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?
A. 5
B. 10
C. 15
D. 20
E. 25
OA is B
What could be the percentage here? Is the OA truly correct?
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Hi Roland2rule,
We're told that 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, 20% liked product 3 and 5% of the people in the survey liked ALL THREE products. We're asked for the percentage of the survey participants who liked MORE than ONE of the three products.
A three-group Overlapping Sets question can be solved in a coupe of ways: with a 3-circle Venn Diagram or with a Formula. Here, we have to also account for those who like NONE of the groups; that would be 100% - 85% = 15% of those surveyed.
Total = (Those who like NONE) + (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)
With the data in the prompt, we can fill in most of the formula:
Total = (None) + (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)
100% = (15%) + (50%) + (30%) +(20%) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(5%)
100% = 115% - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 10%
(Gp 1&2) + (Gp1&3) + (Gp2&3) = 5%
We now know that 5% of those surveyed liked EXACTLY 2 of the products. The question asks for the percentage of people who liked MORE than 1 product, so that includes those who like exactly 2 and those who like ALL 3:
5% + 5% = 10%
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that 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, 20% liked product 3 and 5% of the people in the survey liked ALL THREE products. We're asked for the percentage of the survey participants who liked MORE than ONE of the three products.
A three-group Overlapping Sets question can be solved in a coupe of ways: with a 3-circle Venn Diagram or with a Formula. Here, we have to also account for those who like NONE of the groups; that would be 100% - 85% = 15% of those surveyed.
Total = (Those who like NONE) + (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)
With the data in the prompt, we can fill in most of the formula:
Total = (None) + (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)
100% = (15%) + (50%) + (30%) +(20%) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(5%)
100% = 115% - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 10%
(Gp 1&2) + (Gp1&3) + (Gp2&3) = 5%
We now know that 5% of those surveyed liked EXACTLY 2 of the products. The question asks for the percentage of people who liked MORE than 1 product, so that includes those who like exactly 2 and those who like ALL 3:
5% + 5% = 10%
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
