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

Redeem

overlapping set

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 227
Joined: Sun Apr 08, 2012 4:53 am
Thanked: 12 times
Followed by:3 members

overlapping set

by guerrero » Thu Jun 06, 2013 1:36 pm
Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
A)20
B)60
c)80
D)86
E)92

How to use 3 set overlapping formula to solve this ?

OAB
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 149
Joined: Wed May 01, 2013 10:37 pm
Thanked: 54 times
Followed by:9 members

by Atekihcan » Thu Jun 06, 2013 9:53 pm
We can use 3 overlapping set formula and solve this but there is a better and less time consuming method to solve this.

(56 + 44 - 30)% = 70% people like either strawberry or apple jam
So, at the most (100 - 70)% = 30% people can be in the category "like raspberry jam but do not like either strawberry or apple jam"

30% 0f 200 = 60

Answer : B
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 149
Joined: Wed May 01, 2013 10:37 pm
Thanked: 54 times
Followed by:9 members

by Atekihcan » Thu Jun 06, 2013 10:06 pm
Using formula of 3 overlapping set...

Total = S + A + R - SA - SR - AR + ASR + N
Where, S = number of people who like strawberry jam, SA = number of people who like both strawberry and apple jam, ASR = number of who like all of them, N = number of people who like none of them and so on.

Now, Total = 200, S = 2*56 = 112, A = 2*44 = 88, R = 2*40 = 80, and SA = 2*30 = 60

We need to find out the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam, i.e. the maximum value of [R - (AR + SR) + ASR] = X (say)

Now, total = S + A + R - SA - SR - AR + ASR + N
So, total = [R - (AR + SR) + ASR] + S + A - SA + N
So, total = X + S + A - SA + N
So, X = total - [S + A - SA + N]
So, X = 200 - [112 + 88 - 60 + N]
So, X = 200 - [140 + N]
So, X = 60 - N

Now, X will be maximum when N is minimum.
Minimum possible value of N is 0.
So, maximum possible value of X is 60

Answer : B
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 » Fri Jun 07, 2013 4:14 am
guerrero wrote:Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
A)20
B)60
c)80
D)86
E)92

How to use 3 set overlapping formula to solve this ?

OAB
To MAXIMIZE the number who like only raspberry, all of the 200 people must like at least one of the 3 flavors.
Let S = strawberry, A = apple, and R = raspberry.

T = S + A + R - (SA + SR + AR) - 2(SAR)

The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in S, everyone in A, and everyone in R:
Those who like exactly 2 flavors (SA+SR+AR) are counted twice, so they need to be subtracted from the total ONCE.
Those who like all 3 flavors (SAR) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.

We are told the following:
S = 56%
A = 44%
R = 40%.
SA = 30%.

Let T = 100%.
Plugging these values into the formula, we get:

100 = 56 + 44 + 40 - (30 + SR + AR) - 2(SAR)
100 = 110 - (SR + AR) - 2(SAR)
SR + AR + 2(SAR) = 10.

Since SR + AR + 2(SAR) represents all of the overlaps that include R, the percentage who like R and at least one other flavor = 10%.
Thus, the maximum percentage who could like ONLY R = (total percentage who like R) - (percentage who like R and at least one other flavor) = 40-10 = 30%.
Since there are 200 people, we get:
Maximum number who could like only R = .3(200) = 60.

The correct answer is B.
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
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Thu May 30, 2013 7:54 pm

by makhija1 » Fri Jun 21, 2013 7:31 pm
Hello,

Could someone please explain the difference between these two overlapping statements and how they both yield the same result?

Total = S + A + R - (SA + SR + AR) - 2(SAR)
and
Total = S + A + R - SA - SR - AR + ASR + N

I am getting confused as to which to use when.

Thanks,
Adi
Top
Post new topic Post Reply
• Page 1 of 1