CAT Exam

What is the sum of the reciprocals of all the divisors of 360?

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13/4 is the sum of the reciprocals of all the divisors of 360.
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CAT Other Question

Using the most powerful telescope ever made, scientists observe a class of young aliens on a planet millions of light years away. On the blackboard, their teacher has written these equations: 13 + 15 = 31, 10 x 10 = 100, 6 x 3 = 24 How many fingers do they have? (We count in base ten. What do they count in?)
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Answers :
1) 13/4
2) 729
3) 7 In ABC, D is the midpoint of **. E is a point on AC such that AE : EC = 2 : 1 and F is a point on AB such that AF : FB = 3 : 1. Line segments AD and FE intersect at point O. What is the ratio of the area of DOF to the area of DOE?

1.8:9
2.9:8
3.3:4
4.4:3