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

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

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New post 09 Sep 2017, 01:30
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A
B
C
D
E

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  55% (hard)

Question Stats:

63% (01:44) correct 37% (00:56) wrong based on 108 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. \(x<-2y\)
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Re: If x > 2 and y > -1, then which of the following  [#permalink]

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New post 09 Sep 2017, 03:41
Nice question .But can you please explain difference between 1st and 2nd choice
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Re: If x > 2 and y > -1, then which of the following  [#permalink]

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New post 09 Sep 2017, 04:07
The answer is B
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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Re: If x > 2 and y > -1, then which of the following  [#permalink]

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New post 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
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If x > 2 and y > -1, then which of the following  [#permalink]

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New post 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 :-)
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Re: If x > 2 and y > -1, then which of the following  [#permalink]

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New post 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 &nbs [#permalink] 27 Jan 2018, 05:06
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