A two-digit number has digits summing to 12 and differing by 6. Find the number.
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Answer: E. Either (a) or (b)
Explanation
Setting up simultaneous equations for digit sums and differences identifies potential two-digit integer candidates. Checking digits that sum to twelve and differ by six yields the candidate pairs nine and three. Both ninety-three and thirty-nine satisfy the given numerical digit sum and difference conditions successfully. Two-digit numbers are composed of tens and units digits that can be manipulated using algebraic equations. Absolute difference equations account for either digit being larger than the other in number problems. Multiple valid answers in multiple choice questions are correctly designated by either-or selection options.
Cryptanalysts solve transposition ciphers and numeric puzzles by testing simultaneous digit constraint equations. Programmers write validation algorithms to check numeric input constraints for two-digit administrative codes. Mathematicians study base-ten positional number properties to solve recreational number theory puzzles. Option A suggests ninety-three which is a valid answer but omits the equally valid number thirty-nine. Option B suggests thirty-nine which is a valid answer but omits the equally valid number ninety-three. Option C suggests seventy-five which fails to satisfy the condition that digits differ by six.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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