Multiple choice general knowledge math & puzzles

The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten's place of the original number is equal to twice the difference between its digits. What is the number?

  1. 45

  2. 36

  3. 46

  4. None of the above
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C Correct answer
Explanation

Let the number be 10A + B. Following the operations: square it, divide by half (=multiply by 2), add 36, divide by 2. This gives 10A + B + 18, which equals the reverse 10B + A. Solving: A - B = -2, so B = A + 2. Given A = 2(B - A), we get 3A = 2B, substituting: 3A = 2(A + 2), giving A = 4, B = 6. The number is 46, and 46² ÷ 23 + 36 all divided by 2 = 64.

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