CAT Mentors

Tuesday, March 8, 2016

What is the highest power of 3 which will exactly divide 80! ?

Answer & Explanation:

80/3= 26

26/3=8

8/3=2

The sum of combined powers of 3 = 26+8+2= 36

So the highest power of 3 which will exactly divide 80! Will be 36.

What is the number of diagonals in a polygon of 16 sides?

Answer:

The required answer = 16C2- 16= 104.

If the number 1234......9899100101102 (first 102 natural no.s written in order) is divided by 16, what will be the remainder?

What is the probability that in a throw of two dice, the outcome will be a multiple of either 4 or 7?

Answer & Explanation:

The possible favorable outcomes must have sum of digits as 4, 8 or 7. Such outcomes are:

(1,3), (2,2),(3,1),

(2,6), (3,5), (4,4), (5,3), (6,2),

(1,6),(2,5), (3,4), (4,3), (5,2), (6,1)

The total number of such outcomes= 3+5+6= 14

Required probability= 14/36= 7/18.