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If x < y, which of the following must be true?

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If x < y, which of the following must be true? [#permalink] New post 17 Dec 2017, 14:14
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If \(x < y\), which of the following must be true?

A. \(2x < y\)

B. \(2x > y\)

C. \(x^2 < y^2\)

D. \(2x-y < y\)

E. \(2x-y < 2xy\)
[Reveal] Spoiler: OA

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Re: If x < y, which of the following must be true? [#permalink] New post 31 Jan 2018, 20:50
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In any question asking what must be true, you should try to imagine scenarios in which it isn't true. I'd start with the simplest looking answers and save the complex ones for last.

A. 2x < y
Does this have to be true? Let's pretend x = 5 and y = 6. So x<y but if you double x it's no longer smaller than y. This one's out.
B. 2x > y
OK this time let's imagine x = 1 and y = a billion. If we double x it's obviously not bigger than a billion, so this one's out.
C. x^2 < y^2
This one looks pretty good. It obviously could be true. But let's not settle for that. What if x was a large negative value and y a small positive value? For example, x = -10 and y = 2. This still fulfills the original inequality but when you square both you get 100 < 4, which isn't true. Out!
D. 2x-y < y
Always try to simplify equations and inequalities until they have the fewest number of terms possible. If we add y to both sides of this inequality, it turns into 2x < 2y. Dividing by 2 gets us x < y, which is the original inequality we were given. So this must be it!
E. 2x-y < 2xy
This one is meant to just waste your time. Luckily we already have the answer.
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Re: If x < y, which of the following must be true?   [#permalink] 31 Jan 2018, 20:50
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