Queue positions – A is 18th from the front; B is 16th from the back. C is 20th from the front and exactly in the middle between A and B (equal number of people between C and A and between C and B). How many persons are there in the queue?

Introduction / Context:This is a combined positions problem. “Exactly in the middle” means the number of persons between C and A equals the number between C and B. Convert ranks to positions from the front; then use the back-rank to get the total.

Given Data / Assumptions:

• pos(A) from front = 18.
• pos(C) from front = 20.
• pos(B) from back = 16.
• “C exactly in the middle of A and B” ⇒ the gaps on both sides are equal.

Concept / Approach:If C is the midpoint by count of in-between persons, and A is at 18, C at 20, there is 1 person between A and C. So there must be 1 person between C and B, placing B at 22 from the front. Then use B’s back-rank to get the total.

Step-by-Step Solution:

Verification / Alternative check:Compute B’s from-back rank from N = 37: 37 − 22 + 1 = 16. Matches the given.

Why Other Options Are Wrong:

• 45/46/47/48: Do not satisfy the from-back rank when B is positioned to keep C in the middle.

Common Pitfalls:Interpreting “middle” as average of position numbers instead of equal number of people between; forgetting the +1 in converting a from-back rank to a total.

Final Answer:37