BTGmoderatorLU wrote: ↑

Sat Oct 08, 2022 5:35 pm

Source: Magoosh

In the game Dubblefud, red chips, blue chips and green chips are each worth in \(2, 4\) and \(5\) points respectively. In a certain selection of chips, the product of the point values is \(16,000.\) If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. \(1\)
B. \(2\)
C. \(3\)
D. \(4\)
E. \(5\)

The OA is A

Breaking 16,000 into prime factors, we have:

16,000 = 16 x 1,000 = 2^4 x 10^3 = 2^4 x 2^3 x 5^3 = 2^7 x 5^3

Since there are an equal number of blue chips and green chips, there must be 3 blue chips and 3 green chips (notice that the green chips are worth 5 points each and we have 5^3 as a factor). Since the blue chips are worth 4 points each, we know that we have 4^3 blue chips, and, since 4^3 = 2^6, there must be 1 red chip so that 2^6 x 2 = 2^7.

Answer: A