CAT 2021 Slot 2 QA Question 10: For a real number $x$ the condition $\left|3x-20\right|+\left|3x-40\right|=20$ necessarily holds if

Question

For a real number $x$ the condition $\left|3x-20\right|+\left|3x-40\right|=20$ necessarily holds if

Accepted Answer

Let $t = 3x$. The expression $\left|t - 20\right| + \left|t - 40\right|$ is the sum of distances of $t$ from $20$ and $40$.

This sum equals $20$ exactly when $t$ lies between $20$ and $40$, inclusive.

$20 \leq 3x \leq 40$
$\dfrac{20}{3} \leq x \leq \dfrac{40}{3}$

Now check which option is complet

For a real number xxx the condition ∣3x−20∣+∣3x−40∣=20\left|3x-20\right|+\left|3x-40\right|=20∣3x−20∣+∣3x−40∣=20 necessarily holds if