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 by divisible by 3.

**(iii)** If a number is divisible by 4, it must by 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.

Asked by Sakshi | 1 year ago | 35

**(i) **Right answer is False

**Explanation:-**

Because any number which follows the formula 9n + 3 or 9n + 6 violates the statement.

For example: 6, 12…

**(ii)** Right answer is True

**Explanation:-**

Because 9 is multiple of 3, any number divisible by 9 is also divisible by 3.

**(iii)** Right answer is False

**Explanation:-**

Because any number which follows the formula 8n + 4 violates the statement.

For example: 4, 12, 20….

**(iv)** Right answer is True

**Explanation:-**

Because 8 is multiple of 4, any number divisible by 8 is also divisible by 4.

**(v)** Right answer is False

**Explanation:-**

Because for example 24, this is divisible by both 3 and 6 but not divisible by 18.

**(vi)** IRight answer is True

**Explanation:-**

Because 90 is the GCD of 9 and 10, any number divisible by both 9 and 10 is also divisible by 90.

**(vii)** Right answer is False

**Explanation:-**

Because let us consider an example 6 divide 30, but 6 divides none of 13 and 17 as both are prime numbers.

**(viii)** Right answer is True

**Explanation:-**

Because if x, y and z are three numbers, each of x, y and z is divided by a number (say q), then (x + y + z) is also divisible by q.

**(ix) **Right answer is False

**Explanation:-**

Because 16 and 21 are co-prime but none of them is prime.

**(x) **Right answer is True

**Explanation:-**

Because 3+5=8 which is divisible by 4.

Answered by Aaryan | 1 year agoWhich of the following numbers are divisible by 11:

**(i) **10835

**(ii)** 380237

**(iii)** 504670

**(iv) **28248

In each of the following replace * by a digit so that the number formed is divisible by 11:

**(i) **64 × 2456

**(ii) **86 × 6194

In each of the following replace * by a digit so that the number formed is divisible by 6:

**(i)** 97 × 542

**(ii)** 709 × 94

In each of the following replace × by a digit so that the number formed is divisible by 9

**(i) **49 × 2207

**(ii) **5938 × 623

If 42z3 is a multiple of 9, where z is a digit, what is the value of z?