Which of the following statements is true?
(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.
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(a) False, 6 is divisible by 3 but is not divisible by 9
(b) True, as 9 = 3 × 3. Hence, if a number is divisible by 9, it will also be divisible by 3
(c) False. Since 30 is divisible by both 3 and 6 but is not divisible by 18
(d) True, as 9 × 10 = 90. Hence, if a number is divisible by both 9 and 10 then it is divisible by 90
(e) False. Since 15 and 32 are co-primes and also composite numbers
(f) False, as 12 is divisible by 4 but is not divisible by 8
(g) True, as 2 × 4 = 8. Hence, if a number is divisible by 8, it will also be divisible by 2 and 4
(h) True, as 2 divides 4 and 8, and it also divides 12 (4 + 8 = 12)
(i) False, since 2 divides 12 but it does not divide 7 and 5
