what percentage purchase exactly 2 of the products?

Expert replies

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Dec 31, 2008 2:32 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 products, what percentage of Foodmart customers purchase exactly 2 of the above products?

A. 5%
B. 10%
C. 15%
D. 20%
E. 25%

I am looking for multiple ways to solve this.
The question asks for "exactly 2 of the proucts". If someone can generalize this to handle other cases like
"atleast 1", atleast 2 etc.. I would greatly appreciate.

Also a related question. What if the values were not percentages??
How will the approach change? etc.

Thanks in advance.

Source: Beat The GMAT — Problem Solving | Wed Dec 31, 2008 2:32 am

Zipper: Master | Next Rank: 500 Posts; Posts: 119; Joined: Sun Nov 30, 2008 2:47 am; Thanked: 11 times

by Zipper » Wed Dec 31, 2008 3:51 am

There is a formula about these kind of questions.

ALL = A + B + C - (any two) - 2 x (all three)

You can easily generalize from here.

If all values (including rephrasing the question in a fixed number not %) were numbers the formula won't change.

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Dec 31, 2008 7:28 am

For 3 sets use this:

Total(# unique objects) = Grp 1+ Grp2+Grp3+None(Neither) - grp (1 and 2) - grp(2 and 3) - grp(3 and 4) -2 grp(1 and 2 and 3)

None =0 since everybody buys atleast 1 product

100 = 60 + 50 + 35 + 0 - grp (1 and 2) - grp(2 and 3) - grp(3 and 4) - 2(10)

grp (1 and 2) + grp(2 and 3) + grp(3 and 4) = 145 - 100 -20

= 25

If its was not percents u would be plugging in the regular numbers based on wahts given. Its not any different in terms of the formula .

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Dec 31, 2008 10:27 am

Thanks Cramya and Zipper for the excellent explanation.

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