BTGmoderatorDC wrote:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
A. 1
B. 2
C. 3
D. 4
E. 5
OA B
Source: Manhattan Prep
This question begs for some
prime factorization.
88,000 = (2)(2)(2)(2)(2)(2)(5)(5)(5)(11)
First, we can see that there must be one (11-point) red chip.
Now, what role do these 2's play? Since there are no 2's hiding among the 5-point chips or the 11-point chips, the 2's must be associated with the x-point chips.
Since we know that each purple chip is worth 6, 7, 8, 9 or 10 points, we know that
x must equal 6, 8 or 10.
x cannot equal 6, because we don't have any 3's in the prime factorization.
If x were to equal 10, we'd need six 5's to go with our six 2's. Since we don't have six 5's in the prime factorization of 88,000, we can rule out the possibility that x equals 10.
By the process of elimination, x MUST equal 8.
Since 8 = (2)(2)(2), we can see that the six 2's can be used to create
two products of 8.
Answer: B
Cheers,
Brent
