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among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawbery and apple, what is the LARGEST possible number of ppl who like raspberry but do not like either strawberry or apple?

20 60 80 86 92

is this one considered set theory? can u solve it too? thanks

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

only S = S - SA - SR - SAR
only A = A - SA - AR - SAR
only R = R - SR - AR - SAR

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

to maximize only R = (R - SR - AR - SAR), we need to minimize SR, AR and SAR. so lets make it 0:

200 = S + A + R - (SA + SR + AR) - 2(SAR)
200 = 112 + 88 + R - (60 + 0 + 0) - 2(0)
so R = 60

among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawbery and apple, what is the LARGEST possible number of ppl who like raspberry but do not like either strawberry or apple?

20
60
80
86
92

is this one considered set theory? can u solve it too?
thanks

among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawbery and apple, what is the LARGEST possible number of ppl who like raspberry but do not like either strawberry or apple?

20 60 80 86 92

is this one considered set theory? can u solve it too? thanks

among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawbery and apple, what is the LARGEST possible number of ppl who like raspberry but do not like either strawberry or apple?

20 60 80 86 92

is this one considered set theory? can u solve it too? thanks

the answer is (B) - see my paper

still having a bit of difficulty ... can you show us ?

Among 200 people, 56% like strawberry, 44% like apple, and 40% like raspberry. If 30% of the people like strawbery and apple, what is the greatest possible number of people who like raspberry but do not like either strawberry or apple?

(A) 20
(B) 60
(C) 80
(D) 86
(E) 92

Total = Set1 + Set2 + Set3 + Neither - Both - (All three X 2)

200 = 112 + 88 + 80 + 0 – (60+X) - 0*2

X = 20

This is the additional number of people who like both.

80 – 20 = 60

People who like only strawberry minus the people who like strawberry and something else.

among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawbery and apple, what is the LARGEST possible number of ppl who like raspberry but do not like either strawberry or apple?

20 60 80 86 92

is this one considered set theory? can u solve it too? thanks

This one is 60 ......and would tell us that 0 ppl like all three.

Among 200 people, 56% like strawberry, 44% like apple, and 40% like raspberry. If 30% of the people like strawbery and apple, what is the greatest possible number of people who like raspberry but do not like either strawberry or apple?

(A) 20 (B) 60 (C) 80 (D) 86 (E) 92

Total = Set1 + Set2 + Set3 + Neither - Both - (All three X 2)

200 = 112 + 88 + 80 + 0 – (60+X) - 0*2

X = 20

This is the additional number of people who like both.

80 – 20 = 60

People who like only strawberry minus the people who like strawberry and something else.

The answer is (B)

KS, you are a true contributor to the Quant forum.

In a consumer survey, 85% of those surveyed like at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% like product 3. If 5% of the people in the survey like all 3 of products, what % of the survey participants likes more than one of the three products?

A) 5
B) 10
C) 15
D) 20
E) 25

I understand how you solved this first problem from your attachment. However, I don't understand why you added Both + Neither together. The question clearly asks for the % participants who likes more than one of the three products. Those who are neither means that they don't like any, so how can you include such people to those who like more than one product?

There are 230 students. 80 play football, 42 play soccer and 12 play rugby. 32 play exactly 2 sports and 4 play all three. How many students play none?

a) 94
b) 115
c) 132
d) 136
e) 140

in the problem just before this one, you mentioned that when you have 3 sets in which you also have a number that is included in all the 3 sets, and another number that is included in the 2 sets, you subtract the number that is included in the 3 sets from the number that is included in the 2 sets. how come you didn't do the same with this problem? you considered 32 as it is without subtracting 4 from it in order to end up with 28 as the number for the doubles. would you explain?

There are 230 students. 80 play football, 42 play soccer and 12 play rugby. 32 play exactly 2 sports and 4 play all three. How many students play none?

a) 94 b) 115 c) 132 d) 136 e) 140

in the problem just before this one, you mentioned that when you have 3 sets in which you also have a number that is included in all the 3 sets, and another number that is included in the 2 sets, you subtract the number that is included in the 3 sets from the number that is included in the 2 sets. how come you didn't do the same with this problem? you considered 32 as it is without subtracting 4 from it in order to end up with 28 as the number for the doubles. would you explain?

Tarek, they key on this is the wording of the problem. Note that it says exactly 2 sports. That means that 4 play 3 sports, 32 play only 2 sports, so you don;t subtract 32-4.

There are 230 students. 80 play football, 42 play soccer and 12 play rugby. 32 play exactly 2 sports and 4 play all three. How many students play none?

a) 94 b) 115 c) 132 d) 136 e) 140

in the problem just before this one, you mentioned that when you have 3 sets in which you also have a number that is included in all the 3 sets, and another number that is included in the 2 sets, you subtract the number that is included in the 3 sets from the number that is included in the 2 sets. how come you didn't do the same with this problem? you considered 32 as it is without subtracting 4 from it in order to end up with 28 as the number for the doubles. would you explain?

Tarek, they key on this is the wording of the problem. Note that it says exactly 2 sports. That means that 4 play 3 sports, 32 play only 2 sports, so you don;t subtract 32-4.

Good answer - asdert - It's all in the wording - you should know what you are looking for.

among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawbery and apple, what is the LARGEST possible number of ppl who like raspberry but do not like either strawberry or apple?

20 60 80 86 92

is this one considered set theory? can u solve it too? thanks

You have the same problem solved in my paper - the wording is different the numbers are the same.

In a consumer survey, 85% of those surveyed like at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% like product 3. If 5% of the people in the survey like all 3 of products, what % of the survey participants likes more than one of the three products?

A) 5 B) 10 C) 15 D) 20 E) 25

I understand how you solved this first problem from your attachment. However, I don't understand why you added Both + Neither together. The question clearly asks for the % participants who likes more than one of the three products. Those who are neither means that they don't like any, so how can you include such people to those who like more than one product?

Thanks for the heads up! - This is a misprint, should be "Both + All three"

Re: Set Theory Made Easy [#permalink]
06 May 2012, 14:03

This is a relatively easy question from OG 11 diagnostic test which I got incorrect .

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? (A) 15 (B) 20 (C) 30 (D) 40 (E) 45

As per the set theory attachment at the beginning of the thread

Total = A + B + Neither - Both

200 = 60 + 3x + 80 - x

60 = 2x

therefore x =30.

OG answers this as A = 15 . Can someone kindly correct my understanding.