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Manager
Joined: 05 Jan 2009
Posts: 80

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11 Apr 2009, 16:19
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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 each. A number of beads are then removed from the container. if the product of the point values of the renoved beads is 147,000, how many red beads were removed?

a) 5
b) 4
c) 3
d) 2
e) 0

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Intern
Joined: 26 Jan 2009
Posts: 23

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Schools: University of Toronto, Schulich, Western, Queens

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11 Apr 2009, 16:45
I'm gonna go with 2.

Take all prime factors 147 000, which is

7^2, 3, 5^3, 2^2.....so 2 red beads were removed

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Manager
Joined: 05 Jan 2009
Posts: 80

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12 Apr 2009, 10:28

value of 2 red beads=14 or 49?

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Intern
Joined: 26 Jan 2009
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Schools: University of Toronto, Schulich, Western, Queens

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12 Apr 2009, 11:10
1
KUDOS
Well when i read that question one thing came to mind right away. The value of the different color beads are all prime numbers. The question is stating that THE PRODUCT of all beads removed is 147, 000. So break down 147 000 to its prime factors, which is 7^2, 3^1, 5^3, 2^3. The question tells us how many points each color bead is worth. So we know that there were 2 red beads (7^2), 3 yellow beads (5^3), 1 green bead (3^1), and 3 blue beads (2^3). Remember that the product of all prime factors of 147 000 is =147 000 and the question is stating that the product of all beads removed is=147 000.

red x red x yellow x yellow x yellow x green x blue x blue x blue=147000

red is worth 7
yellow is worth 5
green is worth 3
blue is worth 2

Two reds in this scenario is worth 49 and not 14 since the question is stating that the product of all beads removed is 147 000. It's not stating the sum is 147 000.

Hope this doesn't confuse you.

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Manager
Joined: 05 Jan 2009
Posts: 80

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13 Apr 2009, 17:02
Thanks. I understand it now.

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Current Student
Joined: 13 Jan 2009
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Location: India

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13 Apr 2009, 20:47
That was cool explanation.

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