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OG 11 - PS 234

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OG 11 - PS 234

by taim » Thu Aug 12, 2010 1:43 am
I know the answer to this, but would like to understand why the result is what it is?

In a certain game, a large container is filled with red, yellow, green, and blue beads worth respectively 7,5,3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
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by kvcpk » Thu Aug 12, 2010 1:51 am
taim wrote:I know the answer to this, but would like to understand why the result is what it is?

In a certain game, a large container is filled with red, yellow, green, and blue beads worth respectively 7,5,3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
147000 = 7^2 * 3 * 2^3 * 5^3

hence 2 - 7point items
1 - 3point item
3 - 2point items
3 - 5point items

Hence 2 red beads.

Hope this helps!!
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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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by taim » Thu Aug 12, 2010 1:55 am
Yes, but why is 147000 = 7^2 * 3 * 2^3 * 5^3
Please can you be specific? and detail the approach / logic.
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by kvcpk » Thu Aug 12, 2010 3:16 am
taim wrote:Yes, but why is 147000 = 7^2 * 3 * 2^3 * 5^3
Please can you be specific? and detail the approach / logic.
Simple. Any positive integer can be written as a product of primes.

Hence I factorised 147000 to find what primes, when multiplied, bring 147000

147000 = 147 * 1000 = 49*3 * 125 * 8 = 7^2 * 3 * 5^3 * 2^3

Now we know that 7 is obtained only when red bead is picked.
Hence 2 red beads should have been picked so that their product turns to 7^2

Does it help?
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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