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.

True, True, False

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False, True, False

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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, True, False
Take an example and visualize-
i) 9 and 4 are co-prime but none of them are prime.
ii) 4 divides 12 and 16 separately
4 also divides 12 + 16 = 28
iii) 14 divides 28, but it does not divide 12 and 16.

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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.

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.

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.

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.

(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.

Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

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The correct option is B False, True, FalseTake an example and visualize- i) 9 and 4 are co-prime but none of them are prime. ii) 4 divides 12 and 16 separately 4 also divides 12 + 16 = 28 iii) 14 divides 28, but it does not divide 12 and 16.

The correct option is B False, True, False
Take an example and visualize-
i) 9 and 4 are co-prime but none of them are prime.
ii) 4 divides 12 and 16 separately
4 also divides 12 + 16 = 28
iii) 14 divides 28, but it does not divide 12 and 16.