How many purple chips were selected?

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How many purple chips were selected?

by ST » Sun May 10, 2009 10:21 am
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

Answer is : B
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by VP_Jim » Sun May 10, 2009 11:09 am
Wow, this is a toughie!

First, we need to recognize that the purple chips are worth x points, and x must be between 6 and 10 (5<x<11).

Next, you need to prime factorize 88,000 to find how many we have of each chip. As you study more, you'll realize that pretty much any question that says the sum of something = some big number, you need to prime factor.

The prime factors of 88,000 are:

11 (once)
5 (three times)
2 (six times)

Conveniently (and not coincidentally), the values 1, 5, and 11 are represented. So, the purple chips must be worth 2^some power.

Eight is the only number between 6 and 10 that is 2^some power, so, the purple chips must be worth 8 points each.

From our prime factorization, we know that we have six 2's in 88,000. Now, we need to express this in terms of 8s --

2^6 = 8^2

Therefore, there are two purple chips.

Yikes!
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Thank you

by ST » Sun May 10, 2009 2:30 pm
good explanation. thanks. now I understand.

ST