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I got E as response. 1=> not sufficient because for {x=-1/2 and y=-1} and {x=1/2 and y=0}, can't answer 2=> not sufficient also by the same way Combining the two we have (1)=> x-y=1/2 and (2)=> x-y>0 So the first implies the second, can't tell.

Is there a way to solve these type of problems algebrically?

we know each statement alone is insuff

To resolve for C and E :

1) x-y=1/2

2) x/y>1

easy way; divide 1) by x

1-(y/x) =1/(2*x) ; left hand side quantity will be positive given the condition 2) and so x will be +ve ; since x/y>1 if x is positive y is also positive and you can click on C for answer.

A) 2x - 2y = 1 This could be simplified into 2(x-y) = 1 (x-y) = 1/2 We are not given any info about the values of x or y, so this by itself is NS

B) x/y > 1 This could be simplified in two ways. If y is positive, then x > y, subtract y from both sides of the inequality and you get x - y > 0 If y is negative, then x < y, subtract y from both sides of the inequality and you get x - y < 0 We aren't given any info on x or y so this by itself is NS

From looking at information A), we could see that x - y is 1/2, which is a positive number. From b) we could see that the first simplified inequality, x - y > 0, is the one we choose. Since y is positive, x must be a larger number than y so we have proof that both x and y are positive. Correct Answer: C.