THE GATEBOOK

Normalization Lectures

Let be four integers such that where is a positive integer. Given , which one of the following is necessarily true ?

(A) The minimum possible value of is

(B) The minimum possible value of is

(C) The maximum possible value of is

(D) The maximum possible value of is

m is a positive integer, so, lowest possible value of m=1.

Hence, in order to a+b+c+d = 4m+1, when m=1, at least one of a,b,c,d has to be greater than 1.

Take a=b=c=1; d=2

Hence,

Which is equal to , for other values of a,b,c,d, will be greater than .

Hence, answer is B.