CA Foundation · Quantitative Aptitude · Sequence and Series
Two positive numbers a and b have AM = 10 and GM = 8. Which of the following is the value of the HM, and what is the correct relationship between the three means?
HM is 6.4 and AM > GM > HM. Because GM squared equals AM times HM, HM is 64 divided by 10, which is 6.4. This sits below the GM of 8, which sits below the AM of 10, as the AM-GM-HM inequality requires.
- AHM = 6.4, and AM > GM > HMCorrect
- BHM = 6.4, and HM > GM > AM
- CHM = 9, and AM > HM > GM
- DHM = 12.5, and HM > AM > GM
Explanation
Since GM² = AM × HM, HM = 64/10 = 6.4. Then 10 > 8 > 6.4, so AM > GM > HM. HM = 12.5 comes from wrongly computing AM²/GM... actually 100/8, a wrong formula; it also violates AM ≥ GM ≥ HM.
Did you get it right without looking?
One question tells you little. A timed set on Sequence and Series shows your real accuracy, how long you take and where you lose marks.
More Sequence and Series questions
- A company's annual sales grow so that each year's increase is 10% of the previous year's sales. If sales in the first year are ₹2,00,000, wh…
- A sequence is defined by T1 = 3 and Tn = 2×T(n-1) - 1 for n ≥ 2. What is the value of T5?
- Three positive numbers are in geometric progression. Their sum is 39 and their product is 729. What is the sum of the squares of the three n…
- If Sn = n(n + 3) is the sum of the first n terms of a series, which of the following is true?
- What is the sum of the series 1² + 2² + 3² + ... + 12² minus the sum 1 + 2 + 3 + ... + 12?
- The sum of the first p terms of an AP is 3p² + 5p. What is the sum of the 8th, 9th and 10th terms of this AP?