Bunuel
Of the 600 professionals who took an advanced certification examination, 50 percent passed the written portion of the exam, 30 percent passed the simulation portion of the exam, and 65 percent passed the demonstration portion of the exam. If 20 percent of the examinees passed no portion of the exam, and 35 percent of the subjects passed exactly two portions of the exam, how many of the subjects passed exactly one portion of the exam?
A. 140
B. 180
C. 240
D. 260
E. 300
from the venn diagram below
a+b+c+d+e+f+g+h+i =600
Passed in written = 50% of 600 =300 =a+d+g+e -----equation 1
Passed in simulation portion of the exam = 30% of 600 =180 = b+d+g+f ----- equation 2
Passed in demonstration portion of the exam = 65% of 600 = 390 =c+e+g+f -----equation 3
Passed in no portion of the exam = 20% of 600 = 120
i=120
=>a+b+c+d+e+f+g+h = 380 ------equation 4
Passed in exactly two portions of the exam = 35% of 600 = 210 = d+e+f ---- equation 5
We have to find exactly 1 portion of the program, that is a+b+c = ?
Adding equation 1,2 and 3
a+b+c+2(d+e+f) + 3g = 300+180+390 = 870 ---- equation 6
subtracting equation 4 from 6
d+e+f + 2g = 390
substituting value of d+e+f from equation 5
2g = 490 - 210 = 180
=> g = 90
Putting value of g in equation 6
a+b+c + 2* (210) + 3*90 = 870
a+b+c +420 + 270 = 870
=>a+b+c = 180
Hence IMO B
Attachments

venn2.png [ 13.33 KiB | Viewed 1963 times ]