# 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) 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-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.

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

To do:

We have to find which of the given statements is true.

Solution :

(a) We know that,

If a number is divisible by another number, it is divisible by its factors.

Therefore,

If a number is divisible by 9 it is divisible by 3 but the converse is not necessarily true.

For example,

12 and 15 are divisible by 3 but not by 9.

Therefore, if a number is divisible by 3 it may not be divisible by 9.

The given statement is false.

(b) We know that,

If a number is divisible by another number, then it is divisible by its factors.

Therefore,

If a number is divisible by 9 it is divisible by 3

The given statement is true.

(c) A number is divisible by 18 if it is divisible by both 9 and 2.

The given statement is false.

(d) A number is divisible by 90 if it is divisible by both 9 and 10.

The given statement is true.

(e) When two numbers have no common factors other than 1, then the numbers are co-prime.

8 and 9 are co-primes but both 8 and 9 are not prime numbers.

(f) For example,

12 is divisible by 4 but is not divisible by 8.

Therefore, the given statement is false.

(g) 4 is a factor of 8.

This implies,

All numbers which are divisible by 8 must also be divisible by 4.

Therefore, the given statement is true.

(h) For example,

2 divides 6 and 10.

$6 + 10 = 16$

$16$ is also divisible by 2.

Therefore, the given statement is true.

(i) $10+30=40$ is divisible by 4 but both 10 and 30 are not divisible by 4.

The given statement is false.

Updated on 10-Oct-2022 13:30:33