a school is divided into 4 houses,P,Q,R and S.On sports day,the students line up so that a student from P is first in line,then a student from Q then a student from R then a student from S,then a student from P and so on with same order repeating.From what house will the 66th student come?
every 4 days the cycle is complete.
After 64 days, we're back to the start.
so, the 66th student will be from Q.
To determine the house from which the 66th student will come, we need to understand the pattern of the students lining up.
Since there are 4 houses, the pattern repeats every 4 students.
- For the 1st student, it will be from house P
- For the 2nd student, it will be from house Q
- For the 3rd student, it will be from house R
- For the 4th student, it will be from house S
This pattern repeats for every four students, with each house taking its turn.
To find the house from which the 66th student will come, we can divide 66 by 4 and determine the remainder. If the remainder is 1, the student will be from house P. If the remainder is 2, the student will be from house Q, and so on.
In this case, when we divide 66 by 4, we get a remainder of 2. Therefore, the 66th student will be from house Q.