The average of 44 consecutive odd numbers is 144. What is the largest number?

A. 189

B. 191

C. 187

D. 193

Answer: Option C

Solution(By Examveda Team)

Let the number is x, x + 2, x + 4, . . . . . . x + 86
Total value of 44 number is = 44x + 2 + 4 + . . . . . . 86
Value of 2 + 4 + 6 + . . . . . . 86
= 2(1 + 2 + 3 . . . . . . + 43)
= $$2\left( {\frac{{n \times \left( {n + 1} \right)}}{2}} \right)$$
= 43 × 44
= 1892
According to the question,
1892 + 44x = 144 × 44
44x = 144 × 44 - 1892
x = $$\frac{{44\left( {144 - 43} \right)}}{{44}}$$
x = 101
Largest number = 101 + 86 = 187