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# Is -x < 2y ?

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Senior Manager
Joined: 04 Jan 2006
Posts: 258
Is -x < 2y ?  [#permalink]

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30 Jan 2007, 21:25
1
3
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:43) correct 24% (01:29) wrong based on 183 sessions

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Is -x < 2y ?

(1) y > -1
(2) (2^x) - 4 > 0
Director
Joined: 06 Feb 2006
Posts: 852

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31 Jan 2007, 00:27
I choose C...

Is x>-2y

1) insufficient, we do not know anything about x

y could be negative: -0,5 or positive 1, 3, 2.5

2) insufficient, we do not know anything about y

x>2

1+2) Sufficient. Take worst case scenario: y=-0.99, x=2.1
Plug into
x>-2y

2.1>1.98...
SVP
Joined: 01 May 2006
Posts: 1740

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31 Jan 2007, 00:29
(C) for me

-x < 2y <=> y > -x/2

In a XY Plan, Y is above the line -x/2. I prefer to solve this DS with the XY plan.

Stat1
y > -1. This brings us to y above the line y=-1. The area covered could be either above -x/2 (when x>0) or below -x/2 (wehn x<10). (Fig1)

INSUFF.

Stat2
(2^x) - 4 >0
<=> 2^x > 4 = 2^2
<=> x > 2

In the XY plan, it does mean that the concerned area is at right of the line x=2. One more time, their is 2 case, y could be either above the line -x/2 (when y > 0) or below the line -x/2 (the point (3,-100)). (Fig2)

INSUFF.

Both (1) and (2):
x > 2 and y > -1 represents an area with a not attainable vertice at (-1;2). By drawing the line -x/2 and this point, we observe that this point is on the line. Thus, the whole area of points such that x>2 and y>-1 is above the line -x/2. (Fig3)

SUFF.
Attachments

Fig1_y sup -1.GIF [ 3.17 KiB | Viewed 3660 times ]

Fig2_x sup 2.GIF [ 3.07 KiB | Viewed 3658 times ]

Fig3_x sup 2 and y sup -1.GIF [ 2.91 KiB | Viewed 3713 times ]

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31 Jan 2007, 06:10
1
Is -x < 2y
(1) y > -1
(2) (2^x) - 4 > 0

is

2y+x>0

from one we ve no info about x ......insuff

from two

2^x > 2^2

ie: x>2........no info about y insuff

both together

x>2 , y>-1

thus x+y>1

we need to prove that 2y+x>0 ie +ve

x is always +ve

and the maximum -ve value y can be multiplied by two is less than 0

thus C is my answer too
Senior Manager
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31 Jan 2007, 06:52
yezz wrote:
Is -x < 2y
(1) y > -1
(2) (2^x) - 4 > 0

is

2y+x>0

from one we ve no info about x ......insuff

from two

2^x > 2^2

ie: x>2........no info about y insuff

both together

x>2 , y>-1

a little bit more work from the quote above.

x > 2 (equation 1)
y > -1 or 2y > -2 (equation 2)

(equation 1) + (equation 2)... x + 2y > 2 + (-2)
x + 2y > 0
x > -2y
-x < 2y (this is the same as the question.)

Thus C. is the answer
Director
Joined: 24 Aug 2006
Posts: 660
Location: Dallas, Texas
Re: DS: Property of Number  [#permalink]

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02 Feb 2007, 00:34
We have to determine whether:-x<2y>-2y

From (1) y>-1 ---- insufficient

From (2)
2^x >2^2
x>2 -----------------insufficient

Combining (1) and (2)
We can say x > -2y

(C)
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Joined: 23 Nov 2010
Posts: 2
Re: DS: Property of Number  [#permalink]

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03 Dec 2010, 11:06
I go for (C)
1) y>-1
NOT SUFF
2) 2^x - 4 >0
NOT SUFF

Combine:
From 1: y>-1 <=> 2y>-2
From 2: 2^x -4>0 <=> 2^x>2^2 <=> x>2 <=> -x<-2
Therefore: -x<-2<2y <=> -x<2y. Here we go.
Math Expert
Joined: 02 Sep 2009
Posts: 54369
Re: DS: Property of Number  [#permalink]

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03 Dec 2010, 11:22
devilmirror wrote:
Is -x < 2y
(1) y > -1
(2) (2^x) - 4 > 0

Quite an old thread is resurrected.

Is -x<2y?

Is $$-x<2y$$? --> rearrange: is $$x+2y>0$$?

