When a teacher counted her student in group 4. There were 2 students left over. When she counted them in groups of 5. She had I student left over. If 15 of her students were girls and she had more girls than boys, how many students did she have?

Step-by-step explanation:

Number of students in her class = x students

x is 2 more than a multiple of 4

This means x is an even number because multiples of 4 are even and adding 2 does not change its parity.

X is also 1 more than a multiple of 5. And we know x is and even number it has to be a multiple of 5 ending in 5, not 0. So 5 + 1 is 6.

All multiples of 4 ending in six are 16, 36, 56 ... and so on

Since there are 15 girls and lower no of boys we need to find out which number of boys are there in 16, 36, 56.

16 - 15 = 1

36 - 15 = 21

And 21 is more than 15 therefore the answer is 16 students. 15 girls and 1 boy.