CAT 2022 Slot 1 · Quant · Question 8

Let the number ahead of Pinky be 3k and the number behind her be 5k.

Pinky herself is in the queue too, so the total is 3k+5k+1=8k+1.

The total is fewer than 300, so 8k+1<300.

That gives 8k<299, so k<37.375.

Since k counts whole groups of people, the largest allowed value is k=37.

The number ahead of Pinky is then 3\times 37=111.

Checking the total: 8\times 37+1=297, which is indeed under 300.

Shortcut. Forgetting to count Pinky herself is the trap — it would give 8k<300 and k=37 again here, but the total must be 8k+1, so always add the person in question before applying the bound.