f m and p are positive integers and (m + p) x m is even, which of the following must be true?
A. If m is odd, then p is odd.
B. If m is odd, then p is even.
C. If m is even, then p is even.
D. If m is even, then p is odd.
I choose C is that correct
I choose C but not sure if that's correct
for addition:
the sum of 2 odds is even
e.g. 3+5 = 8
the sum of 2 evens is even
the sum of an even and an odd is odd
e.g. 3 + 4 = 7
for multiplication:
odd x odd = odd, e.g. 3x5=15
even x even = even , e.g. 6x8 = 48
even x odd = even , 4 x 5 = 20
assuming x is also an integer and we have (m+p)(x), it will depend on whether x is even or odd
I suggest you take some actual values of m , p, and x
and test the cases.
The you will be sure of your choice.
No, that is not correct. The correct answer is D. If m is even, then p must be odd.
Since (m + p) x m is even, the product of m and (m + p) must be even.
For the product to be even, at least one of m or (m + p) must be even.
If m is odd, then (m + p) must be even for the product to be even. Therefore, p must be odd.
If m is even, then it satisfies the condition that at least one of m or (m + p) is even. In this case, p can be either even or odd. Therefore, the statement "If m is even, then p is even" is true.
To determine which of the options must be true, we need to analyze the given information.
We know that (m + p) x m is even. To obtain an even product, either (m + p) or m must be even, or both.
Case 1: (m + p) is even, and m is odd.
In this case, since the sum of an even number and an odd number is always odd, p must be odd for (m + p) x m to be even.
Case 2: (m + p) is odd, and m is even.
In this case, since the sum of an odd number and an even number is always odd, p can be either even or odd for (m + p) x m to be even.
Therefore, the correct answer is not C but A: If m is odd, then p is odd.