BTGModeratorVI wrote: ↑Tue Mar 10, 2020 7:26 am
In a certain class, the ratio of girls to boys is 5:4. How many girls are there?
(1) If four new boys joined the class, the number of boys would increase by 20%.
(2) If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23
Answer:
A
Source: Magoosh
Given: In a certain class, the ratio of girls to boys is 5:4.
Let G = number of girls in the class
Let B = number of boys in the class
We can write: G/B = 5/4
Cross multiply to get: 4G = 5B
Rearrange to get:
4G - 5B = 0
Target question: What is the value of G
Statement 1: If four new boys joined the class, the number of boys would increase by 20%.
Here's a word equation for this statement: (new boy population with 4 extra boys) = (old boy population increased by 20%)
In other words: B + 4 = B + (20% of B)
Or: B + 4 = B + 0.2B
Or: B + 4 = 1.2B
Subtract B from both sides: 4 = 0.2B
Solve: B = 4/(0.2) = 40/2 = 20
Once we know that B = 20, we can take
4G - 5B = 0 and plug in B = 20
We get: 4G - 5(20) = 0
Solve to get G = 25
The answer to the target question is
G = 25
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23
So, 1.5G = the NEW number of girls
B = the number of boys
So, 1.5G + B = the NEW number of children.
So, P(selected child is a boy) = B/(1.5G + B)
We're told the probability is 8/23
So, we can write: B/(1.5G + B) = 8/23
Cross multiply to get: 8(1.5G + B) = 23B
Expand to get: 12G + 8B = 23B
Subtract 23B from both sides to get: 12G - 15B
Divide both sides by 3 to get: 4G - 5B = 0
Hmmm, we ALREADY knew that
4G - 5B = 0
So, statement 2 does NOT add any new information.
As such, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
