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Purple balls

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Purple balls

by Cheese12 » Sun Oct 02, 2011 6:57 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

Im stuck with this problem and dont know how to proceed.. My working..

Total points = 88000
factor using primes -> 88000 = (2^6)*(5^3)*(11)

from question we know that ... 88000= B*5G*Px*R11

and 11>x>5... so x = 8 or 10...8= 2^3... and 10= 2*5... both can be a fit into the formula..
also.. what about the Blue balls(B) ?... they could be any number.. and still hold true if x was 8 or 10...

OA:B
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by knight247 » Sun Oct 02, 2011 7:34 am
Actually, u've answered ur own question. 10=2*5 so the 5 would be a part of the green chips picked up. Secondly, when u have 2^6 i.e. 64 left you need to find a number between 5 and 11 which when multiplied by itself a certain number of times would give u 64. Only the number 8 when multiplied twice i.e. 8^2 gives u 64. Hence, there are two chips of 8 that were picked up. Hence, B. Hope that clears ur doubts.
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by edvhou812 » Sun Oct 02, 2011 7:55 am
88,000=11^1*2^6*5^3
2^6=64=8*8
5<8<11
B
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by Cheese12 » Sun Oct 02, 2011 8:08 am
knight247 wrote:Actually, u've answered ur own question. 10=2*5 so the 5 would be a part of the green chips picked up. Secondly, when u have 2^6 i.e. 64 left you need to find a number between 5 and 11 which when multiplied by itself a certain number of times would give u 64. Only the number 8 when multiplied twice i.e. 8^2 gives u 64. Hence, there are two chips of 8 that were picked up. Hence, B. Hope that clears ur doubts.
Hi Knight247,

that means... B*5G*Px= 2^6 * 5^3
so this can mean that G=3,2,1 ... if G=1 and say x = 10=5*2.. that means we have two 10's (2 5's and 2 2's) ..

so then the formula becomes... B =2^4... which is possible right ?

please help to point out my mistake here... thanks!!!
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by knight247 » Sun Oct 02, 2011 8:24 am
It is not B*5G*Px. It should be 5^(the number of times G is picked up) as it is the product of all the Gs picked up and not the sum of them. Similarly for other chips.

88,000=11^1 * 2^6 * 5^3

So we have, 1 Red Chip, 3 Green chips and 2^6 which is not defined yet. We don't consider Blue chips because their value is one, so picking a blue chip multiple times would not affect the product of the points. So the mistake u've made is that u've considered 5G when it should be
5^(the number of times G is picked up). Remember it is the product of all points.Similarly for other chips.
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