The sum of two natural numbers, x and y, is 324, and the HCF of x and y is 18. If x \lt y, how many such possible pairs of x and y are there?
- A. 1
- B. 2
- C. 3 ✓
- D. 4
Correct Answer: C. 3
Explanation
Let numbers be 18a and 18b (with a, b coprime and a \lt b). 18(a+b) = 324 \Rightarrow a+b = 18. Coprime pairs summing to 18 are (1,17), (5,13), and (7,11). Thus, there are 3 pairs.
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