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7, 5, 3, and 2 points each.

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 1 member reply

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sanju09 GMAT Instructor
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7, 5, 3, and 2 points each.

Sat Dec 14, 2013 12:37 am
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?
A. 5
B. 4
C. 3
D. 2
E. 0

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Uva@90 Master | Next Rank: 500 Posts
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Sat Dec 14, 2013 9:23 am
sanju09 wrote:
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?
A. 5
B. 4
C. 3
D. 2
E. 0

Hi,
Since Red bead worth of 7 points.
We need to find how many 7's are there in 147,000.
LCM of 147,000 = 7^2 *3 *1000
Hence 2 Red beads are removed.

Regards,
Uva.

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Brent@GMATPrepNow GMAT Instructor
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Sat Dec 14, 2013 9:32 am
Uva's explanation is perfect.
I'll add that we can determine the number of each colored bead.
red = 7
yellow = 5
green = 3
blue = 2

147,000 = (2)(2)(2)(3)(5)(5)(5)(7)(7)

Cheers,
Brent

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Scott@TargetTestPrep GMAT Instructor
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Tue Jul 28, 2015 2:02 pm
sanju09 wrote:
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?
A. 5
B. 4
C. 3
D. 2
E. 0

Solution:

The first thing we want to do is to decipher the problem. The key word here is â€œproduct;" we are told that the product of the point values of the removed beads is 147,000.

Let's look at an example before we actually solve this problem. Letâ€™s say 2 red beads, 2 yellow beads, 2 green beads, and 2 blue beads were removed. The product of the point values would be:

7 x 7 x 5 x 5 x 3 x 3 x 2 x 2 = 44,100

Conversely, if we were to take 44,100 and break it down into its prime factors, weâ€™d get:

44,100 = 7 x 7 x 5 x 5 x 3 x 3 x 2 x 2

Note that this prime factorization of 44,100 corresponds exactly to the point values of the 2 red beads, the 2 yellow beads, the 2 green beads, and the 2 blue beads from the example.

This example is important because we can now use the same approach for answering the actual question. We are given that the product of the point values of the removed beads is 147,000. Thus, some number of 7â€™s, 5â€™s, 3â€™s, and 2â€™s have been multiplied together to equal 147,000. Since we only care about the red beads, we only care about the number of 7â€™s in the product. Letâ€™s keep this idea in mind as we break down 147,000.

147,000 = 147 x 1,000 = 49 x 3 x 1,000 = 7 x 7 x 3 x 1,000

Since 1,000 does not have 7 as a factor, we see that there are two 7â€™s in the product of 147,000; thus, 2 red beads were removed.

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