Question

When I distribute a packet of chocolates to 7 students, I am left with 4 chocolates. When I distribute the same packet of chocolates to 11 students, I am left with 6 chocolates. How many chocolates will be left with me if I distribute the same packet of chocolates among 13 students (a packet of chocolate contains total number of N chocolates, where 1000 < N <1050)?

• A. 2
• B. 6
• C. 7

Answer 1

Let the number is 11 x+ 6
Divide (11x+6) by 7
$\frac{11x+6}{7}=\frac{7x+4x+6}{7}=\frac{4x+6}{7}$
Now, substitute the value of x in (4x + 6), so that the remainder will be 4, which is x = 3.
Therefore, the value of 11x + 6 = 39. Now, the remainder 39 when divided by 13 is zero.
It remains same for every number that satisfy the given condition.