AlgebraHardTwo-digit number from its digits
Algebra practice question
The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 greater than the original. What is the original number?
Answer: 47
Let the tens digit be t and the units digit u: t + u = 11, and (10u + t) − (10t + u) = 27 → 9(u − t) = 27 → u − t = 3. So u = 7, t = 4: the number is 47 (and 74 − 47 = 27).
Common wrong answers
- If you answered 29
- 29 has digit sum 11, but 92 − 29 = 63.
- If you answered 38
- 38 has digit sum 11, but 83 − 38 = 45, not 27.
- If you answered 74
- 74 is the reversed number.
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