In the triangle above, does AB = BC? (1) x > y (2) d > e

Let the landing point of the altitude from B to AC be D.

(1) x>y

We know that AB*cos(x) = BC*cos(y) = BD

AB/BC = cos(y)/cos(x) and since y < x, cos(y) > cos(x) or cos(y)/cos(x) > 1 or AB/BC > 1 or AB>BC

Clearly Sufficient. (Infact we didn't have to calculate the exact relation between AB & BC, since we had been given x>y we can infer x≠y and thus cos(x)≠cos(y) and thus AB≠BC)

(2) d > e

We know that AB² = BD² + d² and BC² = BD² + e²

Since d>e, d² > e², and AB² > BC² or AB > BC

Clearly Sufficient. (In fact again, we didn't have to calculate the exact relation between AB and BC, since we know that d≠e, d²≠e² and consequently AB²≠BC² or AB≠BC)

Hence, either statement alone is sufficient, option D.

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