Question

One-quarter of the Math Olympiad participants are two-thirds of the Genius Circle students. Eight Genius Circle students did not participate in the Olympiad. What is the total number of students who participated in the Math Olympiad?'

Answer 1

64

Explanation:

This question is actually not hard just requires careful calculations.

So we know that 1/4 of MO (Math Olympiad) = 2/3 of GC (Genius Circle)

It also gives that 8 GC Members did not go to MO

So using these statements, we can find that

a. 1/3 of GC = 8 members --> and

b. 2/3 of GC = 16 which makes -->

c. 1/4 of MO = 16

Using these statements we can simply calculate 16 x 4 = 4/4 = 1

1 = Total amt. of participants in the MO => 16(4)

64

Hope this helps!

Answer 2

Answer: First let’s find how many student are in Genius Circle and we assume it’s Y
Then we have the equation:
2/3Y + 8 = Y
8 = 1/3Y
8 x 3 = Y
24=Y
Now that we know what is Y we can substitute: 2/3Y = 2/3 x 24 = 16
If 16 of the Genius Circle participants equal to 1/4 of the participants of the Math Olympiad which mean:
1/4 = 16
4/4 = 16 x 4
4/4 = 64
And so the answer for the total number of the participant in the Math Olympiad is 64.