Discussion
Suppose given a positive integer k has the property that for any integer \(n \ge k\) can be written as a sum of 3's and/or 8's. Then which of the following is the value of k ?
Answer: D
Of the options, the value that works is \(k = 15\).
For coprime 3 and 8, the largest integer that is not a non-negative combination \(3a + 8b\) is the Frobenius number
\[ 3 \cdot 8 - 3 - 8 = 13 \]
So every integer from 14 onwards can be written with 3's and 8's (14 = 3 + 3 + 8, 15 = 3 × 5, 16 = 8 + 8, and adding 3's covers the rest), while 13 cannot.
Any valid k must therefore exceed 13, which rules out 6, 8 and 9 (each would require 13 to be representable). Of the four choices only 15 has the property; the smallest such k is 14, which is not offered.
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