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
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.