We can TEST CASES to prove insufficiency in this problem.
Warehouse W’s revenue from the sale of sofas was what percent greater this year than it was last year?
Revenue from sales will equal (price of sofas)(quantity sold) --> R = (p)(q)
To answer the question of the proportional difference in revenue, we need to know:
- what was the proportional difference in price?
- what what the proportional difference in quantity sold?
(1) Warehouse W sold 10 percent more sofas this year than it did last year.
This doesn't tell us anything about price. If we sold 10% more sofas at the same price, we'd make 10% more revenue. But if price also went up 10%, then:
(1.1p)(1.1q) = 1.21pq --> 21% increase in revenue
Insufficient.
(2) Warehouse W’s selling price per sofa was $30 greater this year than it was last year.
This doesn't give us any information about how many were sold. We might have sold half as many as last year... or twice as many. Those would give us very different answers about the change in revenue.
Insufficient.
(1) and (2) together
We know the proportional increase in quantity sold, and a numerical difference in price. Let's compare 2 different scenarios:
Scenario A (cheap couches):
last year: sold 100 couches at $100 each --> $10,000 in revenue
this year: sold 110 couches at $130 each --> $14,300 in revenue
43% increase in revenue
Scenario B (very expensive couches):
last year: sold 10,000 couches at $10,000 each --> $100,000,000 in revenue
this year: sold 11,000 couches at $10,030 each --> $110,330,000 in revenue
Barely more than a 10% increase in revenue
Because we don't know what that +$30 means as a PROPORTIONAL difference, we don't know the proportional change to the revenue.
The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
