Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

## Sets !!

This topic has 1 expert reply and 2 member replies
deadmank2s Just gettin' started!
Joined
10 Apr 2012
Posted:
5 messages
Sets !! Sun Apr 15, 2012 11:11 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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 2 of the above products?

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

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
Shalabh's Quants Really wants to Beat The GMAT!
Joined
06 Apr 2012
Posted:
134 messages
Followed by:
5 members
Thanked:
35 times
Sun Apr 15, 2012 11:28 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 2 of the above products?

a) 5%
b) 10%
c) 15%
d) 25%
e) 30%
You can draw a Venn diagram. 3 Intersecting circles!

Say Milk alone buyers = a;
Chicken alone buyers = b;
Apple alone buyers = c;

Milk & Chicken buyers = x;
Milk & Apple buyers = y;
Apple & Chicken buyers = z;

All 3 buyers = 10%; Given.

As total no. of buyers are 100% then, we can write...

100 = a+b+c+x+y+z+10; => (a+b+c)+(x+y+z) = 90 ..........(1)

Again, we can write...

a+x+y+10 = 60 => a+x+y = 50..........(2)
b+x+z+10 = 50 => b+x+z = 40..........(3)
c+z+y+10 = 35 => c+z+y = 25..........(4)

Adding eqn. 2,3, & 4 we get...(a+b+c)+2.(x+y+z) = 115 ..........(5)

By subtracting Eqn. 5 from Eqn 1, we get...

x+y+z = 25. Ans D.

_________________
Shalabh Jain,
e-GMAT Instructor

Thanked by: bobdylan
shubham_k Just gettin' started!
Joined
08 Apr 2012
Posted:
27 messages
Thanked:
20 times
Sun Apr 15, 2012 11:38 am
Basically, if someone is in two groups they're counted twice, so we need to subtract them once; if someone is counted in three groups they're counted three times, so we need to subtract them twice.

So:

Total = total group a + total group b + total group c - (ab + ac + bc) - 2(abc)

100 = 60 + 50 + 35 - (doubles) - 2(triples)

100 = 145 - 2(10) - doubles
doubles = 145 - 20 - 100
doubles= 145 - 120 = 25

Note that if there were also some people in none of the 3 groups, the formula would have been:

Total = total group a + total group b + total group c - (ab + ac + bc) - 2(abc) + total in none of a/b/c

but in this question we know that every shopper buys at least one product.

### GMAT/MBA Expert

Anurag@Gurome GMAT Instructor
Joined
02 Apr 2010
Posted:
3835 messages
Followed by:
465 members
Thanked:
1754 times
GMAT Score:
770
Sun Apr 15, 2012 9:12 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 2 of the above products?

a) 5%
b) 10%
c) 15%
d) 25%
e) 30%
100% = Customers who buy milk + Customers who buy chicken + Customers who buy apples - Customer who buy exactly 2 products - 2 * Customers who by exactly 3 products + Customers who buy neither of the products
100 = 60 + 50 + 35 - x - (2 * 10) + 0
x = 25

The correct answer is D.

_________________
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

GMAT with Gurome
Career Advising with Gurome

### Best Conversation Starters

1 vipulgoyal 32 topics
2 hemant_rajput 23 topics
3 guerrero 18 topics
4 abhirup1711 17 topics
5 sana.noor 16 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

211 posts
2 GMATGuruNY

The Princeton Review Teacher

137 posts
3 Jim@StratusPrep

Stratus Prep

60 posts