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19 Mar 2022, 08:02
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E
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Difficulty:
25%
(medium)
Question Stats:
82% (02:35) correct
18%
(03:02)
wrong
based on 148
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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
19 Mar 2022, 09:05
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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
20 Mar 2022, 12:33
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Bookmarks
BrentGMATPrepNow
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
