Question

if $P$ and $Q$ are the sum and product respectively of all integral value of $x$ satisfying the equation $\left[3\right[x]-4x]=4$, then
(where $[.]$ denotes represent greater integer function)

• A. $P=0$
• B. $P=8$
• C. $P=-16$
• D. $P=-9$

Answer 1

The correct option is A $P=0$

$P$= sum of all values of $x$ and $Q$=their product.

$\left[3\right[x]-4x]=4$

$\Rightarrow 3\left[x\right]-4x\ge 4$ but $3\left[x\right]-4x<5$

$\Rightarrow \left[x\right]\ge \frac{4(1+x)}{3}$ and $\left[x\right]<\frac{5+4x}{3}$

No values $\Rightarrow P=0$