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 - founder of Greenlight Test Prep