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In a certain game, a large container is filled with red, [#permalink]
07 Jan 2005, 09:06

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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?

Prime factorization is best approach. In 147000, forget about the 1000 part because there is no factor of 7 in there. Focus instead on 147 which is just 7^2 * 3. Answer is then 2 red beads worth 7 points each. It takes 10 seconds to do the problem.

Prime factorization is best approach. In 147000, forget about the 1000 part because there is no factor of 7 in there. Focus instead on 147 which is just 7^2 * 3. Answer is then 2 red beads worth 7 points each. It takes 10 seconds to do the problem.

Paul, i am still lost here. Can you please elaborate? What if the question had been how many yellow, green, and blue beads were removed?

[quote="gayathri"][quote="Paul"]Prime factorization is best approach. In 147000, forget about the 1000 part because there is no factor of 7 in there. Focus instead on 147 which is just 7^2 * 3. Answer is then 2 red beads worth 7 points each. It takes 10 seconds to do the problem.[/quote]

Paul, i am still lost here. Can you please elaborate? What if the question had been how many yellow, green, and blue beads were removed?
:oops:[/quote]

I wud say we can have all prime factors separated. Say a, b, c, d are no of beads removed in each case, then

7^a * 5^b * 3^c*2^d = 147000 in prime factors = 7^2 * 5^3* 3 * 2^3

So Red beads (a) = 2
Yellow beads (b) = 3
Green beads (c) = 1
Blue beads (d) = 3

I just realized why I did not understand the solution. The question says "If the product of the point values of the removed beads is 147,000, how many red beads were removed?" while I kept thinking sum of the point values