Last visit was: 11 Aug 2024, 23:31 It is currently 11 Aug 2024, 23:31
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 02 Dec 2012
Posts: 172
Own Kudos [?]: 24695 [119]
Given Kudos: 29
Math Expert
Joined: 02 Sep 2009
Posts: 94854
Own Kudos [?]: 648858 [25]
Given Kudos: 86912
Intern
Joined: 13 May 2014
Posts: 26
Own Kudos [?]: 239 [15]
Given Kudos: 1
Concentration: General Management, Strategy
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30995 [4]
Given Kudos: 799
Re: In a certain game, a large container is filled with red, yel [#permalink]
4
Kudos
Top Contributor
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

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)

General Discussion
Intern
Joined: 12 Jul 2013
Posts: 31
Own Kudos [?]: 8 [0]
Given Kudos: 7
Location: India
Concentration: Finance, Entrepreneurship
Schools:
In a certain game, a large container is filled with red, yel [#permalink]
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?
Math Expert
Joined: 02 Sep 2009
Posts: 94854
Own Kudos [?]: 648858 [4]
Given Kudos: 86912
Re: In a certain game, a large container is filled with red, yel [#permalink]
4
Bookmarks
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.
Intern
Joined: 19 May 2014
Posts: 23
Own Kudos [?]: 62 [2]
Given Kudos: 9
Re: In a certain game, a large container is filled with red, yel [#permalink]
2
Kudos
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.

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.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19291
Own Kudos [?]: 22876 [9]
Given Kudos: 286
Location: United States (CA)
Re: In a certain game, a large container is filled with red, yel [#permalink]
9
Kudos
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.

Intern
Joined: 16 May 2017
Posts: 11
Own Kudos [?]: 5 [4]
Given Kudos: 0
Re: In a certain game, a large container is filled with red, yel [#permalink]
4
Kudos
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.

Intern
Joined: 12 Feb 2019
Posts: 18
Own Kudos [?]: 7 [0]
Given Kudos: 129
Location: India
GPA: 4
Re: In a certain game, a large container is filled with red, yel [#permalink]
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.
Intern
Joined: 11 Jan 2022
Posts: 38
Own Kudos [?]: 1 [0]
Given Kudos: 104
Re: In a certain game, a large container is filled with red, yel [#permalink]
Can this question be solved with algebra
Intern
Joined: 07 Mar 2020
Posts: 33
Own Kudos [?]: 4 [0]
Given Kudos: 256
In a certain game, a large container is filled with red, yel [#permalink]
A2D2 wrote:
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 34381
Own Kudos [?]: 861 [0]
Given Kudos: 0
Re: In a certain game, a large container is filled with red, yel [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: In a certain game, a large container is filled with red, yel [#permalink]
Moderator:
Math Expert
94854 posts