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# If x > 2 and y > -1, then which of the following

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1006
Location: India
GPA: 3.82
If x > 2 and y > -1, then which of the following [#permalink]

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09 Sep 2017, 01:30
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55% (hard)

Question Stats:

62% (01:44) correct 38% (00:53) wrong based on 101 sessions

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If $$x>2$$ and $$y>-1$$, then which of the following statements must be true?

A. $$xy>-2$$
B. $$-x<2y$$
C. $$xy<-2$$
D. $$-x>2y$$
E. $$x<-2y$$
[Reveal] Spoiler: OA
Intern
Joined: 19 Sep 2016
Posts: 15
Re: If x > 2 and y > -1, then which of the following [#permalink]

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09 Sep 2017, 03:41
Nice question .But can you please explain difference between 1st and 2nd choice
VP
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Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
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WE: Manufacturing and Production (Manufacturing)
Re: If x > 2 and y > -1, then which of the following [#permalink]

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09 Sep 2017, 04:07
A xy>−2
x=8 y =0.9
xy =-7.2 so xy<-2 therefore not true

B −x<2y
Notice that the LHS will be always negative as x will always be positive
x=2.1 y=-0.9
-2.1<-1.8 true this will hold true for any valye of Y if it holds for -0.9 as it is the quite close to -1 .
True

C xy<−2

x=2.1 y=-0.9
xy =-1.89
but -1.89 > -2 so not true

D −x>2y

x=2.1 y=6
-2.1< 12 so not true

E x<−2y
Clearly not true
x=2.1 y=0.9
2.1>-1.8
so not true .
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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1006
Location: India
GPA: 3.82
Re: If x > 2 and y > -1, then which of the following [#permalink]

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09 Sep 2017, 09:02
surbhipuri wrote:
Nice question .But can you please explain difference between 1st and 2nd choice

Hi surbhipuri
Mathematically you cannot multiply two inequalities until you know the signs of both the variables. In this inequality we know that $$x$$ is positive but $$y$$ can be positive, negative or $$0$$ (since $$y>-1$$ this implies that $$y$$ can be $$-0.5, 0,$$ or $$1$$ etc.)
if $$y$$ is negative then on multiplying it with $$x$$, the sign of the inequality will change but if $$y$$ is positive then there will be no change in the inequality sign.
so if you are multiplying $$x$$ and $$y$$ directly then Option A cannot be the answer
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1006
Location: India
GPA: 3.82
If x > 2 and y > -1, then which of the following [#permalink]

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10 Sep 2017, 06:57
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niks18 wrote:
If $$x>2$$ and $$y>-1$$, then which of the following statements must be true?

A. $$xy>-2$$
B. $$-x<2y$$
C. $$xy<-2$$
D. $$-x>2y$$
E. $$x<-2y$$

OE

$$x>2$$ this implies $$-x<-2$$ ----------------$$(1)$$
$$y>-1$$, multiplying both side of the inequality by $$2$$, we get $$2y>-2$$ ---------------$$(2)$$
Combining equations $$(1)$$ & $$(2)$$, it is clear that
$$-x<2y$$
Hence Option B

---------------------------------
Another method could be to test some values of $$x$$ & $$y$$ as per the given condition but that might take more than a minute to arrive at the final answer
Senior Manager
Joined: 02 Apr 2014
Posts: 451
Re: If x > 2 and y > -1, then which of the following [#permalink]

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27 Jan 2018, 05:06
x > 2, y > -1
adding two inequalities x + y > 2 - 1 => x + y > 1

(B). -x < 2y
0 < x + 2y
=> 0 < x + y + y
=> 0 < (>1) + y (from above, x+y > 1)
=> 0 < (>1) + (>-1) (from above, y > -1)
=> which will always true => say y = -0.9, then (>1) + (-0.9) will be greater than zero
Re: If x > 2 and y > -1, then which of the following   [#permalink] 27 Jan 2018, 05:06
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