I couldn't find this problem in the search results. I am confused by the below GPrep question:
If x is not equal to y, is (x-y)/ (x+y) < 1?
1) x>0
2) y<0
I rephrased the question to be the following:
Case 1: x+y>0
Cross multiply to get: x-y < x+y
-y < y
0 < 2y
0 < y
Case 2: x-y<0
Cross multiply and switch inequality sign: x-y > x+y
-y > y
0 > 2y
0 > y
So the rephrased question is asking: "Is y>0 or y<0?"
Looking at (1), X is not involved in the rephrase that contains only y, so it is irrelevant and hence insufficient.
Looking at (2), y<0 is given and answers the rephrased question of "is y<0" and the answer is yes. So I assumed B.
[spoiler]But the official answer is E. I realize that I could plug in numbers to get this answer, but isn't that time consuming? Why did my approach not work?[/spoiler]
If x is not equal to y, is (x-y)/ (x+y) < 1?
1) x>0
2) y<0
I rephrased the question to be the following:
Case 1: x+y>0
Cross multiply to get: x-y < x+y
-y < y
0 < 2y
0 < y
Case 2: x-y<0
Cross multiply and switch inequality sign: x-y > x+y
-y > y
0 > 2y
0 > y
So the rephrased question is asking: "Is y>0 or y<0?"
Looking at (1), X is not involved in the rephrase that contains only y, so it is irrelevant and hence insufficient.
Looking at (2), y<0 is given and answers the rephrased question of "is y<0" and the answer is yes. So I assumed B.
[spoiler]But the official answer is E. I realize that I could plug in numbers to get this answer, but isn't that time consuming? Why did my approach not work?[/spoiler]
