1 tells you that x is smaller than y. But again, consider negative numbers:
If x is -3 and y is 2, then of course x < y. But x^2 will be greater than y^2, since 9 > 4.
But of course, if x is 2 and y is 3, then x < y and x^2 < y^2.
2 is insufficient because it does not mention anything about the relationship between x and y.
But put both stmts together to get that x < y < 0. In this case, we know that both x and y are negatives. This is why x^2 will indeed be greater than y^2, since x is farther away from zero. Its square will be greater than the square of y. Just take an example to be 100% sure: x = -5 and y = -4.
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Inequalities (III)
Source: Beat The GMAT — Data Sufficiency |
