Sets

[selango]

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

A) 5

B) 10

C) 15

D) 20

E) 25

[outreach]

Is it A?

# of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups)
85=50+30+20-(?)-2(5)

?=5

[selango]

Give one more try buddy

[kvcpk]

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

50-A
30-B
20-C

5 - A+B+C

85 = 50+30+20 -(liked 2) + 5
liked 2 = 20

more than 1 = liked 2 +liked 3
20+5 = 25


pick E

[mj78ind]

Hi Anand What is the OA? I get 10.......

[outreach]

is it 10
5(# in exactly 2 groups)+5(# in all 3 groups)

Is it A?

# of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups)
85=50+30+20-(?)-2(5)

?=5

[selango]

OA 10

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three)+Neither

Let total be 100

100=50+30+20-x-2(5)+15

x=5

More than 1 =5+5=10

[kvcpk]

OA 10

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three)+Neither

Let total be 100

100=50+30+20-x-2(5)+15

x=5

More than 1 =5+5=10

I am missing something here..

Formula I know is
Total-Neither = G1+G2+G3 -(G1 and G2) - (G2 and G3)- (G3 and G1) + (G1 and G2 and G3)

Is this wrong???

[selango]

I am also having the same doubt.

Why the below formula cannot be used here.

P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(BnC)-P(CnA)+P(AnBnC)

This problem already discussed here.

https://www.beatthegmat.com/three-overla ... 40916.html

[mj78ind]

I am also having the same doubt.

Why the below formula cannot be used here.

P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(BnC)-P(CnA)+P(AnBnC)

This problem already discussed here.

https://www.beatthegmat.com/three-overla ... 40916.html

Guys I am not able to pin point the issue here, but in such questions making a Venn diagram and inputting x,y, z , a, b etc. works best and always gives the right answer.

I think I posted the Venn for one of the questions - https://www.beatthegmat.com/sets-maximum ... tml#266765 ......

Cheers

[GMATGuruNY]

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

A) 5

B) 10

C) 15

D) 20

E) 25

Please see the attached Venn diagram.
We have 100 people.
The total of the 3 circles is 85.
If we add Circle X + Circle Y + Circle Z = 50 + 30 + 20 = 100, we've double-counted everything contained in 2 circles and triple-counted everything contained in all 3 circles.
So the number contained in 2 circles has to be subtracted from the total once, the number contained in all 3 circles has to be subtracted from the total twice.
Let B = number in 2 circles.
85 = 50 + 30 + 20 - B - (2*5)
85 = 90 - B
B = 5
So 5 are in 2 circles, 5 are in all 3 circles.
5 + 5 = 10 who liked more than 1 product.
10/100 = 10%.

The correct answer is B.

When you have groups with a double and triple overlap, remember this rule:

The number contained in 2 out of the 3 groups has to be subtracted once from the total.
The number contained in all 3 groups has to be subtracted twice from the total.

Hope this helps!

[mj78ind]

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

A) 5

B) 10

C) 15

D) 20

E) 25

Please see the attached Venn diagram.
We have 100 people.
The total of the 3 circles is 85.
If we add Circle X + Circle Y + Circle Z = 50 + 30 + 20 = 100, we've double-counted everything contained in 2 circles and triple-counted everything contained in all 3 circles.
So the number contained in 2 circles has to be subtracted from the total once, the number contained in all 3 circles has to be subtracted from the total twice.
Let B = number in 2 circles.
85 = 50 + 30 + 20 - B - (2*5)
85 = 90 - B
B = 5
So 5 are in 2 circles, 5 are in all 3 circles.
5 + 5 = 10 who liked more than 1 product.
10/100 = 10%.

The correct answer is B.

When you have groups with a double and triple overlap, remember this rule:

The number contained in 2 out of the 3 groups has to be subtracted once from the total.
The number contained in all 3 groups has to be subtracted twice from the total.

Hope this helps!

Wow spot on ........Mitch

Thanks!

[Stuart@KaplanGMAT]

I am also having the same doubt.

Why the below formula cannot be used here.

P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(BnC)-P(CnA)+P(AnBnC)

This problem already discussed here.

https://www.beatthegmat.com/three-overla ... 40916.html

Hi,

in this version of the formula, P(A), P(B) and P(C) represent the people who are ONLY members of groups A, B and C respectively.

The information we're given in the stem isn't about people ONLY in 1 group, it's about people in AT LEAST one group. In other words:

50% of those asked liked product 1

means that 50% of people are in the product 1 circle of the venn diagram; that circle includes people who only like product 1, but also includes those that like 1&2 but not 3, 1&3 but not 2 and 1&2&3.

[selango]

Got it....Thanks stuart..