2022 · Q5
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?
Elementary MathematicsHCF and LCM
- A27
- B35
- C45
- Dcannot be determined due to insufficient data
Explanation
Write HCF = d; then LCM = 14d and 14d² = 1134 gives d = 9, LCM = 126. The numbers are 9m and 9n with coprime m, n and mn = 14. But mn = 14 has two coprime factorisations: (14,1) giving the pair (126,9) with difference 117, and (7,2) giving (63,18) with difference 45. Since two different differences are possible, the answer cannot be determined from the data. The tempting option C (45) comes from finding only one of the two valid pairs. Hence the keyed option is D (changed from C).