Numbers

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

  1. 21
  2. 25
  3. 41
  4. 67

Answer

Let the four 2-digit odd numbers be: n-3, n-1, n+1, n+3

Sum of these 4 numbers = 4n

When the sum is divided by 10, you get a perfect square that include 1, 4, 9, 16, 25, 36, 49, and so on.

Possible values of 4n/10 are 4, 16, 36, ...

If 4n/10 = 4, then n = 10; The corresponding numbers are 7, 9, 11, 13 (all of which are 2-digit)

If 4n/10 = 16, then n = 40; The corresponding numbers are 37, 39, 41, 43

If 4n/10 = 36. then n = 90; The corresponding numbers are 87, 89, 91, 93

The correct option is C.