Agroup of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. what is the sum of the two smallest possible values of n?

  46

Step-by-step explanation:

The smallest value of n (found by trial and error) is 13. The next larger value is 4·5 = 20 more than that, 33.

The sum of these values is 13 +33 = 46.

Actually, we looked for solutions to ...

  n = 4k +1 = 5m +3

  4k -5m = 2 . . . . . . subtract 5m+1

We found the smallest solution to be k=3, m=2 giving 12 -10 = 2. Then further solutions are of the form ...

  k = 5p+3, m = 4p+2 . . . . . for any integer p

The corresponding values of n are ...

  n = 4(5p+3)+1 = 20p+13

The two smallest values correspond to p=0 and p=1, so are 13, 33.

d

step-by-step explanation:

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.