In a queue, Mr. X is fourteenth from the front and Mr. Y is seventeenth from…
2023
In a queue, Mr. X is fourteenth from the front and Mr. Y is seventeenth from the end, while Mr. Z is exactly in between Mr. X and Mr. Y. If Mr. X is ahead of Mr. Y and there are 48 persons in the queue, how many persons are there between Mr. X and Mr. Z?
Answer: C. 8 — ConceptWhen a person is r-th from the end in a queue of N people, that person’s position from the front is N − r + 1. The position exactly midway between…
- A.
6
- B.
7
- C.
8
- D.
9
Show answer & explanation
Correct answer: C
Concept
When a person is r-th from the end in a queue of N people, that person’s position from the front is N − r + 1.
The position exactly midway between positions a and b is (a + b) ÷ 2. The number of people strictly between positions p and q is |p − q| − 1.
Application
Mr. Y’s position from the front is 48 − 17 + 1 = 32.
Mr. X is at position 14 and Mr. Y is at position 32, so Mr. Z’s midpoint position is (14 + 32) ÷ 2 = 23.
The number of people strictly between Mr. X and Mr. Z is 23 − 14 − 1 = 8.
Cross-check
From position 14 to position 23 there are nine position-steps. Removing the endpoint occupied by Mr. Z leaves the intervening positions 15 through 22, which contain eight people.
Result
There are 8 persons between Mr. X and Mr. Z.