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.

True, True, False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False, False, True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False, True, True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

True, True, True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
False, False, True

Take an example and visualize-

i) C0-prime do not have any factors in common other than 1; Consider the numbers 9 and 4 ; They are co-prime but both of them are not prime.Hence the 1st statement is false.

ii) Now, 12 + 16 = 28; but 28 does not divide 12 and 16.Hence the second statement is false.

iii) Consider the numbers 4, 12 and 16
12 and 16 are both divisible by 4 and also sum of 12 + 16 = 28 is divisible by 4; Hence the third statement is true

4 also divides 12+16 = 28

Suggest Corrections

Similar questions

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.

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

Join BYJU'S Learning Program

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.