Three mutually co-prime numbers have the product of the first two as 551 and the last two as 1073. What is their sum________?
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Answer: C. 85
Explanation
Factoring the product of the first two numbers reveals nineteen and twenty nine as prime factors. Factoring the product of the last two numbers yields twenty nine and thirty seven as prime factors. Identifying the shared middle factor as twenty nine allows summing all three numbers to get eighty five. Co-prime numbers share no common positive divisors other than the number one. Factoring composite numbers into prime components helps uncover hidden relationships between terms. Finding overlapping factors in overlapping product pairs allows isolating individual values in a sequence.
Number theory applications use co-prime properties in cryptographic key generation algorithms. Algebraic problem solving frequently tests the ability to factor composite products into constituent primes. Mathematical competitions feature similar product overlap puzzles to test analytical deduction. Option A suggests seventy five which underestimates the sum of the three derived numbers. Option B proposes eighty one which fails to match the exact addition of the factors. Option D offers eighty nine which overestimates the correct sum of the numbers.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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