Statement 1: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
Statement 2: If a number exactly divides two numbers, then it must also divide the sum of both numbers.

True, True, False

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False, False, True

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False, True, True

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True, True, True

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Solution

The correct option is B
False, False, True

Take an example and visualize:

Statement 1:

14 divides 28, but it does not divide 12 and 16. Therefore, statement 1 is false.

Statement 2:

4 divides 12 and 16 separately and 4 also divides 12+16 = 28, Therefore, statement 2 is true.
Therefore, the option B is correct.

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Similar questions

Statement 1: If two numbers are co-primes, at least one of them must be prime.

Statement 2: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Statement 3: If a number exactly divides two numbers, then it must also divide the sum of both numbers.

Q. State whether the following statements are true or false in the respective order.
Statement 1: If two numbers are co-primes, at least one of them must be prime.
Statement 2: If a number exactly divides two numbers, then it must also divide the sum of both numbers.
Statement 3: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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

Q. If a number exactly divides two numbers, then it must also divide the sum of both numbers.

Question 1

Which of the following statements are true:
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) If a number is divisible by 18, it must be divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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Statement 1: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. Statement 2: If a number exactly divides two numbers, then it must also divide the sum of both numbers.

Statement 1: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
Statement 2: If a number exactly divides two numbers, then it must also divide the sum of both numbers.