If x < y, which of the following must be true?
(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y
OA D
Source: Manhattan Prep
If x < y, which of the following must be true?
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BTGmoderatorDC wrote: ↑Mon Jan 17, 2022 6:17 pmIf x < y, which of the following must be true?
(A) x < y^2
(B) x^2 < y
(C) x^2 < y^2
(D) (x – y)^2 > 0
(E) x^3 > y
If x < y, then we can also conclude that x ≠ y.
If x ≠ y, then we can be certain that x  y ≠ 0
If x  y ≠ 0, then we can be certain that (x – y)^2 > 0
Answer: D
ASIDE: Another approach would be to take values that satisfy the inequality x < y, and plug them into each answer choice until we eventually eliminate all answer choices other than D.
I'll leave that to you...