(1) y>-1, clearly insufficient as no info about $$x$$.

(2) (2^x)-4>0 --> $$2^x>2^2$$ --> $$x>2$$ --> also insufficient as no info about $$y$$.

(1)+(2) $$y>-1$$, or $$2y>-2$$ and $$x>2$$ --> add this inequalities (remember, you can only add inequalities when their signs are in the same direction and you can only apply subtraction when their signs are in the opposite directions) --> $$2y+x>-2+2$$ --> $$x+2y>0$$. Sufficient.

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Re: Is -x < 2y ?  [#permalink]

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01 Jan 2014, 06:42
devilmirror wrote:
Is -x < 2y ?

(1) y > -1
(2) (2^x) - 4 > 0

Statement 1

y>-1 but no info about 'x'. Not sufficient

Statement 2

x>2, but no info on 'y'. Not sufficient

Statements (1) + (2) together

y + x/2 > 0?

Well, x>2 so x/2>1

And y>-1, so yes it will always be more than zero

Hence C is sufficient

Hope it helps

Cheers!
J
Senior Manager
Joined: 06 Aug 2011
Posts: 331
Re: DS: Property of Number  [#permalink]

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06 Feb 2014, 08:41
Bunuel wrote:
devilmirror wrote:
Is -x < 2y
(1) y > -1
(2) (2^x) - 4 > 0

Quite an old thread is resurrected.

Is -x<2y?

Is $$-x<2y$$? --> rearrange: is $$x+2y>0$$?

(1) y>-1, clearly insufficient as no info about $$x$$.

(2) (2^x)-4>0 --> $$2^x>2^2$$ --> $$x>2$$ --> also insufficient as no info about $$y$$.

(1)+(2) $$y>-1$$, or $$2y>-2$$ and $$x>2$$ --> add this inequalities (remember, you can only add inequalities when their signs are in the same direction and you can only apply subtraction when their signs are in the opposite directions) --> $$2y+x>-2+2$$ --> $$x+2y>0$$. Sufficient.

I chose C.. thats correct.. bt with different approach

bt Bunuel I didnt get this highlighted thing?? How did u do that?
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Posts: 54369
Re: DS: Property of Number  [#permalink]

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07 Feb 2014, 05:12
sanjoo wrote:
Bunuel wrote:
devilmirror wrote:
Is -x < 2y
(1) y > -1
(2) (2^x) - 4 > 0

Quite an old thread is resurrected.

Is -x<2y?

Is $$-x<2y$$? --> rearrange: is $$x+2y>0$$?

(1) y>-1, clearly insufficient as no info about $$x$$.

(2) (2^x)-4>0 --> $$2^x>2^2$$ --> $$x>2$$ --> also insufficient as no info about $$y$$.

(1)+(2) $$y>-1$$, or $$2y>-2$$ and $$x>2$$ --> add this inequalities (remember, you can only add inequalities when their signs are in the same direction and you can only apply subtraction when their signs are in the opposite directions) --> $$2y+x>-2+2$$ --> $$x+2y>0$$. Sufficient.

I chose C.. thats correct.. bt with different approach

bt Bunuel I didnt get this highlighted thing?? How did u do that?

$$2y+x>-2+2$$ --> re-arrange the left hand side as x+2y. As for the right hand side: -2 + 2 = 0. So, we get $$x+2y>0$$.

Hope it's clear.
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Re: Is -x < 2y ?  [#permalink]

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15 Jan 2016, 19:37
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is -x < 2y ?

(1) y > -1
(2) (2^x) - 4 > 0

In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), they become y>-1, 2y>-2 and 2^x>4=2^2 --> x>2, -x<-2, which is -x<-2<2y --> -x<2y. So it is yes and sufficient. Therefore, the answer is C.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Joined: 24 Jul 2016
Posts: 51
Re: Is -x < 2y ?  [#permalink]

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09 Jul 2017, 17:10
devilmirror wrote:
Is -x < 2y ?

(1) y > -1
(2) (2^x) - 4 > 0

From statement 1 we get that the lowest possible value of 2Y must be greater than -2 .

From statement 1 we get that x > 2 or -x <-2. so even the highest possible value of -x cannot exceed -2

So from the original equation in the qn we can see that even the highest possible value of "-x" is less than the lowest possible value of "2y"
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Re: Is -x < 2y ?  [#permalink]

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01 Apr 2019, 22:41
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Re: Is -x < 2y ?   [#permalink] 01 Apr 2019, 22:41
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