Bunuel wrote:
Last week a certain comedian had an audience of 120 people for each of the afternoon performances and 195 people for each of the evening performances. What was the average (arithmetic mean) number of people in an audience if the comedian gave only afternoon and evening performances last week?
(1) Last week the comedian gave 3 more evening performances than afternoon performances.
(2) Last week the comedian gave twice as many evening performances as afternoon performances.
- Number of afternoon performance shows = \(x\)
- Number of evening performance shows = \(y\)
Average number of people = \(\frac{120x + 195y}{(x+y)}\)
Statement 1(1) Last week the comedian gave 3 more evening performances than afternoon performances. y = x + 3
Average number of people = \(\frac{120x + 195y}{(x+y)}\)
Average number of people = \(\frac{120x + 195(x+3)}{(x+ x + 3)}\)
Average number of people = \(\frac{120x + 195x+(195*3)}{2x+3}\)
Average number of people = \(\frac{315x+(195*3)}{2x+3}\)
We have a variable in x. As the value of x is not known to us, we cannot find the average.
The statement alone is not sufficient, and we can eliminate A and D.
Statement 2(2) Last week the comedian gave twice as many evening performances as afternoon performances.y = 2x
Average number of people = \(\frac{120x + 195(2x)}{(x+2x)}\)
Average number of people = \(\frac{x(120 + 195*2)}{3x}\)
The variable x gets canceled out from the numerator and from the denominator. We have a definite answer to the question.
This statement is sufficient to answer the question.
Option B