pankajks2010 wrote:In a consumer survey, 85 percent of those surveyed liked at least one of three products. 50% of those asked liked product 1, 30% like product 2, and 20% liked product 3. If 5% of the people in the survey liked all the three of the products, what percentage of the survey participants liked more than one of the three products:
a) 5%
b) 10%
c) 15%
d) 20%
e) 25%
[spoiler]OA: B[/spoiler]
courtsey: 800score.com
Here is the formula for 3 overlapping groups in which sometimes 2 of the 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 group problems is to
subtract the overlap.
When we add together everyone who likes product 1, everyone who likes product 2, and everyone who likes product 3, those who like exactly 2 of the products get counted twice, so they need to subtracted from the total
once.
Those who like all 3 products get counted 3 times, so they need to be subtracted from the total
twice.
In the problem above:
T = 85
G1+G2+G3 = Product 1 + Product 2 + Product 3 = 50+30+20
Those who like exactly 2 of the products = x
Those who like all 3 products = 5
Plugging into the formula, we get:
85 = 50 + 30 + 20 - x - 2*5
x = 5 consumers who like exactly 2 of the products.
Since 5 consumers like exactly 2 of the products and 5 like all 3 products, the number who like at least 2 of the products = 5+5 = 10.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
