Discussion
If \(a, b\) are two digit numbers such that HCF\((a, b) = 15\). Then how many pairs are available?
Answer: B
Write a = 15m and b = 15n with m and n co-prime. For two-digit numbers m and n lie between 1 and 6. The unordered co-prime pairs with m less than n are 11: (1,2) to (1,6), (2,3), (2,5), (3,4), (3,5), (4,5) and (5,6).
Adding the equal pair (15, 15), whose H.C.F. is also 15, gives 12 pairs, which is the final key (B). The tentative key (11) leaves out that equal pair.
The hundred-based pairs: 15 times 1 to 6 give 15, 30, 45, 60, 75, 90 and the pair (30, 60) is excluded because their H.C.F. is 30, which shows why co-primality of m and n matters.
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