Bunuel
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.
Deconstructing the Question Let \(T\) be the Total number of brands surveyed.
Let \(I\) be the number of brands that Increased their price.
Let \(S\) be the subset of brands that increased their price by
at least $2.
Target: Find the percentage of brands that increased their price (\(\frac{I}{T} \times 100\)).
Analyze Statement (1) "Of the brands that increased their price, 25% increased it by at least $2 per pound."
Equation: \(S = 0.25 \times I\).
This gives a relationship between the subset \(S\) and the group \(I\), but we have no information about the total population \(T\).
We cannot find the ratio \(\frac{I}{T}\).
INSUFFICIENT Analyze Statement (2) "Of all the brands surveyed, 15% increased their price by at least $2 per pound."
Equation: \(S = 0.15 \times T\).
This relates the subset \(S\) to the total population \(T\), but tells us nothing about the intermediate group \(I\) (those who increased by any amount).
INSUFFICIENT Combine Statements (1) and (2) We have two equations for \(S\):
1. \(S = 0.25 I\)
2. \(S = 0.15 T\)
Equating them: \(0.25 I = 0.15 T\)
Now, solve for the ratio \(\frac{I}{T}\):
\(I = \frac{0.15}{0.25} T\)
\(I = \frac{15}{25} T\)
\(I = \frac{3}{5} T\)
\(I = 0.60 T\)
So, 60% of the brands surveyed increased their wholesale price.
SUFFICIENT Answer: C