Aptitude tests / Mental Ability __ tips and tricks

    Aptitude tests / Mental Ability is one stream which is vital in every competitive exam. 

Involving tedious mental calculations and applications , this subject deals with problems which we need to reason out and analyse very closely. 

In this blog, I have put together few important topics and formulas from various  Mental Ability chapters.

Calendar

In an ordinary year, the first day and the last day of the year are same

In a leap year, the first and last day will be subsequent days 

(Odd days -- Odd days basically means the number of days which donot form a complete week , for example 365 days forms 52 weeks and 1 day , hence this extra 1 days forms the odd day in a ordinary year) 

Ordinary year = 1 odd day

Leap year = 2 odd days

100 years = 5 odd days

200 years = 3 odd days

300 years = 1 odd day

400 years = 0 odd days

No. of leap years in 

100 years = 24 leap years

200 years = 48 leap years

300 years = 72 leap years

400 years = 97 leap years 

Repeating Calendar 

* Add 28 to a leap year

* Add 6 to the first year after leap year

* Add 11 to the second year after leap year

* Add 11 to the third year after leap year 

Clocks 

Angle formed between the minute hand and hour hand = 30H - 11/2 M

Every 24 hours -- 44 right angles

            a right angle every 32 minutes 43.64 seconds starting from 12:16: 

Hands of a clock overlap 22 times every 24 hours

Every 1 hour - 2 right angles 

   but between 2 - 3 o'clock -- 1 right angle

          between 8 - 9 o'clock -- 1 right angle

Cubes and Dices 

No. of smaller cubes with 3 surface painted = 8

No. of smaller cubes with 2 surface painted = (n-2) * 12

No. of smaller cubes with 1 surface painted = (n-2)^2 *6

No. of smaller cubes with no surface painted = (n-2) ^3 

Counting Figures

(4*3) + ( 3*2) + ( 2*1) = total number of squares if rows and columns are not equal