Carcass wrote:

If which \(x < y < 0\), of the following inequalities must be true?

A \(y + 1 < x\)

B \(y - 1 < x\)

C \(xy^2 < x\)

D \(xy < y^2\)

E \(xy < x^2\)

Practice Questions

Question: 24

Page: 463

Difficulty: medium/hard

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 < 0A) 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

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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