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Agree. I also got to the same conclusion but was not sure. I believe it is C also.
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

guys wat is the best way to solve such diffcult problems, other than picking numbers??

the confusion starts when u have to decide whether it is C or E .........

Picking numbers is often necessary in DS inequality problems.

The most important thing is to simplify or rearrange the inequality, in order to ease picking numbers. Look at this case:

If you have

y-2 < x < 2y-6

you instantly see that y>4, since otherwise the inequality won't be fullfilled. If you don't arrange it like this, its hard and time consuming to find the actual set; And the problem beteen E and C may become more apparent.

This question will be easier if you know how to sketch linear graph.

Basic rule for plotting linear graph

1) know basic form of linear graph y = ax + b
2) give x = 0, y = b
3) and give y = 0, x = -b/a
4) When you have (0,b) and (-b/a,0), you can sketch graph quickly

A little note about inequality
1) y > ax + b means all area above ax + b graph
2) y < ax + b means all area below ax + b graph

Ok! now go to our question.

xy > ?

1) x - y > -2 or y < x + 2
sketch graph and see the area below this graph, the area will include quadrant 4 which x is always positive and y is always negative (eg. (5, -4) (2, -3))

xy < 0 in quadrant 4; therefore, 1) is insuff.

2) x - 2y < -6 or y > (x/2) + 3
Sketch graph and notice the area above this graph, the area will include quadrant 2 which x is always negative and y is always positive (eg. (-2, 3) (-1, 8)

xy < 0 in quadrant 2; therefore, 2) is insuff.

3) consider 1) and 2) you will get y < x + 2 and y > (x/2) + 3
these two graph will cross each other at point (2, 4) in quadrant 1
the area of graph 1) and 2) will intersect. The intersect area will appear only in quadrant 1 which x and y are always positive

xy > 0 always; therefore, answer is C)

P.S. Sorry if you have a hard time understand my explanation, English is my second language.

this can be solved using simultaneous equations, since we have two equations,

1. x - y > -2 2. x - 2y < -6

we get X > 2 & Y > 4

Goood solution!
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."