BTGmoderatorDC wrote: ↑Sat Jan 18, 2020 2:12 pm
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
OA
A
Source: Magoosh
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Given that the ratio of girls to boys is 5 : 4, say there are 5x girls and 4x boys. We have to get the value of 5x.
Let's take each statement one by one.
(1) If four new boys joined the class, the number of boys would increase by 20%.
=> 5x / (4x + 4) = 5 / (4*120%) = 5/4.8 = 25/24
(5/4)*[x/(x + 1)] = 25/24 => x = 5
Thus, 5x = 5*5 = 25. Sufficient
(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.
Currently, there are 5x girls and 4x boys; after the increase, the number of girls = 5x*150% = 7.5x
So, now there are 7.5x girls and 4x boys; thus, the total no. of students = 7.5x + 4x = 11.5x
Thus, the probability that a randomly chosen student would be a boy = 4x/11.5x = 40/115 = 8/23. We already know this. Statement 2 does not provide additional information. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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