Calc or Probab Challenge

[kanha81]

The Math Challenge attracted students from Cal Tech and MIT. Students may enlist in either the probability challenge or the calculus challenge, but not both. 60 percent of the Cal Tech participants and 40 percent of the MIT participants enlisted in the probability challenge. The remaining participants enlisted in the calculus challenge. If 60 percent of all of the Math Challenge participants come from Cal Tech, what percent of the group enlisted in the calculus challenge?

A) 60%
B) 52%
C) 48%
D) 45%
E) 40%

[p2pg]

IMO C

[truplayer256]

Let X represent the total amount of MIT students that came to the Math challenge and let Y represent the total amount of Cal Tech students that came to the math challenge.

Probability---MIT=.40(X), Cal Tech=.60(Y)
Calculus--- MIT= .60(X), Cal Tech= .40(Y)

.60(X+Y)=Y
.60X=.4Y
3X=2Y
X=2Y/3

What percent of the group enlisted in the calculus challenge?

(.60(X)+.4(Y))/X+Y
Substitute X=2Y/3

4Y/5/5Y/3=4Y/5*3/5Y=12/25*100=48% C.

[raleigh]

This is a good problem to plug in numbers. Suppose there was a total of 100 students. The last line tells us that 60% were from Cal Tech so 60 students were from Cal Tech. That leaves 40 MIT students.

60% of Cal Tech students participated in probability gives us that 40% participated in calculus since students cannot enlist in both. So 40% of the 60 Cal Tech students participated in calculus. .4*60 = 24.

40% of MIT students participated in probability so 60% of MIT students participated in calculus. There are 40 MIT students, so .6*40=24 students participated in calculus.

Therefore 48/100 students participated in calculus. The answer is C, 48%.