Problem Solving

chrisjim5 wrote: Please solve algebraically (not through prime factorization)

This comment concerns me a bit. If you're avoiding prime factorizations, you're going to find it impossible to answer a lot of GMAT questions. Prime factorization is among the most useful techniques you have, particularly on divisibility questions.

The question in your post *is* a prime factorization question; there's no way around it. If we pick r red chips, b blue chips and g green chips, our point total will be (2^r)(4^b)(5^g). We know our point total here was 16,000, so

(2^r)(4^b)(5^g) = 16,000
(2^r)(2^(2b))(5^g) = (2^7)(5^3)
(2^(r + 2b))(5^g) = (2^7)(5^3)

Now, the integer on the left side of the equation above is identical to the integer on the right side, so the power on the 5 must be the same, and g = 3. Similarly, the power on the 2 must be equal, so r + 2b = 7. Since we're told that b = g, we find that r = 1.

The equation you wrote down, (2r)(4b)(5g) = 16,000, was not correct. If, say, we pick two green chips, then the product of our point values is not 5*2 = 10. Instead it is 5*5 = 25 points. If we pick g green chips, we get 5^g points, and not 5g points.