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The product xy can be anything, because x can be 1 trillion, say, and y can be negative (so xy can be very very negative) or positive (so xy can be very very positive). So A and C do not need to be true. If you then notice that D and E say the same thing (multiply D by -1 on both sides, reversing the inequality when you do, and you get E) then you can be sure neither of them can be the right answer, because if one were always true, the other would be too, and then the question would have two different right answers, which is impossible. So the answer has to be B.

We can prove that though: if x > 2, then -x < -2. If y > -1, then 2y > -2. So putting these two inequalities together, -x < -2 < 2y, and -x < 2y.
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Bunuel
If \(x>2\) and \(y>-1\), then which of the following statements must be true?

A. \(xy>-2\)
B. \(-x<2y\)
C. \(xy<-2\)
D. \(-x>2y\)
E. \(x<-2y\)

We can let x = 3 and y = 0, we see that choices A and B are true while the other ones are false. Now let’s let x = 3 and y = -0.9, we see that xy = -2.7 which is not greater than -2. However, -x = -3, which is less than 2y = -1.8. So only B is the correct answer.

Answer: B
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Hello from the GMAT Club BumpBot!

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