Is x + y positive?(1) x - y is positive.(2) y - x is negative.

Question

A.if statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not;
B. if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;
C.if statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient;
D.if either statement by itself is sufficient to answer the question;
E.if statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem

Answer 1

Let: x = 2 and y = 1

Then,

x – y > 0
2 – 1 > 0
1 > 0 True

y – x < 0
1 – 2 < 0
–1 < 0 True

x + y > 0
2 + 1 > 0
3 > 0 True

Now let’s use some negative numbers. We always want to check all possibilities including zero, if there is no restriction. This includes fractions when appropriate.

Let: x = –1 and y = –2

x – y > 0
–1 – (–2) > 0
1 > 0 True

y – x < 0
(–2) – (–1) < 0
–1 < 0 True

x + y > 0
–1 + (–2) > 0
–3 > 0 False

Therefore, answer choice E is correct.

 

Answer 2

Let's use 3 for x and -5 for y 

 

X- y = 3 - (-5)= 3+5 = 8

 

Y - X = -5 - 3 = -8 

 

X + y = -2

 

E