Aptitude - Numbers

Let the two consecutive even integers be 2n and (2n + 2). Then,

(2n + 2)² = (2n + 2 + 2n)(2n + 2 - 2n)

     = 2(4n + 2)

     = 4(2n + 1), which is divisible by 4.

551 > 22

All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.

119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.

So, none of the given numbers is prime.

Required sum = (2 + 4 + 6 + ... + 30)

This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.

Let the number of terms be n. Then,

t_n = 30    a + (n - 1)d = 30

2 + (n - 1) x 2 = 30

n - 1 = 14

n = 15

Sn =	n	(a + l)	=	15	x (2 + 30)   = 240.
	2			2