Divisibility and Primes Question From CAT Exam

[aashray.thatai]

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

My approach:
i figured out the prime box for 88,000 to be 11*5^3*2^6, i also know that our x; 5<x<11 from the above question. I also saw that we could eliminate 11 as it doesn't satisfy 5<x<11, now we are left with 5^3 and 2^6, from here i dint know how to proceed ? could you please help me figure out this question . The correct answer is b.

[RonPurewal]

now we are left with 5^3 and 2^6, from here i dint know how to proceed ?

You've actually figured out all the major pieces of the puzzle; now, you just have to put them together.

Here's what you've already figured out:
• The mystery value must be 6, 7, 8, 9, or 10.
• All you have left is 2's and 5's.

So, just consider these possibilities-- 6, 7, 8, 9, and 10-- and ask yourself whether you can make them from only 2's and/or 5's.

Only two of those numbers can be made from 2's and 5's. Try each of them in the problem, and see whether everything else works out.

[aashray.thatai]

we can eliminate 7,9 because they both are not divisible by 2 or 5. we can also eliminate 6 as ;6=2*3 and we do not have 3 in our prime box . Now we are left with 8 and 10 . Could you tell me how to eliminate 10 and get 8?
Thanks for your help

[GovindL878]

After you have broken down 88,000 in its prime factors - 11^2, 5^3 and 2^6.

2^6 can also be written as 8^2. Since, the purple point has to lie between 5 and 11. There is only one possibility there are 2 8 point balls to add up to 88,000.

Hope that helps

[RonPurewal]

we can eliminate 7,9 because they both are not divisible by 2 or 5. we can also eliminate 6 as ;6=2*3 and we do not have 3 in our prime box . Now we are left with 8 and 10 . Could you tell me how to eliminate 10 and get 8?
Thanks for your help

Try letting that color of ball be worth 10. Then try to make the product out of allowable point values. See whether you can actually get the entire product you want.

With one of the two values, you'll be able to get the entire product. With the other one, you won't.