Question

When the sum of four consecutive two-digit odd numbers divided by 10, the result obtained is a perfect square. Which of the following can possibly be one of these four numbers?

a) 21
b) 31
c) 41
d) 51

Answer 1

The sum of four consecutive two-digit odd numbers divided by 10 must be a perfect square. None of the answer choices can be one of the four numbers.

Step-by-step explanation:

Solution:

Let's assume the four consecutive two-digit odd numbers are x, x+2, x+4, and x+6.

Their sum is x + (x+2) + (x+4) + (x+6) = 4x + 12.

If we divide this sum by 10, we get (4x + 12)/10 = 4/10 * x + 12/10 = 2/5 * x + 1.2.

In order for this result to be a perfect square, 2/5 * x + 1.2 must be a perfect square.

Let's check each answer choice:

a) 21 -> (2/5 * 21 + 1.2) = 9 + 1.2 = 10.2 -> not a perfect square

b) 31 -> (2/5 * 31 + 1.2) = 12.4 + 1.2 = 13.6 -> not a perfect square

c) 41 -> (2/5 * 41 + 1.2) = 16.4 + 1.2 = 17.6 -> not a perfect square

d) 51 -> (2/5 * 51 + 1.2) = 20.4 + 1.2 = 21.6 -> not a perfect square

None of the answer choices can possibly be one of the four numbers.