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 isd divisible by 9, it must be divisible by 3. (c) A number is divisible by 18, if it is 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-prime, 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 su, (i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Question

Philoid · Accepted Answer

(a) False.

For example – 6 is divisible by 3, but it is not divisible by 9.

(b) True.

Example- 18, is divisible by 3 as well as 9 so, yes, If a number is divisible by 9, it must be divisible by 3.

(c) False.

If a number is divisible by 18, it is not neccessory that it is also divisible by 3 and 6.

Example – 42 it is divisible by 6 and 3 but not by 18.

(d) True.

As 9 × 10 = 90 So, if a number is divisible by 9 and 10 both, then it must be divisible by 90.

(e) False.

Example – 15 and 32 are co-prime and composite.

(f) False.

Example – 20 is divisible by 4 but not by 8. So, its not neccessory that all numbers which are divisible by 4 must also be divisible by 8.

(g) True.

As we know 8 = 2 × 4 so all numbers which are divisible by 8 must also be divisible by 2 and 4.

(h) True.

Example – 3 divides 6 and 9 separatly and 15, which is the sum of 9 and 6. So, if a number exactly divides two numbers separately, it must exactly divide their sum.

(i) False.

Example- 2 divide 12 but it doesn’t divide 3 and 9. So, if a number exactly divides the sum of two numbers, its not neccessory that it also divide the two numbers separately.