BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Overlapping Sets problem. Please help.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 142
Joined: Sat Oct 20, 2012 3:31 am
Location: New Delhi
Thanked: 20 times
Followed by:3 members

Overlapping Sets problem. Please help.

by aman88 » Tue Dec 18, 2012 2:17 am
In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

a) 27.5 %
b) 35.5 %
c) 41.5 %
d) 22%
e) 67%

OA C

Thanks.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Dec 18, 2012 7:16 am
aman88 wrote:In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

a) 27.5 %
b) 35.5 %
c) 41.5 %
d) 22%
e) 67%

OA C

Thanks.
Let the total = 100 and let AB = the people who like BOTH candidates.

Only A + Only B + AB = Total A + Total B - AB.
On the lefthand side, AB is ADDED because it is not included among those who like ONLY A and ONLY B.
On the righthand side, AB is SUBTRACTED because TOTAL A = Only A + AB and TOTAL B = Only B + AB, with the result that AB has been double-counted.

Since Total A = 30 and Total B = 48, we get:
Only A + Only B + AB = 30 + 48 - AB
2(AB) = 78 - (Only A + Only B).

Since the percentage who like only ONE CANDIDATE is equal to TWICE the percentage who like BOTH candidates, we get:
Only A + Only B = 2(AB).

Substituting Only A + Only B = 2(AB) into 2AB = 78 - (Only A + Only B), we get:
2(AB) = 78 - 2(AB)
4(AB) = 78
AB = 19.5.

Thus:
Only A + Only B = 2(AB) = 2(19.5) = 39.

Since Only A + Only B + AB + Neither = 100, we get:
Neither = 100 - 39 - 19.5 = 41.5.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Tue Nov 06, 2012 4:15 am
Thanked: 1 times

by viveksingh222 » Tue Dec 18, 2012 7:21 am
aman88 wrote:In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

a) 27.5 %
b) 35.5 %
c) 41.5 %
d) 22%
e) 67%

OA C

Thanks.

Total = 100

Let x be the percentage who like both.
The percentage of people who like only A =30-x
The percentage of people who like only B = 48-x

According to the statement

"If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates"
2(x) = 30-x + (48 -x)
x = 19.5
Now let people who like neither be y
Total population 100 = 10.5+ 28.5 + 19.5 + y
y = 41.5
Top
Master | Next Rank: 500 Posts
Posts: 142
Joined: Sat Oct 20, 2012 3:31 am
Location: New Delhi
Thanked: 20 times
Followed by:3 members

by aman88 » Tue Dec 18, 2012 9:18 am
I still didn't understand it properly. I am not very familiar with this topic. Can someone please explain this to me briefly?

I studied this formula:
Total = Set A + Set B + Neither - Both
But there is some variation in this formula in this question. How do I know about that?

Thanks.
Top
Master | Next Rank: 500 Posts
Posts: 116
Joined: Sun May 22, 2011 1:11 am
Thanked: 7 times

by shreerajp99 » Wed Dec 19, 2012 11:18 am
Hi,
Can some1 plz explain this using the tabular method?

Thanks,
Shreeraj
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Dec 19, 2012 1:39 pm
aman88 wrote:In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

a) 27.5 %
b) 35.5 %
c) 41.5 %
d) 22%
e) 67%

OA C

Thanks.
An alternate approach is to use a GRID.

Let LA = like A, DA = dislike A, LB = like B, DB = dislike B..
Let the total = 100.
It is given that the total LA = 38 and the total LB = 40.
Here's the grid:

______________LA________DA_________T

LB_________________________________48

DB_________________________________52

T_____________30_______70________100

Let:
x = the percentage who LIKE A but DISLIKE B
y = the percentage who LIKE B but DISLIKE A.
Thus, x + y = the percentage who like EXACTLY ONE candidate.

Since the percentage who like one candidate is TWICE the percentage who like both candidates, we get:
x+y = 2(LA and LB)
LA and LB = (x+y)/2.

Inserting these values into the grid, we get:

______________LA________DA_________T

LB__________(x+y)/2_____ y_________48

DB____________x_______52-x________52

T_____________30_______70_________100


Leftmost column:
(x+y)/2 + x = 30
x+y + 2x = 60
3x + y = 60.

Middle column:
y + 52-x = 70
-x + y = 18.

Subtracting the second equation from the first, we get:
4x = 42
x = 10.5.

According to the CENTER BOX, the percentage who like neither A nor B = 52-x.
Thus:
Neither = 52 - 10.5 = 41.5.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Sat Sep 29, 2012 3:22 am
Location: Pakistan
Thanked: 1 times
Followed by:1 members

by sharoonsaleem » Thu Dec 20, 2012 2:07 am
Thanks vivek, really liked your approach, reminded me of sets from O-levels days.
Top
Master | Next Rank: 500 Posts
Posts: 122
Joined: Tue May 01, 2012 6:05 am
Thanked: 3 times

by ihatemaths » Fri Dec 21, 2012 3:38 am
@Aman i would advice to go through Arun sharma quants and pictorial representation of this chapter in that book.excellent and you can get a picture of whats being asked
Top
Post new topic Post Reply
• Page 1 of 1