CAT 1999 — QA Question 10
Prime and Composite NumbersEasy
If n = 1 + x where x is the product of four consecutive positive integers, then which of the following
is/are true?
A. n is odd
B. n is prime
C. n is a perfect square
Answer & solution
A and C only
- B
A and B only
- C
A only
- D
None of these
Solution
Use the method of simulation, viz. take any sample values of x and verify that n is both odd as well as a perfect square.
Alternate solution:
Let x = (n – 1) n (n + 1) (n + 2)
= (n2 – 1) n(n + 2)
= n4 + 2n3 – n2 – 2n
p = x + 1 = n4 + 2n3 – n2 – 2n + 1
= (n2 – n + 1)2
Hence, option (a).ââââ