(i) All numbers divisible by 3 must also be divisible by 6

(ii) All numbers divisible by 6 must also be divisible by 3

(i) is False, (ii) is True

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(i) is False, (ii) is False

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(i) is True, (ii) is True

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(i) is True, (ii) is False

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Solution

The correct option is A
(i) is False, (ii) is True

If a number is divisible by a number 'n', it is also divisible by the factors of 'n'.

Factors of 6 = 1, 2, 3, 6

Any number divisible by 6 will also be divisible by 3.

But vice-versa is not true.

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Similar questions

Choose the correct option regarding the accuracy of the given statements:
Statement 1: All numbers divisible by 4 must also be divisible by 8
Statement 2: All numbers divisible by 8 must also be divisible by 4

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. All numbers that are divisible by 3 are also divisible by 6.

18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by 4 × 6 = 24? If not, give an example to justify our answer:

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(i) All numbers divisible by 3 must also be divisible by 6 (ii) All numbers divisible by 6 must also be divisible by 3

The correct option is A (i) is False, (ii) is True If a number is divisible by a number 'n', it is also divisible by the factors of 'n'. Factors of 6 = 1, 2, 3, 6 Any number divisible by 6 will also be divisible by 3. But vice-versa is not true.

(i) All numbers divisible by 3 must also be divisible by 6

(ii) All numbers divisible by 6 must also be divisible by 3

The correct option is A
(i) is False, (ii) is True

If a number is divisible by a number 'n', it is also divisible by the factors of 'n'.

Factors of 6 = 1, 2, 3, 6

Any number divisible by 6 will also be divisible by 3.

But vice-versa is not true.