If x is a positive odd integer and y is a negative even integer, which

If x is a positive odd integer and y is a negative even integer, which of the following must be true?

A. x^3 + y is a positive odd integer
B. x^2 + y^2 is a negative odd integer
C. x^0 + y^11 is a negative odd integer
D. x + y is a positive odd integer
E. x + y is a negative odd integer

If X - positive odd integer and y is a negative even integer.

Lets assume x = 1 and y = -2.

A: Not True - Eliminate.
B: This statement is always positive. Not true. Eliminate.
C: This is true based on assumed values - Keep.
D: 1 + (-2) = -1 Hence not a positive odd no - Eliminate.
E: 1 + (-2) = -1. True. Keep.

So we are left with C and E.

For E - if x is 101 and y is -2; x + y is 99 (positive odd). Hence not always true.

Therefore Answer C.

Option C

Odd: O, Even: E & Fraction: F.
x = +O & y = -E

A. x^3 + y is a positive odd integer : (+O)^3 + (-E) = O - E = O or -O
B. x^2 + y^2 is a negative odd integer : (+O)^2 + (-E)^2 = O + E = +O
C. x^0 + y^11 is a negative odd integer : (+O)^0 + (-E)^11 = 1 - E = -O
D. x + y is a positive odd integer : (+O) + (-E) = +O or -O
E. x + y is a negative odd integer : (+O) + (-E) = +O or -O

We are given that x is a positive odd integer and y is a negative even integer, and we need to determine which answer choice is true. Let’s examine the answer choices.

A) x^3 + y is a positive odd integer

Although x^3 is odd and y is even, since we do not know the relative value of each number, we cannot determine whether x^3 + y is positive. Thus, answer choice A does not have to be true.

B) x^2 + y^2 is a negative odd integer

The sum of two squares can never be negative. Answer choice B cannot be true.

C) x^0 + y^11 is a negative odd integer

Since x^0 = 1 and y is a negative even integer, we know that y^11 is a negative integer less than -1, and thus x^0 + y^11 is a negative odd integer.

Answer: C