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by chrisjim5 » Sat Oct 09, 2010 10:25 am
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips 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?

Answer Choices: 1 ; 2 ; 3 ; 4 ; 5


If solved algebraically:

2R * 4B * 5G = 16000

If B = G

40 R (B^2) = 16000

R (B^2) = 400

From this equation after checking the answer choices, R can either be 1 or 4.

Why is the answer 1 instead of 4? Please solve algebraically (not through prime factorization)
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by selango » Sat Oct 09, 2010 10:42 am
2^R*4^B*5^G=16000

B=G

2^R*4^G*5^G=16000

2^R*(20)^G=16000

2^(R+G) * 10^G=2^4*10^3

G=3 and R+G=4-->R=1
--Anand--
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by Ian Stewart » Sat Oct 09, 2010 10:55 am
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.
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