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In a certain game, a large container is filled with red, yel

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In a certain game, a large container is filled with red, yel  [#permalink]

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New post 29 Dec 2012, 06:10
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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?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 0
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post 29 Dec 2012, 06:14
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Walkabout 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


\(147,000=2^3*3*5^3*7^2\).

Since no other beads value is a multiple of 7, then there must be two red beads removed.

Answer: D.

Similar question to practice: in-a-certain-game-a-large-bag-is-filled-with-blue-green-126425.html

Hope it helps.
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post 22 May 2014, 13:01
5
MavenQ wrote:
Dear amarmeena1992

This is not a Combinations question. (And it cannot be, since you are not even told what the total number of balls is.)

You are told that the product of the scores of all the balls that were taken out is 147000.
Now, \(147000 = 7^2*5*3*4*2^3\)

From this expression, you can easily deduce that:

2 Red balls were taken out, along with
3 Yellow balls, 1 Green ball and 3 Blue balls.

Hope this helps.


Hi MavenQ,
Kindly correct the factors :
\(147,000 = 7^2*5^3*3*2^3\)

which would mean
2 R, 3 Y , 1 G and 3 B beads

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Dear amarmeena1992,
The beads R,Y,G,B are allotted some numbers which are prime.
So now since the product of the values of removed beads are known,
we can decompose or factorize the product into unique combination/product of the bead values
as shown :
147,000 = 7*7*3*5*5*5*2*2*2 = \(7^2*5^3*3*2^3\)

that is 2 R, 3 Y , 1 G and 3 B
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In a certain game, a large container is filled with red, yel  [#permalink]

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New post 22 May 2014, 11:18
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

I am not able to comprehend the question correctly. There could be a lot of combinations for removing the beads. How could we find any particular answer?
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post 22 May 2014, 11:29
amarmeena1992 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

I am not able to comprehend the question correctly. There could be a lot of combinations for removing the beads. How could we find any particular answer?


Merging similar topics. please refer to the discussion above and ask if anything remains unclear.

Similar questions to practice:
in-a-certain-game-a-large-bag-is-filled-with-blue-green-126425.html
a-cargo-ship-carrying-four-kinds-of-items-doohickies-geega-167523.html

All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html

Hope this helps.
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post Updated on: 22 May 2014, 14:37
2
Dear amarmeena1992

This is not a Combinations question. (And it cannot be, since you are not even told what the total number of balls is.)

You are told that the product of the scores of all the balls that were taken out is 147000.
Now, \(147000 = 7^2*5^3*3*4*2^3\)

From this expression, you can easily deduce that:

2 Red balls were taken out (since each Red ball has a score of 7. So, number of Red balls = power of 7 in the expression), along with
3 Yellow balls, 1 Green ball and 3 Blue balls.

Hope this helps.
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Originally posted by JapinderKaur on 22 May 2014, 12:15.
Last edited by JapinderKaur on 22 May 2014, 14:37, edited 2 times in total.
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post 15 Jul 2016, 04:43
3
Walkabout 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


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. 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 would 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 is 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 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.

The answer is D.
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post 18 May 2017, 11:26
2
Red – 7
Yellow – 5
Green – 3
Blue – 2

How many read beads have been removed, when the product of point values is 147 000.

Here we have a problem with prime factorization.

In other words, the problem is asking how many 7 factors are in 147 000

Using factor tree =>
147 000 = 147 * 1000
1000 = 10*10*10 =>2*5 * 2*5 *2*5 => no factors of 7 here

147 = 7*21
21=3*7 here we have 2 factors of 7.

The correct answer is D.
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Re: In a certain game, a large container is filled with red, yel  [#permalink]

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New post 10 Aug 2019, 02:51
147000=7^2 ∗ 5^3 ∗ 3 ∗ 4 ∗2^3

From this expression, you can easily deduce that:

2 Red balls were taken out (since each Red ball has a score of 7. So, number of Red balls = power of 7 in the expression), along with
3 Yellow balls, 1 Green ball and 3 Blue balls.
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Re: In a certain game, a large container is filled with red,  [#permalink]

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Re: In a certain game, a large container is filled with red,   [#permalink] 13 Sep 2019, 05:45
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