Suppose p and q are the LCM and HCF respectively of two positive numbers. If p:q=14:1 and pq=1134, then what is the difference between the two numbers?
- A. 27
- B. 35
- C. 45
- D. Cannot be determined due to insufficient data ✓
Correct Answer: D. Cannot be determined due to insufficient data
Explanation
We have p=14q and pq=1134, so 14q^2 = 1134 \implies q=9 (HCF) and p=126 (LCM). The numbers can be 18 and 63 (difference 45), or 9 and 126 (difference 117). Hence, the unique difference cannot be determined.
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