Multiple choice general knowledge math & puzzles

How many two digit numbers have their squares as 1 more than a multiple of 24?

  1. 30

  2. 31

  3. 32

  4. 29

  5. 27
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A Correct answer
Explanation

We need n² congruent to 1 mod 24, meaning 24 divides n²-1. For 2-digit numbers (10 to 99), testing shows 30 numbers satisfy this: 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97.

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