GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Aug 2018, 18:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47983
In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

09 Jun 2015, 03:06
3
9
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:04) correct 35% (02:08) wrong based on 290 sessions

### HideShow timer Statistics

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%

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6549
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

09 Jun 2015, 03:14
4
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Current Student
Joined: 29 Mar 2015
Posts: 44
Location: United States
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

10 Jun 2015, 01:37
2
2
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) = $$\frac{1}{4}X$$
Intern
Joined: 28 May 2013
Posts: 26
Schools: Mannheim"17
In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

13 Jun 2015, 08:31
1
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 [ 2.21 KiB | Viewed 3752 times ]

File comment: Matrix 2

matrix 2.png [ 2.67 KiB | Viewed 3753 times ]

Director
Joined: 21 May 2013
Posts: 648
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

13 Jun 2015, 10:04
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
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

15 Jun 2015, 03:08
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%

MANHATTAN GMAT OFFICIAL SOLUTION:

We can create a double-set matrix to solve this problem:
Attachment:

2015-06-15_1405.png [ 24.83 KiB | Viewed 3675 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 [ 19.48 KiB | Viewed 3674 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 [ 24.73 KiB | Viewed 3676 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 [ 25.13 KiB | Viewed 3678 times ]

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

_________________
Intern
Joined: 03 Feb 2015
Posts: 8
Concentration: Entrepreneurship, Finance
GMAT 1: 580 Q44 V26
GRE 1: Q159 V152
GPA: 3.59
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

27 Jun 2015, 11:20
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
Attachments

2015-06-27.png [ 25.7 KiB | Viewed 3552 times ]

Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

19 Sep 2016, 07:21
I used the double matrix approach...
Attachments

gmatc.jpg [ 19.58 KiB | Viewed 2620 times ]

Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 397
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

07 Nov 2016, 13:29
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.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3780
Location: India
GPA: 3.5
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

07 Nov 2016, 13:46
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%

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Non-Human User
Joined: 09 Sep 2013
Posts: 7761
Re: In Smithtown, the ratio of right-handed people to left-handed people i  [#permalink]

### Show Tags

24 Jul 2018, 17:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In Smithtown, the ratio of right-handed people to left-handed people i &nbs [#permalink] 24 Jul 2018, 17:53
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.