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 Post subject: GMAT Percentage
PostPosted: Fri Jun 18, 2010 10:22 pm 
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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?


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 Post subject: Re: GMAT Percentage
PostPosted: Fri Jun 18, 2010 10:46 pm 
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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):


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 Post subject: Re: GMAT Percentage
PostPosted: Tue Jun 14, 2011 3:52 am 
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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.


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 Post subject: Re: MAT Percentage
PostPosted: Tue Jun 14, 2011 4:17 am 
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 Post subject: Re: GMAT Percentage
PostPosted: Fri Dec 07, 2012 6:30 am 
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More than one of the three products, means 2 products and also includes 3 products.
Thus the answer is: 10 + 5 = 15%


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