BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

percentage

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 89
Joined: Sun Aug 10, 2008 8:35 pm

percentage

by ritula » Sat Sep 20, 2008 4:04 pm
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?

5%
10%
15%
25%
30%
Philosophers have interpreted world in various ways, the point is to change it!
Top
Source: — Problem Solving |
Legendary Member
Posts: 1153
Joined: Wed Jun 20, 2007 6:21 am
Thanked: 146 times
Followed by:2 members

Re: percentage

by parallel_chase » Sat Sep 20, 2008 5:50 pm
ritula 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 above products?

5%
10%
15%
25%
30%

x = customers who bought 2 products

Total = product 1 + product 2 + product 3 - x - 2*(all three)

100 = 60+50+35 -x - 2*10

x = 145 - 20 - 100

x = 25%

Whats the OA?
Top
Senior | Next Rank: 100 Posts
Posts: 87
Joined: Tue Jul 15, 2008 10:23 am
Location: Lima
Thanked: 4 times
Followed by:1 members

by Fab » Sat Sep 20, 2008 6:13 pm
Why?
- 2*(all three)
specially, why are you multiplying by 2....?

Thanks
Top
Legendary Member
Posts: 1153
Joined: Wed Jun 20, 2007 6:21 am
Thanked: 146 times
Followed by:2 members

by parallel_chase » Sat Sep 20, 2008 6:18 pm
Here is the formula for three set overlapping

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
Top
Senior | Next Rank: 100 Posts
Posts: 87
Joined: Tue Jul 15, 2008 10:23 am
Location: Lima
Thanked: 4 times
Followed by:1 members

by Fab » Sat Sep 20, 2008 6:57 pm
Thank you.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 248
Joined: Mon Aug 11, 2008 9:51 am
Thanked: 13 times

by earth@work » Sat Sep 20, 2008 7:09 pm
formula explanation...

use venn diagram in this problem:
Let those who buy milk=m, those who buy chicken=C, who buy apples=A
Total = only M+only C+onlyA + those who buy two+ those who buy all three
let x=those who buy both M&C
y=C&A
z=M&A
only M =(60-x-z-10)
only C = (50-x-y-10)
only A = (35-z-y-10)
Total=(60-x-z-10)+(50-x-y-10)+(35-z-y-10)+(x+y+z)+10
total=60+50+35-who buy two-2*10
proved
Last edited by earth@work on Sun Sep 21, 2008 9:51 am, edited 1 time in total.
Top
Senior | Next Rank: 100 Posts
Posts: 89
Joined: Sun Aug 10, 2008 8:35 pm

Ans

by ritula » Sun Sep 21, 2008 2:54 am
Nice explanation. Made the things so simple. Thanks
yes Ans is 25%
earth@work wrote:formula explanation...

use venn diagram in this problem:
Let those who buy milk=m, those who buy chicken=C, who buy apples=A
Total = only M+only C+onlyA + those who buy two+ those who buy all three
let x=those who buy both M&C
y=C&A
z=M&A
only M =(60-x-z-10)
only C = (50-x-y-10)
only A = (35-z-y-10)
Total=(60-x-z-10)+(50-x-y-10)+(35-z-y-10)-(x+y+z)+10
total=60+50+35-who buy two-2*10
proved
Philosophers have interpreted world in various ways, the point is to change it!
Top
User avatar
Legendary Member
Posts: 871
Joined: Wed Aug 13, 2008 7:48 am
Thanked: 48 times

by stop@800 » Sun Sep 21, 2008 12:35 pm
Just use the formula:

total = A + B + C - 2*(all3) - (only two)

The question: why multiply by 2?

We are actually subtracting overlaps from A + B + C
in A+B+C, the AB + BC + CA has been counted twice so we are subtracting it once
and
ABC has been counted thrice [one with each AB BC CA] so we are subtracting it twice.

Please draw the venn diagram, you will get absolutely clear picture.
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Sat Jan 30, 2010 8:20 am
Thanks! :-)

I never came across this formula before...
i hope this would help me during D-day :)
parallel_chase wrote:Here is the formula for three set overlapping

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
Top
Post new topic Post Reply
• Page 1 of 1