CA Foundation · Quantitative Aptitude · Sequence and Series
Two positive numbers a and b have AM = 10 and HM = 6.4. What is the absolute difference between the two numbers?
The difference is 12. Since GM squared equals AM times HM, the product is 64, and the sum is 20. Then (a−b) squared is 400 minus 256, which is 144, so the numbers are 16 and 4 and differ by 12.
- A6
- B12Correct
- C8
- D10
Explanation
GM² = AM × HM = 10 × 6.4 = 64, so ab = 64. Also a+b = 20. Then (a−b)² = (a+b)² − 4ab = 400 − 256 = 144, so |a−b| = 12. The numbers are 16 and 4, which check: AM = 10, HM = 2×64/20 = 6.4. The option 8 results from forgetting to multiply ab by 4.
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