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How many purple chips ??

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How many purple chips ??

by mavesum » Sat Apr 18, 2009 12:28 pm
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

couldnt even figure out the starting approach ...

[spoiler]Ans : 2[/spoiler]
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by m&m » Sat Apr 18, 2009 12:43 pm
Funny you should ask this, I just did a practice test yesterday that had this...

If you look at all prime factors of 88,000 it includes:

11^1, 5^3, and 2^6

so we have an 11 (red chip), we have a 5(green chip) and we need to find a number between 5 and 11 that makes up the rest. We can't pick 6 since it is made up for a 2 and a 3 (no 3 in prime factors), can't pick 7 (no 7 prime factor), can pick 8 (since it's a 2^3), can't pick 9 (no 3s in prime factor), can pick 10 since we have 5 and 2.

so let's try 8
if we pick 1*11pts, 3*5pts, and 2*8 pts (which is 2^3 twice = 2^6), then we are done.

let's try the 10
there is no combination that will give us 5^3, and 2^6
ie we can take 3 10pt chips but we still have 2^3 left over.

so x=8 and number of chips =2
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