Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Aug 2211:00 AM EDT
-11:59 PM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.
Aug 2910:00 PM IST
-11:30 PM IST
With brand new features like:AI-driven Planner tool, 850+ data Insights practice questions and GMAT Focus Edition Adaptive mock tests with ESR+ analysis and personal mentor support, our course is the most comprehensive course for GMAT Focus Edition.
Aug 3112:00 PM EDT
-03:00 PM EDT
Save 20% on Target Test Prep and Score in the 100th Percentile in GMAT Verbal! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Aug 3103:00 PM EDT
-11:59 PM EDT
For a limited time use code FALL20 to save on prep. Valid on Complete Course, Advanced Course, Bootcamp Course, Tutoring, and the Executive Assessment Course. This discount ends September 16th.
Sep 0212:01 AM PDT
-11:59 PM PDT
On Monday the 2nd, GMAT Club Tests will be Absolutely Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PST- Sep 07
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Given Kudos: 799
Location: Canada
A box contains red balls, blue balls, and green balls only. If 16 red
[#permalink]
19 Mar 2022, 08:02
19 Mar 2022, 08:02
3
Kudos
8
Bookmarks
Expert Reply
Top Contributor
Show timer
00:00
A
B
C
D
E
Difficulty:
25%
(medium)
Question Stats:
83% (02:33) correct
17%
(03:01)
wrong
based on 107
sessions
A box contains red balls, blue balls, and green balls only. If 16 red balls were removed from the box, the ratio of the number of red balls to the number of blue balls would be 2 to 3. If 24 blue balls were added to the original collection of balls, the ratio of the number of blue balls to the number of green balls would be 5 to 2. What is the ratio of the number of red balls to the number of green balls in the original collection?
A) 5 to 8
B) 3 to 2
C) 2 to 1
D) 8 to 5
E) 5 to 3
A) 5 to 8
B) 3 to 2
C) 2 to 1
D) 8 to 5
E) 5 to 3
Manager
Joined: 27 Oct 2021
Posts: 110
Given Kudos: 130
Location: India
Re: A box contains red balls, blue balls, and green balls only. If 16 red
[#permalink]
19 Mar 2022, 09:05
19 Mar 2022, 09:05
1
Kudos
IMO E
Using simple Algebra , Forming 2 equations.
let the number of of balls be r,b, and g as original count
If 16 red balls were removed from the box, the ratio of the number of red balls to the number of blue balls would be 2 to 3 means
r-16/b=2/3
= 3r-48=2b--- (1)
If 24 blue balls were added to the original collection of balls, the ratio of the number of blue balls to the number of green balls would be 5 to 2 means
b+24/g=5/2
=2b+48=5g
=2b=5g-48----(2)
As we want relation between r and g
lets equate 2b from both equations
3r-48=5g-48
->r/g=5/3
Using simple Algebra , Forming 2 equations.
let the number of of balls be r,b, and g as original count
If 16 red balls were removed from the box, the ratio of the number of red balls to the number of blue balls would be 2 to 3 means
r-16/b=2/3
= 3r-48=2b--- (1)
If 24 blue balls were added to the original collection of balls, the ratio of the number of blue balls to the number of green balls would be 5 to 2 means
b+24/g=5/2
=2b+48=5g
=2b=5g-48----(2)
As we want relation between r and g
lets equate 2b from both equations
3r-48=5g-48
->r/g=5/3
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Given Kudos: 799
Location: Canada
Re: A box contains red balls, blue balls, and green balls only. If 16 red
[#permalink]
20 Mar 2022, 12:33
20 Mar 2022, 12:33
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
BrentGMATPrepNow wrote:
A box contains red balls, blue balls, and green balls only. If 16 red balls were removed from the box, the ratio of the number of red balls to the number of blue balls would be 2 to 3. If 24 blue balls were added to the original collection of balls, the ratio of the number of blue balls to the number of green balls would be 5 to 2. What is the ratio of the number of red balls to the number of green balls in the original collection?
A) 5 to 8
B) 3 to 2
C) 2 to 1
D) 8 to 5
E) 5 to 3
A) 5 to 8
B) 3 to 2
C) 2 to 1
D) 8 to 5
E) 5 to 3
Let R = the number of red balls in the (original) collection
Let B = the number of blue balls in the (original) collection
Let G = the number of green balls in the (original) collection
If 16 red balls were removed from the box, the ratio of the number of red balls to the number of blue balls would be 2 to 3.
We can write: (R - 16)/B = 2/3
Cross multiply: 3(R - 16) = 2B
Expand: 3R - 48 = 2B
If 24 blue balls were added to the original collection of balls, the ratio of the number of blue balls to the number of green balls would be 5 to 2.
We can write: (B + 24)/G = 5/2
Cross multiply: 2(B + 24) = 5G
Expand: 2B + 48 = 5G
What is the ratio of the number of red balls to the number of green balls in the original collection?
In other words, what is the value of R/G?
We have the following system of equations:
3R - 48 = 2B
2B + 48 = 5G
Take the top equation and add 48 both sides to get:
3R = 2B + 48
2B + 48 = 5G
Since 3R and 5G are both set equal to 2B + 48, it must be the case that: 3R = 5G
Divide both sides of the equation by G to get: 3R/G = 5
Divide both sides of the equation by 3 to get: R/G = 5/3
Answer: E
