Quantitative Aptitude - Arithmetic Ability Questions

Given Number series is 18     37     76     155     314     635

follows a pattern that, 

18

18 x 2 +1 = 37

37 x 2 +2 = 76

76 x 2 +3 = 155

155 x 2 +4 = 314

314 x 2 +5 = 633 not 635

Hence, the odd man is 635.

When at least 2 women are included.

The committee may consist of 3 women, 2 men : It can be done in  4C3*6C2  ways

or, 4 women, 1 man : It can be done in  4C4*6C1ways

or, 2 women, 3 men : It can be done in 4C2*6C3 ways.

Total number of ways of forming the committees

= 4C2*6C3+4C3*6C2+4C4*6C1

= 6 x 20 + 4 x 15 + 1x 6

= 120 + 60 + 6 =186

Ratio of times taken by A and B = 1 : 2.

The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/60

(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.