A SCHOOL IS DIVIDED INTO 4 HOUSES P,Q,R,S. ON SPORTS DAY,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? PLEAE EXPLAIN HOW OU WORK IT OUT,THANKS

Answer 1

House P has students numbers
1 5 9 13 17 ........ (4n-3)
House Q has students numbers
2 6 10 14 ...... (4n-2)
etc

4n-3 = 66
4n = 69 --> no whole number solution

4n-2 = 66
4n = 68
n = 17 ----- Yeah
The 66th student is in house Q

or

make 4 columns
P...Q...R....S
1 .. 2 .. 2 .. 4
5 .. 6 .. 7 .. 8
9 .. 10 11 12
13 14 15 16
17 18 19 20
...
65 66 67 68

for P -- remainder of 1 when divided by 4
for Q -- remainder of 2 when divided by 4 ---- 66
for R -- remainder of 3 when divided by 4