48 DS with inequalities

[ern5231]

1)Is X-y greater than zero?

(1) 2x-y is greater than 0
(2) Y is less than 0

2)Is 5x + y greater than 0?

(1) x-y is greater than 0
(2) xy is greater than 0

[marie]

IMO the answer is C. What is OA? Here is my work. Let me know if there is a shorter/quicker way to resolve.
I) Is x-y > 0
1) 2x-y>0
2) y<0

From the stem we can rephrase and the question becomes Is x>y?

Statement 1: Can be rephrased to state that 2x>y. Pick numbers for x, lets try x=2. For x=2 this implies y is any value less than 4 which includes both positive and negative numbers. Can we say then that x>y? Sometimes yes, sometimes no. INSUFFICIENT

Statement 2: Says that y is negative. Picking numbers we can find values of x and y such that sometimes x>y and sometimes not, i.e., x=-2 y=-4 and x=-4 y=-2. INSUFFICIENT

Together: We have 2x>y and y is negative. Pick numbers using x=2 from our work in Statement 1 we know that y is any value less than 4 which includes both positive and negative numbers. However add the restriction from Statement 2 that y is negative and we can see that x is always greater than y. But wait! What happens when x is negative? Pick a number x= -2. This implies from Statement 1 that y is less than -4 which is also always negative. Is x>y? Yes Always. SUFFICIENT

Answer C


IMO the answer this answer is E. What is OA? Here is my work. Let me know if there is a shorter/quicker way to resolve.

II) Is 5x + y > 0?

(1) x-y > 0
(2) xy > 0

Statement 1 can be rephrased to state that x>y. We can pick numbers for x and y to show that sometimes 5x+y>0 and sometimes not when x>y, i.e., x=4 y=2, x=1 y=-5 and x=-2 y=-6. INSUFFICIENT

Statement 2 implies that x and y have the same sign, i.e., are both positive or are both negative. INSUFFICIENT since this only means the sum will be either positive or negative which menas sometimes the sum will be greater than 0 and sometimes not.

Together: INSUFFICIENT since x=4 y=2 and x=-2 y=-6 gives different results.

ANSWER E

[crackgmat007]

1. C
2. E