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23 Apr 2022, 11:25
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Given: 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.
Asked: 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?
Screenshot 2022-04-23 at 11.56.55 PM.png [ 45.53 KiB | Viewed 1378 times ]
50% + 30% + 20% = 100% = Percentage who liked only 1 product + 2* Percentage who liked 2 products + 3* Percentage who liked all 3 products
Percentage who liked exactly 1 product + 2 * Percentage who liked exactly 2 products + 3*5% = 100%
Percentage who liked exactly 1 product + 2 * Percentage who liked exactly 2 products = 85%
85% = Percentage who liked exactly 1 product + Percentage who liked exactly 2 products + Percentage who liked all 3 products (5%)
Percentage who liked exactly 1 product + Percentage who liked exactly 2 products = 85% - 5% = 80%
Percentage who liked exactly 2 products = 85% - 80% = 5%
Percentage who liked exactly 1 product = 80% - 5% = 75%
Percentage who liked more than one of the three products = Percentage who liked exactly 2 products(5%) + Percentage who liked all 3 products (5%) = 5% + 5% = 10%
IMO B
Asked: 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?
Attachment:
Screenshot 2022-04-23 at 11.56.55 PM.png [ 45.53 KiB | Viewed 1378 times ]
50% + 30% + 20% = 100% = Percentage who liked only 1 product + 2* Percentage who liked 2 products + 3* Percentage who liked all 3 products
Percentage who liked exactly 1 product + 2 * Percentage who liked exactly 2 products + 3*5% = 100%
Percentage who liked exactly 1 product + 2 * Percentage who liked exactly 2 products = 85%
85% = Percentage who liked exactly 1 product + Percentage who liked exactly 2 products + Percentage who liked all 3 products (5%)
Percentage who liked exactly 1 product + Percentage who liked exactly 2 products = 85% - 5% = 80%
Percentage who liked exactly 2 products = 85% - 80% = 5%
Percentage who liked exactly 1 product = 80% - 5% = 75%
Percentage who liked more than one of the three products = Percentage who liked exactly 2 products(5%) + Percentage who liked all 3 products (5%) = 5% + 5% = 10%
IMO B
25 Sep 2024, 01:39
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Bunuel
isn't it way simpler to calculate the "at least 2" here?
we know that
A 50
B 30
C 20
ABC 5
at least 2 = AB + AC + BC - 2ABC
let's call AB + AC + BC = x
tot-none = 85 = A + B + C - (AB + AC + BC) - ABC = 50 + 30 + 20 - x + 5
x = 20 = AB + AC + BC
thus at least 2 is 20 - 2*5 = 20-10 = 10
isn't it way simpler to calculate the "at least 2" here?
we know that
A 50
B 30
C 20
ABC 5
at least 2 = AB + AC + BC - 2ABC
let's call AB + AC + BC = x
tot-none = 85 = A + B + C - (AB + AC + BC) - ABC = 50 + 30 + 20 - x + 5
x = 20 = AB + AC + BC
thus at least 2 is 20 - 2*5 = 20-10 = 10
