Since we have one positive and one negative multiple, the resulting product must be negative. 

By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number.  When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8.  Plugging in the other options gives a positive answer.  You can try other negative numbers, if needed, to confirm this still works. 

x: –7 – 7= –7 + –7 = –14

y: –7 – (–7) = –7 + 7 = 0

when subtracting a negative number, turn it into an addition problem

Subtracting a negative number is just like adding its absolute value.

If the largest of the three consecutive odd integers is d, then the three numbers are (in descending order):

d, d – 2, d – 4

This is true because consecutive odd integers always differ by two. Adding the three expressions together, we see that the sum is 3d – 6.

Since  and must be positive, eliminate choices with negative numbers or zero. Since they must be distinct (different), eliminate choices where .  This leaves 4 and 5 (which is the only choice that does not add to 20), and the correct answer, 5 and 15.

Consecutive odd integers differ by 2. If the smallest integer is x, then

x + (x + 2) + (x + 4) = 93

3x + 6 = 93

3x = 87

x = 29

The three numbers are 29, 31, and 33, the largest of which is 33.

The odd/even status of  is not known, so no information can be determined about that of .

 is known to be an integer, so  is an even integer. Added to odd number , an odd sum is yielded; this is .

 is known to be odd, so  is also odd. Added to odd number , an even sum is yielded; this is .

 is known to be even, so  is even. Added to odd number ; an odd sum is yielded; this is .

The numbers known to be odd are  and ; the number known to be even is ; nothing is known about .

A power of an integer takes on the same odd/even status as that integer. Therefore, without knowing the odd/even status of , we do not know that of , and, subsequently, we cannot know that of . As a result, we cannot know the status of any of the other values of the other three variables in the subsequent statements. Therefore, none of the four choices are correct.

, the product of an even integer and another integer, is even. Therefore,  is equal to the sum of an odd number  and an even number , and it is odd.

, the product of odd integers, is odd, so , the sum of odd integers  and , is even.

, the product of an odd integer and an even integer, is even, so , the sum of an odd integer  and even integer , is odd.

, the product of odd integers, is odd, so , the sum of odd integers  and , is even.

The correct response is that  and  are odd and that  and  are even.