Q93 / 180 · COMEDK 2026 (9 May Shift 2) · Mathematics
A student needs to buy notebooks ($n$) for a semester. Double the number of notebooks plus 5 must strictly exceed 15, but the number of notebooks plus 10 must be no more than 22. What is the range of notebooks they can buy?
- A$\{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}$
- B$\{5, 6, 7, 8, 9, 10, 11, 12\}$
- C$\{6, 7, 8, 9, 10, 11\}$
- Correct answerD$\{6, 7, 8, 9, 10, 11, 12\}$
Solution
From the first condition, double the number of notebooks plus $5$ strictly exceeds $15$:
$2n + 5 > 15$
$2n > 10$
$n > 5$
From the second condition, the number of notebooks plus $10$ is no more than $22$:
$n + 10 \le 22$
$n \le 12$
Combining the two inequalities, we get $5 < n \le 12$.
Since the number of notebooks must be an integer, the possible values for $n$ are $6, 7, 8, 9, 10, 11, 12$.
The set of possible values is $\{6, 7, 8, 9, 10, 11, 12\}$.
Answer: $\{6, 7, 8, 9, 10, 11, 12\}$
$2n + 5 > 15$
$2n > 10$
$n > 5$
From the second condition, the number of notebooks plus $10$ is no more than $22$:
$n + 10 \le 22$
$n \le 12$
Combining the two inequalities, we get $5 < n \le 12$.
Since the number of notebooks must be an integer, the possible values for $n$ are $6, 7, 8, 9, 10, 11, 12$.
The set of possible values is $\{6, 7, 8, 9, 10, 11, 12\}$.
Answer: $\{6, 7, 8, 9, 10, 11, 12\}$
Hence, the correct answer is option: 'D'.