-06-15_1406.png [ 24.73 KiB | Viewed 4091 times ]


To maximize the number of right-handed men, we assign all the men to the “right-handed men” cell and fill in the remaining cells:
Attachment:
2015-06-15_1406_001.png
2015-06-15_1406_001.png [ 25.13 KiB | Viewed 4093 times ]

Therefore, left-handed women represent 5/20 = 1/4 = 25% of the population.

The correct answer is C.
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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 27 Jun 2015, 10:20
1
Bunuel wrote:
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%


because this is percentage question. lets take 100 as a total
the ratio of Right-Handed people to Left-hanged people(3:1) can be written as 75:25. making the total 100
same way ratio of Men to Women(3:2) can be written as 60:40. again making the total 100
fill all this information in double-matrix table
Now because we want to maximize the number of right-handed men. fill 0 for left-handed men.
because 0+25=25. 25% of women are left-handed
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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 19 Sep 2016, 06:21
I used the double matrix approach...
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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 07 Nov 2016, 12:29
This was a fun problem!

I looked at the ratios given and set up a population of 20 (because it would allow for nice clean numbers when dealing with the ratios)

20 people --> 3/5 are men (M) & 2/5 are women (W) --> 12M & 8 W

Further --> 3/4 indiv R.H. & 1/4 indiv L.H. --> 15 R.H. & 5 L.H.

If we're maximizing the number of men who are right handed, that means that all men are right handed, leaving us with 3 R.H. and 5 L.H. to give out to women. Thus, 5/20 will be left handed women.
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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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New post 07 Nov 2016, 12:46
Bunuel wrote:
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent of all the people in Smithtown are left-handed women?

(A) 50%
(B) 40%
(C) 25%
(D) 20%
(E) 10%


3 + 1 = 4 and 3 +2 = 5 , LCM of 4 & 5 = 20

So, Let the no of people in the town be 20

Rh = 15 ; Lh = 5

M = 12 ; W = 8

Maximizing Rh Men = 12 Right handed men and 3 right handed women 5 left handed women...

So, Percentage of left handed women = 5/20*100 => 25%

Hence, answer will be (C) 25%

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Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

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