A certain number of people wait in line

[Vincen]

A certain number of people wait in line at a bank until served. How many people are presently in line?

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.

The OA is C.

I don't know how to solve this DS question. May any expert help me here please?

[ErikaPrepScholar]

Hey Vincen,

Let's approach this problem by building equations. We'll let x equal the number of people in presently in line.

Statement 1

x + 2 ≥ 10
or simplified
x ≥ 8

So there might be 8 people in line. But there might also be 9, or 10, or 5000. We don't know. Insufficient.

Statement 2

x - 4 < 5
or simplified
x < 9

So there might be 8 people in line. But there might also be 7, or 6, or 0. Insufficient.

BOTH

8 ≤ x < 9
or
x = 8

So there must be 8 people in line, no more, no less. Both statements together are sufficient.

Let me know if I can provide more detail on how to build these equations based on the info in the question!