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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?
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A
46
💡 Explanation:
Let the number be 10x + y where x is tens digit, y is units digit. Square: (10x+y)² = 100x² + 20xy + y². Dividing by half the number (5x + y/2) and adding 36 then dividing by 2 gives the reversed number 10y + x. Also x = 2(y-x). Testing option B: 46² = 2116, half of 46 = 23, 2116/23 = 92, 92+36 = 128, 128/2 = 64 ✓ And 4 = 2(6-4) = 4 ✓ The number is 46.