If a number is divisible by both 6 and 5 then it must be divisible by all the following numbers except ______.

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answer is D.

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Detailed Solution

According to the rule of divisibility, if a number is divisible by two co-prime numbers then it is divisible by their product also.

In the given question, the number is divisible by 6 and 5.

Factors of 5: 1, 5
Factors of 6: 1, 2, 3, 6

We can see that the only common factor between the two numbers is 1. Therefore, these two numbers are co-prime numbers. That means if a number is divisible by both 6 and 5 then it must be divisible by their product which is 30.

According to another rule of divisibility, if a number is divisible by another number then it is divisible by each of the factors of that number.
Therefore, the number will be divisible by 2 and 3.

However, the number may or may not be divisible by 11. Therefore, option D is the correct answer.

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