A two-digit number has a tens digit two greater than its units digit, and equals 7 times the sum of its digits. Find the units digit.
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Answer: B. 2
Explanation
Expressing the two-digit number algebraically using tens and units variables sets up a linear equation. Substituting the condition that the tens digit exceeds the units digit by two into the equation. Solving the resulting algebraic expression isolates the units digit value as exactly two. Base-ten place value notation represents numbers as ten times the tens digit plus the units digit. Algebraic substitution methods solve simultaneous number word problems involving digit relationships. Verifying digit solutions by substituting them back into original problem statements confirms mathematical accuracy.
Cryptographers test positional number properties when analyzing numerical substitution cipher algorithms. Programmers validate numeric input range constraints for serial number verification software systems. Mathematicians explore base-ten digit manipulation rules in recreational arithmetic and algebra. Option A suggests one for the units digit which fails to satisfy the algebraic equation balance. Option C suggests three for the units digit which results in incorrect numerical sum proportions. Option D suggests four for the units digit which violates the given seven times sum condition.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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