There are 15 chairs in a row. Position of P is at the middle, and Q is at 12th position counting from the right. How many chairs are there between P and Q ?
3
Three chairs lie between them — option 3.
Step 1 — find P. With 15 chairs in a row, the middle one is
\(\dfrac{15+1}{2}=8\)
so P is 8th from the left. (Seven chairs lie on either side, which is what makes it the middle.)
Step 2 — convert Q to the same reference point. Q is 12th from the right. To express a position from the left :
\(\text{position from left}=\text{total}-\text{position from right}+1=15-12+1=4\)
so Q is 4th from the left.
Step 3 — count what lies between. P is at 8 and Q is at 4, so the chairs strictly between them are those at positions 5, 6 and 7 — three chairs.
The formula is
\(\text{number between}=|8-4|-1=4-1=3\)
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | … | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Who | Q | ✓ | ✓ | ✓ | P |
The two traps. The first is the conversion formula: it is total − position + 1, and forgetting the “+ 1” puts Q at 3 and gives the answer 4, which is option 1. The second is confusing “between” with “from one to the other”: the difference of positions is 4, but that counts one of the endpoints, so the number strictly between is one less.
The general rule to carry away : in a row of n, position from left + position from right = n + 1. That single identity handles every question of this family.
Hence, the answer is 3.
Important Questions from Ordering and Ranking
Three persons A, Band Care standing in a queue not necessarily in the same order. There are 4 persons between Aand B, and 7 persons between Band C. If there are 11 persons ahead of Cand 13 behind A, what could be the minimum number of persons in the queue?
In a class of 60 students, where the number of girls is twice that of boys, Kamal, a boy, ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is:
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled on Monday?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is scheduled between Statistics and English?
Examine the information given in the following paragraph and answer the items that follow: Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture. Which lecture is the last one in the week?
