OG 11 - PS 234

[taim]

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?

[kvcpk]

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!!

[taim]

Yes, but why is 147000 = 7^2 * 3 * 2^3 * 5^3
Please can you be specific? and detail the approach / logic.

[kvcpk]

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?