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Date
45 product of two integers is 630. If one integer is
1-13 Find the other.
Answers
Step-by-step explanation:
Step-I: Given Info
The question tells us about two integers & and asks us if their product is odd.
Step-II: Interpreting the Question Statement
To find if the product of two numbers is odd/even, we need to establish if either of the number is even or not. In case either of the number is even, the product would be even else the product would be odd.
Step-III: Statement-I
Statement- I tells us that is the number of factors of a perfect square, since the no. of factors of a perfect square is odd, we can deduce that is odd. Since is not even, to find the nature of product of & , we need to find if is odd/even.
It’s given that , since we have established that is odd, will also be odd. Subtracting 1 from an odd number will give us an even number, hence we can deduce that is even.
Since, we know now that is even it is sufficient for us to deduce that the product of & would be even.
Thus Statement-I is sufficient to get the answer.
Step-IV: Statement-II
Statement- II tells us that is a product of two consecutive prime numbers, so may be even if one of the prime number is 2 and may be odd if none of the prime number is 2. So, we can’t establish with certainty the even/odd nature of .
The statement also tells us that odd, since 3 is an odd number, would also be odd and subtracting an odd from an odd number would give us an even number. So, we can rewrite
even which would imply that either both , are even or both are odd. In both the cases the nature of product of & can’t be established with certainty, it will be even if both & are even and will be odd if both & are odd.
So, Statement- II is not sufficient to answer the question.
Step-V: Combining Statements I & II
Since, we have a unique answer from Statement- I we don’t need to be combine Statements- I & II.
Hence, the correct answer is Option A