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

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Director
Joined: 25 Feb 2013
Posts: 567

Kudos [?]: 257 [1], given: 35

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
If x > 2 and y > -1, then which of the following [#permalink]

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09 Sep 2017, 01:30
1
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Difficulty:

65% (hard)

Question Stats:

48% (01:13) correct 52% (00:55) wrong based on 62 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

Kudos [?]: 257 [1], given: 35

Intern
Joined: 19 Sep 2016
Posts: 11

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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

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VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1082

Kudos [?]: 82 [0], given: 541

Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: 314 Q157 V157
GPA: 3.4
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 .
_________________

We are more often frightened than hurt; and we suffer more from imagination than from reality

Kudos [?]: 82 [0], given: 541

Director
Joined: 25 Feb 2013
Posts: 567

Kudos [?]: 257 [0], given: 35

Location: India
Schools: Mannheim"19 (S)
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

Kudos [?]: 257 [0], given: 35

Director
Joined: 25 Feb 2013
Posts: 567

Kudos [?]: 257 [1], given: 35

Location: India
Schools: Mannheim"19 (S)
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

Kudos [?]: 257 [1], given: 35

If x > 2 and y > -1, then which of the following   [#permalink] 10 Sep 2017, 06:57
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