Multiple choice

The sum of 4 consecutive two-digit natural numbers, when divided by 10, becomes a perfect square. What is the least possible value of the largest of the four numbers?

  1. 5.5

  2. 93

  3. 13

  4. Can’t be determined

  5. 163
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C Correct answer
Explanation

Let the 4 consecutive odd numbers be x - 3, x - 1, x + 1 and x + 3. Sum of these numbers is 4x. √4x/10 or 2√x/10 is a perfect square. Now take different values of x. At x = 10, it becomes a perfect square. So, the four numbers are 7, 9, 11 and 13.

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