GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
OA: 4
Here's an efficient non-algebraic approach:
The original ratio of cooks to waiters = 3:13, so the original number of waiters is a multiple of 13:
13,26,39,
52,65...
When 12 waiters are added, the new ratio = 3:16, so the increased number of waiters is a multiple of 16:
16,32,48,
64,80...
The values in red are 12 apart.
Thus, the original number of waiters = 52.
Since 3:13 = 12:52, the original number of cooks = 12.
The correct answer is
D.
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