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If Y < 0 and -1 < -1 + X/Y < 0, which must be true?

If Y < 0 and -1 < -1 + X/Y < 0, which must be true?

1. X < 0
2. Y/X>1
3. Y^2-X^2 > 0

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Answer

If X is negative, and we already know that Y is negative, than X/Y would have to be positive (a negative divided by a negative is always positive). This means that for all values in which Y is smaller than X, X/Y would be between 0 and 1.

More importantly, X must be negative, because if it were positive, the fraction X/Y would be negative. Statement I must be true. Statement II claims that Y/X>1.

We already know that both X and Y are negative. We also know that Y has a larger absolute value. Statement II must also be true.

On statement III, since we're talking about numbers squared, we can forget about the signs. We only need to figure out which of the two variables is greater. Statement III is true as well.

Correct Answer - Choice E

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