heshamelaziry 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?

OA 2

breaking 88000 into factors 2^6*5^3*11

from this it is clear the point for x is a multiple of 2

and also we r given that 5<x<11

only one value possible x=8
and 2^6=64
therefore two ;purple balls selected ; then only 8*8=64

hence 2

xcusemeplz2009 wrote:

heshamelaziry 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?

OA 2

breaking 88000 into factors 2^6*5^3*11

from this it is clear the point for x is a multiple of 2

and also we r given that 5<x<11

only one value possible x=8
and 2^6=64
therefore two ;purple balls selected ; then only 8*8=64

hence 2

Why x has to be a multiple of 2 based on the prime factorization of 88,000 ? and why 8 and not 6?

Why x has to be a multiple of 2 based on the prime factorization of 88,000 ? and why 8 and not 6?[/quote]

because one of the factors is 2, that makes it multiple of 2.
It's eight because the factors are 2^6*5^3*11, and 5 and 11 are already points given for a ball taken from the bag, so we know these values belong to the pointing system, but 2^6 is not any 5 or 11 multiple, so this is the one missing: 64=8*8