Question

The sum of twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. The sum of thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The smallest of the even numbers is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is C

6

Let's assume the five consecutive odd number be (2x +1) (2x -1) (2x + 3) (2x -3) (2x +5)

Let's assume the four consecutive even number be (2y) (2y +2) (2y -2) (2y + 4)

According to question

2(10x + 5) + 3(8y +4) = 178

20 x + 24 y = 156 -------(i)

3(10x + 5) + 2 (8y + 4) = 177

30x + 16 y = 154 --------(ii)

Solving equation (i) and (ii), we will get

y = 4 and x = 3.

The four consecutive even numbers are 6, 8, 10, 12.

Smallest even number is 6.