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Numbers

by KItuz » Wed May 25, 2011 7:53 pm
This is a problem from MGMAT. Solution provided is unclear. Can you explain how to solve this?

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? Choice: 1,2,3,4,5

Also, what is point value? Is it number of chips * corresponding points or just the product of points?
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by manpsingh87 » Wed May 25, 2011 8:01 pm
KItuz wrote:This is a problem from MGMAT. Solution provided is unclear. Can you explain how to solve this?

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? Choice: 1,2,3,4,5

Also, what is point value? Is it number of chips * corresponding points or just the product of points?
blue->1 point;
green-> 5 points;
purple-> x points;
Red-> 11 points;

also 5<x<11;

now as per question product of the point values of selected chip is 88000;
11*2^3*5^3*2^3; since x i.e (point value of purple chip) lies between 5 and 11; therefore 2^3=x=8;
11*8*5^3*8;
11*8^2*5^3; i.e. there are 2 purple chips..!!!
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by Frankenstein » Wed May 25, 2011 8:13 pm
Hi,
Point value of the chip is the points worth of the chip.
e.g point value of blue chip is 1, that of red is 11.
The product of point values of chips is 88,000
88,000= 8.11.(2.5)^3 = 2^6.5^3.11. As there is not cip corresponding to point value 2 we need to express it as a power of some number between 5 and 11.So, we express 2^6 as 8^2
So, 88000=1^n.5^3.8^2.11
So, there are 3 green(value:5), 2purple(value:8) and 1red (value:11) chips.
Hence, answer is 2 purple chips.

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by SoCan » Wed May 25, 2011 8:13 pm
A point value is how much each chip is worth. Usually when you're asked to figure out how many "things" (in this case, chips) multiply to a given number, it's helpful to break down that given number into its prime factors - especially when those "things" are assigned prime number values (like the green and red chips are in this case - ignore the blue chips since their value is 1 and we're looking at the product).

88,000 prime factors break down like this: 11, 5^3, 2^6. So you know there are 3 green chips and 1 red chip selected. You know the purple chip has to be between 5 and 11 and only has 2 as a prime factor. The only number between 5 and 11 that only has 2 as a prime factor is 8 (2^3). Since there's a 2^6 in the product of 88,000, that means there are two purple chips with a value of 8 (2^3 * 2^3 = 2^6). Check the work: 5*5*5*8*8*11 = 88,000.
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