It is currently Fri Jan 18, 2019 6:43 am

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 6 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT PercentagePosted: Fri Jun 18, 2010 10:22 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
In a consumer survey, 85 percent of those surveyed liked at least one of three products. 50 percent of those surveyed liked Product 1, 30 percent liked Product 2, and 20 percent liked Product 3. If 5 percent of the people in the survey liked all three of the products, what percent of the survey participants liked more than one of the three products?

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

(B) Overall, 85% of the surveyed people like at least one product, but when we add up the percent of people who like each product individually, we get a sum that is more than 85%: 50% + 30% + 20% = 100%. These two figures differ because the people that like all three products are counted three times in the 100% figure, and the people that like exactly two products are counted twice.

To correct for the triple-counting, we can subtract 2 times the number of people that like all three products, so these people are now counted just once. We can also correct for the double-counting by subtracting the number of people that were double counted, so they are now counted just once. The equation will look like this:
85% = 100% – 2 × (like all three) – (like exactly 2).
85% = 100% – 2 × (5%) – (like exactly 2)
85% = 90% – (like exactly 2)
5% = the number of people that like exactly 2 products.

Since 5% like all three products, and 5% like exactly 2 products, 10% like more than one product. The correct answer is choice (B).
-------------

Why shouldn't the number of people who like all 3 be subtracted 3 times since this would logically make sense?

Top

 Post subject: Re: GMAT PercentagePosted: Fri Jun 18, 2010 10:46 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
If we subtract three times the percentage of people who have been counted three times then we will not count them at all.

A Venn diagram can be very useful in this question:

People who liked at least one of the products:

People who liked all three products:

People who liked only two out of three products:

People who liked at least two products (more than one):

Top

 Post subject: Re: GMAT PercentagePosted: Tue Jun 14, 2011 3:52 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
There is nothing in the question to suggest there are only 3 outcomes. Product a , b anc c. It is possible that 15% did not like any of the 3 products. This would then yield A as the answer.

Top

 Post subject: Re: MAT PercentagePosted: Tue Jun 14, 2011 4:17 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
questioner wrote:
There is nothing in the question to suggest there are only 3 outcomes. Product a , b anc c.
The question does NOT suggest there are only 3 outcomes. It suggests there are 8 possible outcomes:
- did NOT like any
- liked Product 1 only
- liked Product 2 only
- liked Product 3 only
- liked Products 1 and 2 only
- liked Products 1 and 3 only
- liked Products 2 and 3 only
- liked ALL the Products

questioner wrote:
It is possible that 15% did not like any of the 3 products. This would then yield A as the answer.
It is not only possible, but the question IMPLIES that 15% did NOT like any of the products, because 85% liked at least one. (100% - 85% = 15%). So this fact does NOT change the reasoning and the correct answer is B, NOT A.

Probably, you got confused with the figure 100% = 50% + 30% + 20%. Note, that this figure "100%" does NOT refer to all surveyed people, but it refers to 85% (that liked at least one of the product) + some extra counted groups.

Take a look at Venn diagrams above to clearly understand what groups and how many times are counted in 100% = 50% + 30% + 20%. First of all, think what groups these 20%, 30%, 50%, 85% consist of. Think of those groups as of areas. When they overlap, the overlapping parts are counted twice or more times (depending on how many areas overlap).

50% = liked Product 1 only + liked Products 1 and 2 only + liked Products 1 and 3 only + liked all the Products
30% = liked Product 2 only + liked Products 1 and 2 only + liked Products 2 and 3 only + liked all the Products
20% = liked Product 3 only + liked Products 1 and 3 only + liked Products 2 and 3 only + liked all the Products
85% = liked Product 1 only + liked Product 2 only + liked Product 3 only + liked Products 1 and 2 only + liked Products 1 and 3 only + liked Products 2 and 3 only + liked all the Products

Also note, that
LIKED MORE THAN ONE = liked Products 1 and 2 only + liked Products 1 and 3 only + liked Products 3 and 4 only + liked all the Products

When you get a good understanding of how different groups overlap, you will be able to deal with larger groups instead of 8 original small disjoint ones. For example, to solve this problem, you can deal with "liked at least one", "liked two only", "liked all three".

To practice, think what groups and how many times are counted in 80% = 50% + 30% or 70% = 50% + 30%.

Top

 Post subject: Re: GMAT PercentagePosted: Fri Dec 07, 2012 6:30 am

Joined: Thu Dec 13, 2012 1:34 pm
Posts: 3
More than one of the three products, means 2 products and also includes 3 products.
Thus the answer is: 10 + 5 = 15%

Top

 Post subject: Re: GMAT PercentagePosted: Fri Dec 07, 2012 6:37 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Brams wrote:
More than one of the three products, means 2 products and also includes 3 products.
Thus the answer is: 10 + 5 = 15%
More than one of the three products = exactly 2 products + exactly 3 products

More than one of the three products = 5% + 5% = 10%

The percentage of the surveyed, who liked exactly 2 products, is 5%, not 10%.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 6 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 4 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group