CAT 2021 Slot 2 · Quant · Question 16

Read \left| 3x-20 \right|+\left| 3x-40 \right| as the total distance from 3x to the two points 20 and 40 on a number line.

That total is exactly 20 (the gap between them) precisely when 3x lies between them, and is more than 20 otherwise.

So the condition holds exactly when 20\le 3x\le 40, that is \frac{20}{3}\le x\le \frac{40}{3}, roughly 6.67\le x\le 13.33.

The word necessarily means we need the option whose every value satisfies this, so the option must sit entirely inside that interval.

Option A starts at 6, below \frac{20}{3}.

Options C and D run to 15 and 14, above \frac{40}{3}. Only 7<x<12 fits entirely inside.