Question

If x - y = 8, then which of the following must be
true?
I. Both x and y are positive.
II. If x is positive, y must be positive.
III. If x is negative, y must be negative.
(a) I only
(b) II only
(c) I and II
(d) III only​

Answer 1

Given that: x=y+8x=y+8.

I. Both x and y are positive. Not necessarily true. Consider x=7 and y=-1.

II. If x is positive, y must be positive. Not necessarily true. Consider the same numbers.

III. If x is negative, y must be negative. If x is negative, then we have that x=negative=y+8x=negative=y+8 --> y cannot be a positive number, because in this case y+8y+8 would be positive+positive=positive≠negativepositive+positive=positive≠negative. Thus, in this case y must be a negative number.

Answer: C.

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Answer 2

Answer: I think it will be both I and III

Step-by-step explanation:

If X and y are both positive, it is possible

X+y=8

X=2;y=6

If X is negative , then y must be negative.

X= -2

y= -10

X+y= -2-(-10)= -2+10 = 8