In a certain game, a large bag is filled...(

[Guest]

(Source: MGMAT CAT Question "How much for those chips"

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

The product of the point values of the selected chips = 88,000

I interpret this to mean...

88,000 = 1(Blues) x 5(Greens) x ?(Purples) x 11(Reds) (((((Is this my problem?)))))

We do some quick math and see that 880= 11 x 8 x 10.

We know that 5(2) = 10 so that can satisfy our chip count for the green ones and we know that the "?" has to be 8 because its the only number thats less than 11 and more then 5 that a proper factor of 88,000.

88,000 = 1(1) x 5(2) x 8(1) x 11(100)

88,000 = 1 x 10 x 8 x 1,100

How many purple chips were selected? I got just 1...."A"


THE RIGHT ANSWER IS "B" AND ITS DRIVING ME INSANE!!! Help!!!!

[Mike]

Just take into account that 88,000 = 2^6 * 5^3 * 11

Therefore, the number of purple chips selected multiplied by purple chip's point value = 2^6.
The point value of the purple chip could be:
2, then 6 purple chips are selected
4, then 3 purple chips are selected
8, then 2 purple chips are selected
64, then 1 purple chip is selected

We know that purple chip's point value is between 5 and 11. Consequently, the purple chip's value is 8.

Thus 2 purple chips were selected.

[rfernandez]

Nice work, Mike!

[vscidd]

Why can't we have 1 Red, 1 Green, 200 Blue and 1 Purple chip?

[tim]

Why can't we have 1 Red, 1 Green, 200 Blue and 1 Purple chip?

because that would only work if the purple chips were worth 1600, which violates the constraints of the problem..

[alecarlos]

I got an easier one with the same structure of factorizing to primes, but all the balls were worth <2 pts...
I still managed to get this correctly, but something bothers me in the 1pt = how does this affect the factorization and points achieved because
2 ^6 x 5^3 X 11 is 88,000... where is the 1 in here?

[tim]

Good question. Inherent in any prime factorization is the ability to include an arbitrary number of 1's. In other words, we can factor 12 as 3*2*2 or as 3*2*2*1*1*1*1*1*1*1*1*1... if we like. We usually just leave it off because it's understood that multiplying by 1 as many times as we like leaves things the same (and because 1 is technically not a prime!)..

[sadartaud]

nvm

[tim]

:)