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 |  49

1 Answer

Solution :-

(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 ago

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