Question

One hundred twenty-five (125) aliens descended on a set of film as Extra-Terrestrial beings 40 had two noses, 30 had three legs, 20 had four ears, 10 had two noses, and three legs, 12 had 3 legs and four ears, 5 had two noses and four years and 3 had all the unusual features. How many were there without any of these unusual features?

• A. 5
• B. 35
• C. 80
• D. None of these

Answer 1

The correct option is D None of these

Let the number of aliens with all unusual features $=a=3$ (given)

From the figure

$a+b=5$ $\therefore b=2$

$a+c=12$ $\therefore c=9$

$a+d=10$ $\therefore d=7$

$e+b+a+c=20$ $\therefore e=6$

$a+c+d+f=30$ $\therefore f=11$

$a+b+d+g=40$ $\therefore g=28$

Now total number of aliens with unusual features = $a+b+c+d+e+f+g=3+2+9+7+6+11+28=66$

So number of aliens without any unusual features $=125-66=59$