ugcnet_june_2008_II

Question

5.  In a set of 8 positive integers, there always exists a pair of numbers having the same remainder when divided by:

.(A) 7                   (B) 11            

(C) 13                 (D) 15

Comments

Take 1 to 8 numbers ..

only 7 will give same remainder

Answer 1

option A)

using pigeon hole principle

7 can have  7 remainder values i.e 0,1,2,3,4,5,6

so in 8 integers atleast 1 remainder value will occur twice