If x is an odd negative integer and y is an even integer, which of the following statements must be ...
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer
Answer/Solution
I
Steps/Work
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (x - 2y) is odd
x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 - x) is an odd negative integer
y can be 0 => -x will be positive => III statement is not true
basing on above, only I statement will always be true
answer is D
I. (x - 2y) is odd
x - is always negative and odd
2y - can be 0, when y=0, or always even integer (positivie or negative)
odd integer +/- even integer = always odd
I statement is always true
II. xy^2 is an even negative integer
y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true
III. (y^2 - x) is an odd negative integer
y can be 0 => -x will be positive => III statement is not true
basing on above, only I statement will always be true
answer is D