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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

Foodmart customers regularly buy at least one...

by AAPL » Thu Dec 14, 2017 11:18 am

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 product, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

A. 5%
B. 10%
C. 15%
D. 25%
E. 30%

The OA is D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Quote

Source: Beat The GMAT — Problem Solving | Thu Dec 14, 2017 11:18 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Thu Dec 14, 2017 11:28 am

Hi AAPL,

We're told that 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 and 10% of the customers buy all 3 products. We're asked for the percentage of Foodmart customers that purchase EXACTLY 2 of the products listed above.

This is an example of a 3-group Overlapping Sets question. You can solve it with a drawing or with the following equation:

Total = (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gps. 1 & 2) - (Gps. 1 & 3) - (Gps. 2 & 3) - 2(All 3 groups)

Using the information in the prompt, the equation becomes....

100% = (60%) + (50%) + (35%) - (Gps. 1 & 2) - (Gps. 1 & 3) - (Gps. 2 & 3) - 2(10%)
100% = 125% - (Gps. 1 & 2) - (Gps. 1 & 3) - (Gps. 2 & 3)
(Gps. 1 & 2) + (Gps. 1 & 3) + (Gps. 2 & 3) = 25%

Thus, 25% of the customers buy exactly 2 of the three listed products.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Foodmart customers regularly buy at least one...

by Scott@TargetTestPrep » Thu Apr 02, 2020 10:18 am

AAPL wrote: ↑
Thu Dec 14, 2017 11:18 am
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 product, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

A. 5%
B. 10%
C. 15%
D. 25%
E. 30%

The OA is D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

We can use the formula:

Total = n(M) + n(C) + n(A) - n(exactly two) - 2 * n(all three)

100 = 60 + 50 + 35 - n(exactly two) - 2 * 10

100 = 125 - n(exactly two)

n(exactly two) = 25

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]