another set question

[Gurpinder]

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

I know this problem has been answered. But my question is specific.

I like to use venn diagrams to answer these set problems. However, how would I write the 85% of those surveyed liked at least one of three products: 1, 2, and 3. in the venn diagram? What is that part's significance in the problem?

sorry for the dumb question, but im confused.

[outreach]

Hi Gurpinder

do not feel that u r asking a dumb q. all of us are here to learn from each other and lot of people in BTG patiently answer Q..

coming to ur Q, i do not have a facility to upload whatever i have sketch on my notepad. i refer the following link to clarify my doubt on venn diagrams for 3 sets(check for author "Bunuel")
https://gmatclub.com/forum/formulae-for- ... 69014.html

incase u have some Q, we can discuss


Thanks
Amar

[selango]

Gurpinder,

Pls check this link for the venn diagram.

https://www.beatthegmat.com/difficult-ma ... -t728.html

[Gurpinder]

Thanks Amar and Anand. I get it now. : )

[Tani]

WHen faced with a confusing Venn diagram I resort to the formula:

Total = Number in group 1 + number in group 2 + number in group 3 - number in both 1 and 2 - number in both 1 and 3 - number in both 2 and 3 - 2 times the number in all three + the number not in any group.


In this problem, you would find that (number in both 1 and 2 + number in both 1 and 3 + number in both 2 and 3) would give you the number favoring two products. That would have to be added to the number favoring all three to get the number favoring more than one. (Note: 15% represents the number liking none of the products.) You won't need to break out 1 and 2 versus 2 and t3, etc.