IMC 2010 Q20
20. Shahbaz thinks of an integer, \(n\), such that the difference between \(\sqrt{n}\) and 7 is less than 1.
How many different possibilities are there for \(n\)?
- A 13
- B 14
- C 26
- D 27
- E 28
Intermediate Mathematical Challenge 2010, Question 20. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 27
If the difference between \(\sqrt{n}\) and 7 is less than 1, then \(6 < \sqrt{n} < 8\).
Therefore \(36 < n < 64\), so there are 27 possible values of \(n\).
Solution © UK Mathematics Trust, from the IMC 2010 solutions.