Solution

The question could become complex to evaluate theoretically. So the best way is to pick numbers

The stem can be tricky: it does not say that the numbers \(MUST\) be integers. As such, you need to take in account both options:\(X= -2\) and \(Y=-1\) OR \(X=\frac{-3}{2}\) and \(Y=\frac{-1}{2}\)

Testing all the answer choices we will end up that E will be \(-3<4\) and it is true;\(\frac{3}{4}<\frac{9}{4}\) and this is also true

The correct answer is \(E\)
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Given

\(x < y < 0\)

Here we understand that x is the most negative between x and y. So, whenever we square it , we get the maximum value which is greater than y.

Thus the best answer is E.

is there an explanation

The question asks, "What MUST be true?"

So if we can find a case in which an answer choice is NOT true, then we can ELIMINATE that answer choice.

GIVEN: x < y < 0

A) y + 1 < x
If x < y < 0, then it's possible that x = -3 and y = -1
When plug these values into the above inequality, we get: -1 + 1 < -3
Simplify to get: 0 < -3, which is NOT true
ELIMINATE A

B) y - 1 < x
If x < y < 0, then it's possible that x = -3 and y = -1
When plug these values into the above inequality, we get: -1 - 1 < -3
Simplify to get: -2 < -3, which is NOT true
ELIMINATE B

C) xy < x
If x < y < 0, then it's possible that x = -3 and y = -1
When plug these values into the above inequality, we get: (-3)(-1) < -3
Simplify to get: 3 < -3, which is NOT true
ELIMINATE C


D) xy < y²
If x < y < 0, then it's possible that x = -3 and y = -1
When plug these values into the above inequality, we get: (-3)(-1) < (-1)²
Simplify to get: 3 < 1, which is NOT true
ELIMINATE D

By the process of elimination, the correct answer must be E

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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