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test 38 #15

This topic has 2 expert replies and 1 member reply

test 38 #15

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15. 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,
The answer is D) but could not figure out - can you help?

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Junior | Next Rank: 30 Posts Default Avatar
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31 Jan 2007
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Hi,
you have the factorize the number 147000

147000 = 147 x 1000

147 = 3 x 7 x 7
1000 = 5 x 5 x 5 x 2 x 2 x 2

hence, the following number of beads were removed:
Red 2
Yellow 3
Green 1
Blue 3

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dunkin77 wrote:
15. 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
The first thing we want to do is to decipher the problem. The key word here is “product;" 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. Let’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, we’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 7’s, 5’s, 3’s, and 2’s have been multiplied together to equal 147,000. Since we only care about the red beads, we only care about the number of 7’s in the product. Let’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 7’s in the product of 147,000; thus, 2 red beads were removed.

Answer: D

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scott@targettestprep.com



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dunkin77 wrote:
15. 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
red = 7
yellow = 5
green = 3
blue = 2

147,000 = (2)(2)(2)(3)(5)(5)(5)(7)(7)
So, there are 3 blue beads, 1 green bead, 3 yellow beads and 2 red beads.

Cheers,
Brent

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