Can someone help me understand how to approach this 'revenue comparison' DS question? The statements seem related but I can’t figure out if either is sufficient.?
Yesterday Bookstore B sold twice as many softcover books as hardcover books. Was Bookstore B’s revenue from the sale of softcover books yesterday greater than its revenue from the sale of hardcover books yesterday?
1. The average (arithmetic mean) price of the hardcover books sold at the store yesterday was $10 more than the average price of the softcover books sold at the store yesterday.
2. The average price of the softcover and hardcover books sold at the store yesterday was greater than $14.
1. The average (arithmetic mean) price of the hardcover books sold at the store yesterday was $10 more than the average price of the softcover books sold at the store yesterday.
2. The average price of the softcover and hardcover books sold at the store yesterday was greater than $14.
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Asked by R Sandhya 9 months ago
Senior Assistant Manager in Operations Management
Statement 2 says the average price across all books is more than $14. So:
(s * S + h * H) / (s + h) > 14
We already know s = 2h. Let’s plug that in:
(2h * S + h * H) / (3h) > 14 → (2S + H)/3 > 14 → 2S + H > 42
Now use Statement 1: H = S + 10
So: 2S + (S + 10) > 42 → 3S > 32 → S > 10.67
That means softcover books are priced over $10.67, and hardcover books are over $20.67
Multiply by quantities: softcover revenue = 2h * S, hardcover = h * H
With these values, 2h * S > h * H ends up being true
So when you use both together, it works. Answer is C — only sufficient when combined.
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