Q.)If n = 1+X where X is the product of four consecutive positive integers , then which of the following is/are true? [CAT Question , CAT 1999 Question , MBA Exam , Number System]

A. n is odd

B. n is prime

C. n is a perfect square

(a) A and C only

(b) A and B only

(c) A only

(d) None of these

Solution : Let the four consecutive integers be (a-1),a,(a+1),(a+2).

X = product of four consecutive positive integers

= (a-1)a(a+1)(a+2)

=

=

n = 1+X = + 1

=

X will be even number as it is the product of four consecutive positive integers(one of the integers will be even).

1+X = 1+even = odd

Hence, n is odd and a perfect square also.

Hence, OPTION(a)