Quantitative Aptitude - Arithmetic Ability Questions

The given number series is 90 72 56 42 36 20

9 x 10 = 90

8 x 9 = 72

7 x 8 = 56

6 x 7 = 42

5 x 6 = 30 (not 36) 

4 x 5 = 20

Hence, the odd man in the given number series is 36.

Correct Sum = (36 * 50 + 48 - 23) = 1825.

Correct mean = = 1825/50 = 36.5

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.

The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005.

So it has 1 odd day only.

The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.

Given that, 6th March, 2005 is Monday.

6th March, 2004 is Sunday (1 day before to 6th March, 2005).

Let the numbers be x and (100-x).

Then,x100-x=5*495

 =>  x2-100x+2475=0

 =>  (x-55) (x-45) = 0

 =>  x = 55 or x = 45

  The numbers are 45 and 55

Required difference = (55-45) = 10