If the sum of the digits in a number is a _____ of 3, then the number is divisible by 3.

Given below are two pairs of statements. Combine these two statements using if and only if: p: if the sum of the digits of a number is divisible by 3, then the number is divisible by 3.q: if a number is divisible by 3, then the sum of its divisible by 3.

Given below are some pairs of statements. Combine each pair using if and only if: (i) p: If a quadrilateral-is equiangular, then it is a rectangle. q: If a quadrilateral is a rectangle, then it is equiangular. (ii) p: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q: If a number is divisble by 3, then the sum of its digits is divisible by 3. (iii) p: A quadrilateral is a parallelogram if its diagonals bisect each other. q: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. (iv) p: If f(a) = 0, then (x -a) is a factor of polynomial f(x). q: If (x-a) is a factor of polynomial f(x), thenf(a) = 0. (v) p: If a square matrix A is invertible, then |A| is nonzero. q: If A is a square matrix such that |A| is nonzero, then A is invertible.

Given below are two pairs of statements. Combine these two statements using "if and only if". (i) p: If a rectangle is a square, then all its four sides are equal. q: If all the four sides of a rectangle are equal, then the rectangle is a square. (ii) p: If the sum of digits of a number is divisible by 3, then the number is divisible by 3. q: If a number is divisible by 3, then the sum of its digits is divisible by 3.

The sum of all the 3 digit numbers is

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 9.

If the sum of digits of a number is divisible by three, then the number is always divisible by

How many positive integers less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3 ?