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Consider the following statements: Statement 1: A number which is exactly divisible by 2 is always a composite number Statement 2: A number which is exactly divisible by 2 is always an even number. Which one of the following is correct about the above statements?
- a)Statement 1 is true and 2 is false
- b)Statement 1 is false and 2 is true
- c)Both statements are false
- d)Both statements are true
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements: Statement 1: A number which is exac...
Statement 1: A number which is exactly divisible by 2 is always a composite number.
Statement 2: A number which is exactly divisible by 2 is always an even number.
The correct answer is Option B: Statement 1 is false and 2 is true.
Explanation:
To understand the correctness of the statements, let's define the terms mentioned in the statements.
Composite Number: A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself. In simpler terms, a composite number is a number that can be divided evenly by numbers other than 1 and itself.
Even Number: An even number is an integer that is evenly divisible by 2. In other words, an even number can be divided by 2 without leaving a remainder.
Now let's evaluate each statement separately:
Statement 1: A number which is exactly divisible by 2 is always a composite number.
This statement is false. A number that is divisible by 2 does not necessarily have to be a composite number. For example, the number 2 is divisible by 2 but it is not a composite number. It is a prime number since it only has two positive divisors, 1 and 2. Therefore, statement 1 is false.
Statement 2: A number which is exactly divisible by 2 is always an even number.
This statement is true. By definition, an even number is one that can be divided by 2 without leaving a remainder. Therefore, any number that is exactly divisible by 2 will always be an even number. For example, 4, 10, 20, etc. are all divisible by 2 and they are also even numbers. Hence, statement 2 is true.
Therefore, the correct answer is Option B: Statement 1 is false and 2 is true.
Statement 2: A number which is exactly divisible by 2 is always an even number.
The correct answer is Option B: Statement 1 is false and 2 is true.
Explanation:
To understand the correctness of the statements, let's define the terms mentioned in the statements.
Composite Number: A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself. In simpler terms, a composite number is a number that can be divided evenly by numbers other than 1 and itself.
Even Number: An even number is an integer that is evenly divisible by 2. In other words, an even number can be divided by 2 without leaving a remainder.
Now let's evaluate each statement separately:
Statement 1: A number which is exactly divisible by 2 is always a composite number.
This statement is false. A number that is divisible by 2 does not necessarily have to be a composite number. For example, the number 2 is divisible by 2 but it is not a composite number. It is a prime number since it only has two positive divisors, 1 and 2. Therefore, statement 1 is false.
Statement 2: A number which is exactly divisible by 2 is always an even number.
This statement is true. By definition, an even number is one that can be divided by 2 without leaving a remainder. Therefore, any number that is exactly divisible by 2 will always be an even number. For example, 4, 10, 20, etc. are all divisible by 2 and they are also even numbers. Hence, statement 2 is true.
Therefore, the correct answer is Option B: Statement 1 is false and 2 is true.
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Consider the following statements: Statement 1: A number which is exactly divisible by 2 is always a composite number Statement 2: A number which is exactly divisible by 2 is always an even number. Which one of the following is correct about the above statements?a)Statement 1 is true and 2 is falseb)Statement 1 is false and 2 is truec)Both statements are falsed)Both statements are truee)None of theseCorrect answer is option 'B'. Can you explain this answer?
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