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LCM- points

by venmic » Sun Dec 11, 2011 12:14 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?


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by Anurag@Gurome » Sun Dec 11, 2011 1:30 am
venmic 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?
5 < x < 11

88000 = 88*1000 = 8*11*8*125 = (2^6)*(5^3)*11

As the point of blue, green and red chips are odd integers, their product is not going to give us a multiple of 2^6. Hence, the products of the points of purple chips, i.e. must be a multiple of 2^6.

Hence, x can be 6, 8 or 10.

If x = 6, then the product of the points will have 3 in it. But the product has no 3 in it.
If x = 10, then to get 2^6 we need to multiply x six times which will give us six 5's. But the product has only three 5's.

Hence, x must be 8 = 2^3.
Therefore, x has to be multiplied twice to get 2^6.

Hence, two purple chips were selected.
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