Discussion
Consider the following pairs:
| 1. | A number divisible by 2 and 3 | Divisble by 6 |
| 2. | A number divisible by 4 | Divisble by 8 |
| 3. | A number divisible by 5 and 10 | Divisible by 10 |
How many of the above pairs are correctly matched?
Answer: B
Only two pairs are correctly matched.
Pair 1 is right: 2 and 3 are coprime, so a number divisible by both is divisible by their product, 6.
Pair 2 is wrong: 4, 12 and 20 are divisible by 4 but not by 8. Divisibility passes down to factors, not up to multiples.
Pair 3 is right: the condition already includes divisibility by 10, and divisibility by 5 adds nothing, because 5 is a factor of 10. Note that the rule in pair 1 does not extend to non-coprime pairs: divisible by 2 and 4 does not mean divisible by 8.
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