Students in a marching band want to line up for their performance. The problem is that when they Line up in twos there is 1 left over. When they line up in threes there are 2 left over. When they line up in fours there are 3 left over. When they line up in fives there are 4 left over. When they line up in sixes there are 5 left over. When they line up in sevens there are no students left over. How many students are there?

x = 119

Step-by-step explanation:

Solution:-

- The number of students in a marching band = x

- When they Line up in "twos" there is 1 left over, That if we mathematically express it:

Division: x / 2, Remainder = 1

- When they Line up in "threes" there is 2 left over, That if we mathematically express it:

Division: x / 3, Remainder = 2

- When they Line up in "fours" there is 3 left over, That if we mathematically express it:

Division: x / 4, Remainder = 3

When they Line up in "fives" there is 4 left over, That if we mathematically express it:

Division: x / 5, Remainder = 4

When they Line up in "sixes" there is 5 left over, That if we mathematically express it:

Division: x / 6, Remainder = 5

When they Line up in "sevens" there are no left over, That if we mathematically express it:

Division: x / 7, Remainder = 0

- It means that the total number of "x" students are perfectly divisible by 7. If it is not divisible by 2, then it is an odd number.

- So,

x = 7 * a

Where, x > 7 and exclude derivative multiples of (5, 4, 6)

- So from trial and error, a = 17

x = 119