If w+x<0, is w-y>0? : GMAT Data Sufficiency (DS)
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# If w+x<0, is w-y>0?

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04 Dec 2010, 05:33
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If w + x < 0, is w - y>0?

(1) x + y < 0
(2) y < x < w
[Reveal] Spoiler: OA

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Re: If w + x < 0, is w - y . 0? [#permalink]

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04 Dec 2010, 05:50
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gmatbull wrote:
If w + x < 0, is w - y . 0?
(1) x + y < 0
(2) y < x < w

I don't know why i missed this question; with regards to (1)

If w + x < 0 , is w - y > 0 ?

Question: is $$w>y$$?

(1) x + y < 0 --> for this statement best way would be to pick numbers: on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

If $$x=0$$, $$w=-1$$ and $$y=-2$$ then the answer would be YES but if $$x=0$$, $$w=-2$$ and $$y=-1$$ then the answer would be. Not sufficient.

(2) $$y<x<w$$ --> ignore $$x$$ --> $$y<w$$, directly tells us the answer. Sufficient.

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Re: If w + x < 0, is w - y . 0? [#permalink]

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04 Dec 2010, 14:23
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This one appears okay for an algebraic option, but missed out due to some careless mistakes.

I combined the equations given in the stimulus as well as in the options.
stem: w + x < 0..........(a) required to answer: is w > y?
(1) y + x < 0...........(b) SUBTRACTING: (a) - (b)
we get w - y < 0 ==> w<y..... answer to the question is NO

But again SUBTRACTING: (b) - (a)
we get: y-w <0 ==> w>y ..... answer to the question is YES
INSUFFICIENT
I simply did not take into consideration this second part.

(2) I have no problem resolving (2)...SUFFICIENT

Bunuel: Thanks buddy for your awesome contributions.
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Re: If w + x < 0, is w - y . 0? [#permalink]

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04 Dec 2010, 14:38
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gmatbull wrote:
This one appears okay for an algebraic option, but missed out due to some careless mistakes.

I combined the equations given in the stimulus as well as in the options.
stem: w + x < 0..........(a) required to answer: is w > y?
(1) y + x < 0...........(b) SUBTRACTING: (a) - (b)
we get w - y < 0 ==> w<y..... answer to the question is NO

But again SUBTRACTING: (b) - (a)
we get: y-w <0 ==> w>y ..... answer to the question is YES

INSUFFICIENT
I simply did not take into consideration this second part.

(2) I have no problem resolving (2)...SUFFICIENT

Bunuel: Thanks buddy for your awesome contributions.

The red part is not correct. You can not subtract inequalities with signs in the same direction, you can only add them.

You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

As for algebraic way.
We can add $$w+x<0$$ and $$y+x<0$$ and we'll get $$w+y+2x<0$$, which tells us nothing whether $$w>y$$. In DS questions when after certain algebraic manipulations you don't have clear answer then you can quite safely assume that this statement is not sufficient, though in order to get definite answer you must use number plugging.
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Re: If w + x < 0, is w - y . 0? [#permalink]

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13 Dec 2010, 12:41
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Re: If w + x < 0, is w - y . 0? [#permalink]

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13 Dec 2010, 13:32
Precaution taken not to subtract two negative inequalities and assuming a single value;
the solution could be either negative, zero (e.g -2 - (-2)) or positive (e.g -2 -(-10)).

Thanks Bunuel.
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Re: If w + x < 0, is w - y . 0? [#permalink]

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14 Dec 2010, 07:01
Good explanation. +1 for B
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Re: If w + x < 0, is w - y . 0? [#permalink]

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14 Dec 2010, 21:26
can u guys estimate the level of this question?

thanks.
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If w + x < 0, is w - y > 0 ? [#permalink]

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06 May 2011, 09:24
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If w + x < 0, is w - y > 0 ?

(1) x + y < 0

(2) y < x < w
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Re: If w + x < 0, is w - y > 0 ? [#permalink]

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06 May 2011, 10:50
a expression says nothing about w.Hence not sufficient.

b question is asking if w> y

the option directly states that.

also w + x < 0 and y < x < w means

y,x,w are all < 0 . Means if we take values -3, -2 and -1 for y,x and w it will give w+x > 0

Hence B
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Re: If w + x < 0, is w - y > 0 ? [#permalink]

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06 May 2011, 14:18
Rephrasing the given expression we have

w>y?

