First slide

Theory of expressions

Question

lf n > 0 and exactly 15 integers satisfy $(x + 6) (x - 4) (x - 5) (2 x - n) \leq 0$ then sum of digits of the least possible value of n is

Moderate

A

10
B

12
C

14
D

16

Solution

$(x + 6) (x - 4) (x - 5) (2 x - n) \leq 0$
Hence, $x \in [- 6, 4] \cup [5, \frac{n}{2}]$
Now, there are 11 integers in [-6, 4].
So, there must be 4integers in $[5, \frac{n}{2}]$
So, $\frac{n}{2} \in [8, 9)$
$\Rightarrow n \in [16, 18)$

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