Which of the following statements are true?(i) If a number exactly d

1.	Which of the following statements are true?(i) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.(ii) If a number divides three numbers exactly, it must divide their sum exactly.(iii) If two numbers are co-prime, at least one of them must be a prime number.(iv) The sum of two consecutive odd numbers is always divisible by 4.
Answer» (i) False If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately. Because let us consider an example 6 divide 30, but 6 divides none of 13 and 17 as both are prime numbers. (ii) True If a number divides three numbers exactly, it must divide their sum exactly. Because if x, y and z are three numbers, each of x, y and z is divided by a number (say q), then (x + y + z) is also divisible by q. (iii) False If two numbers are co-prime, at least one of them must be a prime number. Because 16 and 21 are co-prime but none of them is prime. (iv) True The sum of two consecutive odd numbers is always divisible by 4. Because 3+5=8 which is divisible by 4.

Which of the following statements are true?(i) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.(ii) If a number divides three numbers exactly, it must divide their sum exactly.(iii) If two numbers are co-prime, at least one of them must be a prime number.(iv) The sum of two consecutive odd numbers is always divisible by 4.

Answer»

(i) False

If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

Because let us consider an example 6 divide 30, but 6 divides none of 13 and 17 as both are prime numbers.

(ii) True

If a number divides three numbers exactly, it must divide their sum exactly.

Because if x, y and z are three numbers, each of x, y and z is divided by a number (say q), then (x + y + z) is also divisible by q.

(iii) False

If two numbers are co-prime, at least one of them must be a prime number.

Because 16 and 21 are co-prime but none of them is prime.

(iv) True

The sum of two consecutive odd numbers is always divisible by 4.

Because 3+5=8 which is divisible by 4.