1. Not sufficient
because doesnt say anything about w.

2. Sufficient

because it directly states that y<w

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Re: If w + x < 0, is w - y > 0 ? [#permalink]

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11 May 2011, 04:41
(1)
y can be equal to w, so insufficient.

(2)

y < w

=> w-y > 0, sufficient

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Re: If w+x<0, is w-y>0? [#permalink]

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17 Jan 2012, 22:22
Is plugging numbers the best way to solve inequality probs or their is any other best method as this method takes lot of time
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Re: If w+x<0, is w-y>0? [#permalink]

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18 Jan 2012, 03:55
Eshika wrote:
Is plugging numbers the best way to solve inequality probs or their is any other best method as this method takes lot of time

Well it REALLY depends on the problem. Algebraic approach will work in many cases, though sometimes other approaches might be faster or/and simpler, also there are certain GMAT questions which are pretty much only solvable with plug-in or trial and error methods (well at leas in 2-3 minutes).
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Re: If w+x<0, is w-y>0? [#permalink]

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18 Jan 2012, 04:05
Ok ..I need to practice lots of them..Thanks Bunuel
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Re: If w + x < 0, is w - y . 0? [#permalink]

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01 Jun 2012, 17:00
Bunuel wrote:
gmatbull wrote:
This one appears okay for an algebraic option, but missed out due to some careless mistakes.

I combined the equations given in the stimulus as well as in the options.
stem: w + x < 0..........(a) required to answer: is w > y?
(1) y + x < 0...........(b) SUBTRACTING: (a) - (b)
we get w - y < 0 ==> w<y..... answer to the question is NO

But again SUBTRACTING: (b) - (a)
we get: y-w <0 ==> w>y ..... answer to the question is YES

INSUFFICIENT
I simply did not take into consideration this second part.

(2) I have no problem resolving (2)...SUFFICIENT

Bunuel: Thanks buddy for your awesome contributions.

The red part is not correct. You can not subtract inequalities with signs in the same direction, you can only add them.

You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

As for algebraic way.
We can add $$w+x<0$$ and $$y+x<0$$ and we'll get $$w+y+2x<0$$, which tells us nothing whether $$w>y$$. In DS questions when after certain algebraic manipulations you don't have clear answer then you can quite safely assume that this statement is not sufficient, though in order to get definite answer you must use number plugging.

Thanks, Bunuel! Didn't know that property about inequalities. If inequalities facing the same direction, you can only add them, never subtract. Nice!
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Re: If w+x<0, is w-y>0? [#permalink]

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08 Dec 2012, 18:01
Bunuel,
I understand we cannot subtract inequalities with same sign but I can subtract if the signs are different, right? if so is this correct
Given w+ x < 0
Statement (1) x+ y < 0--- now multiply with -1 it results -x -y > 0

so now we combine the given information with statement 1 info we get

w+ x < 0
-y -x > 0
_________
w-y < 0

I know this contradicts what we get in statement 2 but I don't understand why we can't multiply with -1 and subtract statement 1 from given info?
can you help?
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Re: If w+x<0, is w-y>0? [#permalink]

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09 Dec 2012, 06:00
Simba2012 wrote:
Bunuel,
I understand we cannot subtract inequalities with same sign but I can subtract if the signs are different, right? if so is this correct
Given w+ x < 0
Statement (1) x+ y < 0--- now multiply with -1 it results -x -y > 0

so now we combine the given information with statement 1 info we get

w+ x < 0
-y -x > 0
_________
w-y < 0

I know this contradicts what we get in statement 2 but I don't understand why we can't multiply with -1 and subtract statement 1 from given info?
can you help?

If you subtract -y -x > 0 from w+ x < 0 you'll get w+x-(-y-x)<0 --> w+x+y+x<0, not w-y < 0.

Hope it's clear.
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Re: If w+x<0, is w-y>0? [#permalink]

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09 Dec 2012, 08:23
I Totally missed that part to assign the - sign. Thanks Bunuel!
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