Being exactly divisible by 4 is a ______ condition for a number being even. Options: - Necessary - Sufficient
Answer (1)
In order to solve this question, we need to understand the concepts of 'necessary' and 'sufficient' conditions in the context of divisibility and even numbers.
Even Numbers : A number is considered even if it is divisible by 2, meaning there is no remainder when the number is divided by 2.
Divisibility by 4 : A number is divisible by 4 if when you divide it by 4, the remainder is 0.
Let's break it down:
Necessary Condition : A necessary condition must be met for a statement to be true. For example, if being divisible by 4 was necessary for a number to be even, then every even number would also have to be divisible by 4. However, this is not the case. Numbers like 2, 6, and 10 are even, but they are not divisible by 4.
Sufficient Condition : A sufficient condition means that if the condition is met, the statement must be true. If a number is divisible by 4, it's certainly divisible by 2, and thus it is even. So, divisibility by 4 guarantees that a number is even.
Therefore, being divisible by 4 is a 'sufficient' condition for a number to be even, but not a 'necessary' condition.
Thus, the answer is: Sufficient .
