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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.
Asked by Ratna Last Modified
Answer 
Vishaka Bhutia
Home Tutor
(a) False
6 is divisible by 3, but not by 9.
(b) True, as 9 = 3 × 3
Therefore, if a number is divisible by 9, then it will also be divisible by
3.
(c) False
30 is divisible by 3 and 6 both, but it is not divisible by 18.
(d) True, as 9 × 10 = 90
Therefore, if a number is divisible by 9 and 10 both, then it will also be divisible by 90.
(e) False
15 and 32 are co-primes and also composite.
(f) False
12 is divisible by 4, but not by 8.
(g) True, as 8 = 2 × 4
Therefore, if a number is divisible by 8, then it will also be divisible by 2 and 4.
(h) True
2 divides 4 and 8 as well as 12. (4 + 8 = 12)
(i) False
2 divides 12, but does not divide 7 and 5.
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