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

Let's first find the prime factorization of 147,000....

147,000 = (147)(1,000)
= (3)(49)(1,000)
= (3)(7)(7)(1,000)
= (3)(7)(7)(10)(10)(10)
= (3)(7)(7)(2)(5)(2)(5)(2)(5)

Since there is only one unique way to write 147,000 as the product of prime numbers, we know that:
- three beads worth 2 points each were removed (i.e., three blue beads were removed)
- one bead worth 3 points each were removed (i.e., one green bead was removed)
- three beads worth 5 points each were removed (i.e., three yellow beads were removed)
- two beads worth 7 points each were removed (i.e., two red beads were removed)

Answer: D

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

Hope this helps.

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.

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.

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.

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.

Can this question be solved with algebra

anything can be solved with algebra but i doubt it will be any more easier.

So, if you had a problem understanding the problem as I did, I will be more than happy to explain it.

Here it goes

there are number of beads in a jar. Each color is worth a certain number of points, for our example here 1 red bead is equal to
points.

Then some number of beads is removed from the jar, and the product of this number is 147000. to make it easier if we know that a green bead is worth 3 points, so if we have a product of 6 it could be 2 green beads (3 pts. per bead) were removed.

So for the 147,000, the prime factorization is 147,000 = 147*1000=7*7*3*1000. here is the catch, this is number of the removed beads since we have two beads then it means that 2 reds have been removed. That's it.

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