Problem Solving

Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

a. 5%
b. 10%
c. 15%
d. 25%
e. 30%

OA after sometime

Now, Let the people who buy single portions be a,b,c. People who buy two products= d,e,f
I made a venn diagram, I wanted to upload it but cudn't!!

a+d+e+10 = 60; a+d+e = 50------- (a)
Similarly,
b+d+f = 40------(b)
c+e+f = 25----------(c)

also given: a+b+c+d+e+f+10 = 100 or a+b+c+d+e+f = 90 ----- (d)

Add (a), (b), (c)

gives u: a+b+c+d+e+d+f+e+f = 115;

Now put (d) in this equation: 90 + d+e+f = 115; d+e+f = 25

I hope I am correct!!

IMO: D

GmatKiss wrote:Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

a. 5%
b. 10%
c. 15%
d. 25%
e. 30%

OA after sometime

Here is the formula for 3 overlapping groups in which sometimes 2 groups overlap and sometimes all 3 groups overlap:

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

The big idea with overlapping groups is to subtract the overlaps. When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total twice.

In the problem above:
T = 100.
G1+G2+G3 = milk + cheese + apples = 60+50+35 = 145.
Those buy exactly 2 products = x.
Those who buy all 3 products = 10.

Plugging these values into the formula, we get:

100 = 145 - x - 2*10
x = 25.

The correct answer is D.

D too.

GMATGuruNY wrote:

GmatKiss wrote:Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

a. 5%
b. 10%
c. 15%
d. 25%
e. 30%

OA after sometime

Here is the formula for 3 overlapping groups in which sometimes 2 groups overlap and sometimes all 3 groups overlap:

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

The big idea with overlapping groups is to subtract the overlaps. When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total twice.

In the problem above:
T = 100.
G1+G2+G3 = milk + cheese + apples = 60+50+35 = 145.
Those buy exactly 2 products = x.
Those who buy all 3 products = 10.

Plugging these values into the formula, we get:

100 = 145 - x - 2*10
x = 25.

The correct answer is D.

Hi,

Why is 10 multiplied by 2 in the solution?
Please help

TIA,
GK

GmatKiss wrote:

GMATGuruNY wrote:

GmatKiss wrote:Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

a. 5%
b. 10%
c. 15%
d. 25%
e. 30%

OA after sometime

Here is the formula for 3 overlapping groups in which sometimes 2 groups overlap and sometimes all 3 groups overlap:

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

The big idea with overlapping groups is to subtract the overlaps. When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total twice.

In the problem above:
T = 100.
G1+G2+G3 = milk + cheese + apples = 60+50+35 = 145.
Those buy exactly 2 products = x.
Those who buy all 3 products = 10.

Plugging these values into the formula, we get:

100 = 145 - x - 2*10
x = 25.

The correct answer is D.

Hi,

Why is 10 multiplied by 2 in the solution?
Please help

TIA,
GK

Please revisit the sentence in bolded red above.
The 10 people who buy all 3 products get counted 3 times -- when we count the 60 who buy milk, the 50 who buy cheese, and the 35 who buy apples -- so these 10 people must be subtracted TWICE so that we don't triple-count them.

I solved it following way

Let 100 be the people who bought fruits. 10 people bought all three.
So now we have 50, 40 & 25 people to fit in 90.

50 + 40 + 25 = 115.

115 - 90 = 25 people have to buy two fruits.