Discussion
The sum and difference of the arithmetic mean and the geometric mean of two positive integers are respectively, 18 and 8. Then the values of the two numbers are
Answer: E
The numbers are 1 and 25.
Let the arithmetic mean be A and the geometric mean G. From A + G = 18 and A - G = 8, A = 13 and G = 5. So for the two numbers a and b:
\[ \begin{aligned} a + b &= 2A = 26 \\ ab &= G^{2} = 25 \end{aligned} \]
They are the roots of \(t^{2} - 26t + 25 = 0\), that is \((t - 1)(t - 25) = 0\), giving 1 and 25. Check: AM 13, GM 5, sum 18, difference 8.
The other pairs fail the check. For 8 and 18, the AM is 13 but the GM is 12; for 2 and 24 the GM is not even an integer.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development