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In Smithtown, the ratio of righthanded people to lefthanded people i
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09 Jun 2015, 02:06
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Re: In Smithtown, the ratio of righthanded people to lefthanded people i
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10 Jun 2015, 00:37
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 righthanded people to lefthanded people i
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09 Jun 2015, 02:14
Bunuel wrote: In Smithtown, the ratio of righthanded people to lefthanded people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of righthanded men is maximized, then what percent of all the people in Smithtown are lefthanded 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 righthanded people to lefthanded people i
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13 Jun 2015, 07:31
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
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File comment: Matrix 1
matrix 1.png [ 2.21 KiB  Viewed 4167 times ]
File comment: Matrix 2
matrix 2.png [ 2.67 KiB  Viewed 4169 times ]



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Re: In Smithtown, the ratio of righthanded people to lefthanded people i
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13 Jun 2015, 09:04
Bunuel wrote: In Smithtown, the ratio of righthanded people to lefthanded people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of righthanded men is maximized, then what percent of all the people in Smithtown are lefthanded 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=7560=15 Number of left handed women=4015=25 Answer=25/100=25% C



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Re: In Smithtown, the ratio of righthanded people to lefthanded people i
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15 Jun 2015, 02:08
Bunuel wrote: In Smithtown, the ratio of righthanded people to lefthanded people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of righthanded men is maximized, then what percent of all the people in Smithtown are lefthanded women?
(A) 50% (B) 40% (C) 25% (D) 20% (E) 10% MANHATTAN GMAT OFFICIAL SOLUTION:We can create a doubleset matrix to solve this problem: Attachment:
20150615_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 SolutionSince the question specifies that the number of righthanded men be as large as possible, we can assume that all the men are righthanded, 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:
20150615_1405_001.png [ 19.48 KiB  Viewed 4089 times ]
Thus, lefthanded women represent y/(4y) = 25% of the total population. Smart Number SolutionSince 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 righthanded based on the ratios given in the problem: Attachment:
20150615_1406.png [ 24.73 KiB  Viewed 4091 times ]
To maximize the number of righthanded men, we assign all the men to the “righthanded men” cell and fill in the remaining cells: Attachment:
20150615_1406_001.png [ 25.13 KiB  Viewed 4093 times ]
Therefore, lefthanded 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 righthanded people to lefthanded people i
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27 Jun 2015, 10:20
Bunuel wrote: In Smithtown, the ratio of righthanded people to lefthanded people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of righthanded men is maximized, then what percent of all the people in Smithtown are lefthanded 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 RightHanded people to Lefthanged 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 doublematrix table Now because we want to maximize the number of righthanded men. fill 0 for lefthanded men. because 0+25=25. 25% of women are lefthanded
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Re: In Smithtown, the ratio of righthanded people to lefthanded people i
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19 Sep 2016, 06:21
I used the double matrix approach...
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Re: In Smithtown, the ratio of righthanded people to lefthanded people i
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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 righthanded people to lefthanded people i
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07 Nov 2016, 12:46
Bunuel wrote: In Smithtown, the ratio of righthanded people to lefthanded people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of righthanded men is maximized, then what percent of all the people in Smithtown are lefthanded 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 righthanded people to lefthanded people i
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