Among the given statements, the true statements are:
- If a number is divisible by 3 and 4, then it is divisible by 12.
- The number 119 is a composite number.
In the question, we are asked for the true statements among the given options:
1. All even numbers are composite numbers.
Answer - False
Reason - 2 is an even number, which is not a composite number.
2. If a number is divisible by 3 and 4, then it is divisible by 12.
Answer - True
Reason - If any number, n, is divisible by any two numbers, x and y, then it is also divisible by their LCM, and the LCM of 3 and 4 is 12.
3. All prime numbers are odd numbers.
Answer - False
Reason - 2 is a prime number, which is not odd.
4. The number 119 is a composite number.
Answer - True
Reason - The number 119 is a composite number, as it is not a prime number, as it is divisible by 7 and 17 too, other than 1 and itself.
5. 12 is a factor of 6.
Answer - False.
Reason - When 6 is divided by 12, the integral quotient that we get is 0, and the remainder is 6, but for any number x, to be a factor of y, on dividing y by x, the remainder should be 0.
6. If a number is divisible by 6 and 4, then it is also divisible by 4.
Answer - False
Reason - If any number, n, is divisible by any two numbers, x and y, then it is also divisible by their LCM, and the LCM of 6 and 4 is 12.
Thus, a number divisible by 6 and 4 is divisible by 12 but not necessarily by 24. Example 12 is divisible by both 6 and 4 but not divisible by 24.
Thus, among the given statements, the true statements are:
- If a number is divisible by 3 and 4, then it is divisible by 12.
- The number 119 is a composite number.
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