Final answer:
The only correct statement about Reena's number, which is divisible by both 13 and 19, is that it is a common multiple of these two numbers. Hence, the accurate answer is that B)only Karan's statement is correct.
Step-by-step explanation:
Reena wrote a number that is divisible by both 13 and 19. We need to evaluate if this number can only be odd, if it is a common factor, or a common multiple of 13 and 19.
Tina claims the number can only be odd. However, the product of any two numbers, regardless of them being odd or even, can result in even or odd numbers. There is no rule which stipulates that a multiple of these two specific numbers (13 and 19) must be odd. Therefore, Tina's statement cannot be considered universally correct.
Mohan says it is a common factor of 13 and 19. This is incorrect, as common factors are numbers that divide into other numbers without a remainder. In the case of 13 and 19, which are both prime, the only common factor is 1, not their multiples.
Karan says it is a common multiple of 13 and 19. This is accurate, as any number Reena writes that is divisible by both 13 and 19 is by definition a common multiple of the two.
The correct statement about the number Reena wrote, which is divisible by both 13 and 19, is that it is a common multiple of these two numbers. Therefore, the correct answer is B) Only Karan.