If Mrs Murphy separates her class into groups of 4 students each, 1 student is left over. If she separates her class into groups of 5 students each, 2 students are left over. What is the least number of students the class could have?

The question means that when the number is 1 more than a multiple of 4 and two more than a multiple of 5. Write out multiples of 4 with one added on to them.

5,9,13,17,21,

Then write out multiples of 5 with one added on to them

7,12,17,22,

The smallest number that both lists share is 17, so that is the answer