Carcass wrote:
If \(x>1\) and \(y >-1\), then
(A) \(xy >-1\)
(B) \(xy <-1\)
(C) \(-x>y\)
(D) \(-x<y\)
(E) \(x<y\)
APPROACH #1: Inequality propertyGiven:
x > 1
y > -1If two inequalities are such that their inequality
symbols are facing the same direction, we can add the two inequalities.
In this case we get:
x + y > 1 + (-1)Simplify to get:
x + y > 0From here we can subtract x from both sides to get
y > -x, which can be rearranged to also get
-x < yAnswer: D
APPROACH #2: Process of eliminationIf x > 1 and y > -1, then it could be the case that x = 2 and y = 1
When we plug x = 2 and y = 1 into each answer choice, we get:
(A) (2)(1) > -1
TRUE(B) (2)(1) < -1
FALSE - ELIMINATE(C) -2 > 1
FALSE - ELIMINATE (D) -2 < 1
TRUE(E) 2 < 1
FALSE - ELIMINATESo, we can already see that the correct answer is either A or D.
Let's test another pair of values.
If x > 1 and y > -1, then it could also be the case that x = 4 and y = -0.5
When we plug x = 4 and y = -0.5 into each remaining answer choice, we get:
(A) (4)(-0.5) > -1
FALSE - ELIMINATE (D) -4 < -0.5
TRUEBy the process of elimination, the correct answer must be D