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At a recent trade show, a survey was conducted on coffee brands. Each brand was categorized based on whether it increased its wholesale price per pound this year compared to last year. What percentage of the brands surveyed increased their wholesale price this year?
(1) Of the brands that increased their price, 25% increased it by at least $2 per pound.
(2) Of all the brands surveyed, 15% increased their price by at least $2 per pound.
(1) Of the brands that increased their price, 25% increased it by at least $2 per pound.
(2) Of all the brands surveyed, 15% increased their price by at least $2 per pound.
13 Jan 2026, 09:22
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Official Solution:
At a recent trade show, a survey was conducted on coffee brands. Each brand was categorized based on whether it increased its wholesale price per pound this year compared to last year. What percentage of the brands surveyed increased their wholesale price this year?
(1) Of the brands that increased their price, 25% increased it by at least $2 per pound.
Let the number of brands that increased their price be \(x\). Then \(0.25x\) brands increased their prices by at least $2 per pound. This gives a relationship within the group that increased, but it does not provide any information about how many brands increased relative to the total number of brands. Not sufficient.
(2) Of all the brands surveyed, 15% increased their price by at least $2 per pound.
This says that 15% of all brands increased their price by at least $2 per pound. This provides information only about a subset of brands that increased by a certain amount. It does not give any information about brands that increased by less than $2 or about brands that did not increase their price. Not sufficient.
(1)+(2) Say there were 100 brands in total. Then from (2) we'd get that 15 brands increased their price by at least $2 per pound, while from (1) we have that \(0.25x\) brands increased their price by at least $2 per pound. Thus, \(15 = 0.25x\), which gives \(x = 60\). Therefore, 60 brands out of 100, which is 60% of the brands surveyed increased their wholesale price this year. Sufficient.
Answer: C
At a recent trade show, a survey was conducted on coffee brands. Each brand was categorized based on whether it increased its wholesale price per pound this year compared to last year. What percentage of the brands surveyed increased their wholesale price this year?
(1) Of the brands that increased their price, 25% increased it by at least $2 per pound.
Let the number of brands that increased their price be \(x\). Then \(0.25x\) brands increased their prices by at least $2 per pound. This gives a relationship within the group that increased, but it does not provide any information about how many brands increased relative to the total number of brands. Not sufficient.
(2) Of all the brands surveyed, 15% increased their price by at least $2 per pound.
This says that 15% of all brands increased their price by at least $2 per pound. This provides information only about a subset of brands that increased by a certain amount. It does not give any information about brands that increased by less than $2 or about brands that did not increase their price. Not sufficient.
(1)+(2) Say there were 100 brands in total. Then from (2) we'd get that 15 brands increased their price by at least $2 per pound, while from (1) we have that \(0.25x\) brands increased their price by at least $2 per pound. Thus, \(15 = 0.25x\), which gives \(x = 60\). Therefore, 60 brands out of 100, which is 60% of the brands surveyed increased their wholesale price this year. Sufficient.
Answer: C
