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If w + x < 0, is w – y > 0? (1) x + y < 0 (2

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If w + x < 0, is w – y > 0? (1) x + y < 0 (2

by theCodeToGMAT » Mon Sep 16, 2013 9:49 pm
If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

I am not sure of the Source of this Question. The OA is B
But, I am getting the answer is D

My Steps to Solutions:
w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)

Statement 1 says x + y < 0 ... So, w - y > 0 ... Sufficient
Statement 2 says y < x < w ... So,
Either w is +ve , x is - ve hence y is also -ve
or w,x,y all are negative.. in both the cases w-y >0 ... Sufficient
So,[spoiler] [D] [/spoiler]..
BUT, OA is different.
Please help
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by vinay1983 » Mon Sep 16, 2013 11:13 pm
According to me, the question stem can be made as is W>y

So,

Statement 1

No relation given between w and y Not sufficient

Statement 2

y < x < w
Implies y < w

So we can answer our revised question with this, Sufficient

B to me. I hope I am correct.
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by theCodeToGMAT » Mon Sep 16, 2013 11:34 pm
Yeah Vinay, the way you solved the question is correct; Even I did that method once I was stuck with the first method I applied to solve it (Method is stated below the question).

The problem is .. I am not able to catch the problem in my First Method.

The approach you applied does gives ambiguous values for "W" ranging from Positive Values 1 to 4 to any negative value. Hence, Statement 1 is Insufficient.
vinay1983 wrote:According to me, the question stem can be made as is W>y

So,

Statement 1

No relation given between w and y Not sufficient

Statement 2

y < x < w
Implies y < w

So we can answer our revised question with this, Sufficient

B to me. I hope I am correct.
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by sanju09 » Tue Sep 17, 2013 1:18 am
rahulmittal87 wrote:If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

I am not sure of the Source of this Question. The OA is B
But, I am getting the answer is D

My Steps to Solutions:
w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)

Statement 1 says x + y < 0 ... So, w - y > 0 ... Sufficient
Statement 2 says y < x < w ... So,
Either w is +ve , x is - ve hence y is also -ve
or w,x,y all are negative.. in both the cases w-y >0 ... Sufficient
So,[spoiler] [D] [/spoiler]..
BUT, OA is different.
Please help
Hi rahulmittal87,

I. On GMAT, relying too much on algebraic approaches can sometimes make us overlook few ground facts that may be some hidden constraints throughout the question. In your pre-work, the introduction of y took place accidentally, simply because of its unpredictable sign and size in compare to w and x, which can change the inequality altogether. When nothing had been mentioned about y so far, how can we really play with it inside a risky inequality? This can be better understood by picking suitable set of easy numbers for w, x, and y, and realize the liberty to have so many different suitable set of easy numbers and weird verities for w, x, and y that can change the meaning of the inequality.

Hence, statement 1 is not sufficient.
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by phsr » Tue Sep 17, 2013 1:23 am
rahulmittal87 wrote:If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

I am not sure of the Source of this Question. The OA is B
But, I am getting the answer is D

My Steps to Solutions:
w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)

Statement 1 says x + y < 0 ... So, w - y > 0 ... Sufficient
Statement 2 says y < x < w ... So,
Either w is +ve , x is - ve hence y is also -ve
or w,x,y all are negative.. in both the cases w-y >0 ... Sufficient
So,[spoiler] [D] [/spoiler]..
BUT, OA is different.
Please help
------------------------------------------------------------------------------
why A is not insufficient is that ...x + w < 0 means x or w is negative or both are so.

However, with only this 2 fact
x + y < 0 (x or y is negative or both) , x + w < 0 (x or w is negative or both)

it's is impossible to know whether x is greater than y.(w - y > 0)

So A is insuffient..
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by theCodeToGMAT » Tue Sep 17, 2013 2:14 am
Yeah i know this fact; Actually, I was looking for possible problem in the method which i had used at the first place. I tried to solve the question using the same old algebric tricks in which we try to introduce some variable/value without affecting the balance between LHS & RHS. I wrote "0" as "y-y", which should always be satisfied for any possible value of Y.

Anyways, thanks Sanju for the explanation.


phsr wrote:
rahulmittal87 wrote:If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

I am not sure of the Source of this Question. The OA is B
But, I am getting the answer is D

My Steps to Solutions:
w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)

Statement 1 says x + y < 0 ... So, w - y > 0 ... Sufficient
Statement 2 says y < x < w ... So,
Either w is +ve , x is - ve hence y is also -ve
or w,x,y all are negative.. in both the cases w-y >0 ... Sufficient
So,[spoiler] [D] [/spoiler]..
BUT, OA is different.
Please help
------------------------------------------------------------------------------
why A is not insufficient is that ...x + w < 0 means x or w is negative or both are so.

However, with only this 2 fact
x + y < 0 (x or y is negative or both) , x + w < 0 (x or w is negative or both)

it's is impossible to know whether x is greater than y.(w - y > 0)

So A is insuffient..
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by GMATGuruNY » Tue Sep 17, 2013 4:53 am
rahulmittal87 wrote:If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w
Question rephrased: Is w > y?

Statement 1: x+y < 0.
Rewritten, y < -x.
Rewritten, w+x < 0 becomes w < -x.
Now we can see that both w and y are less than -x, but no information is given about whether w>y.
Insufficient.

Statement 2: y < x < w.
Thus, y < w.
Sufficient.

The correct answer is B.
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by gmattesttaker2 » Tue Oct 01, 2013 11:29 pm
Hello,

I was wondering why this would be wrong since I thought that we can add/subtract in-equalites as long as they have the same sign:

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

So, w + x < 0
& y + x < 0

So, w - y < 0


Thanks,
Sri
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by rakeshd347 » Tue Oct 01, 2013 11:35 pm
theCodeToGMAT wrote:If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

I am not sure of the Source of this Question. The OA is B
But, I am getting the answer is D

My Steps to Solutions:
w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)

Statement 1 says x + y < 0 ... So, w - y > 0 ... Sufficient
Statement 2 says y < x < w ... So,
Either w is +ve , x is - ve hence y is also -ve
or w,x,y all are negative.. in both the cases w-y >0 ... Sufficient
So,[spoiler] [D] [/spoiler]..
BUT, OA is different.
Please help
Hi Rahul,

To clarify your confusion on adding variable and show you where you went wrong here is my explanation:

w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)

Now statement 1 says that x+y<0 or -(x+y)>0 we are clear on this.
Now here is what you made the mistake.
-(x+y)>0
-(x+y)>w-y so you concluded that w-y>0 thats wrong.

example:

A>0 ; A>C now you are saying that so C has to be more than 0. no it doesn't have to be true. A could be 5 and C could be -2 or C could be 1 or may be or may be not situation.

Another example:
A>B
A>C here may be the sequence is A>B>C or A>C>B....So two outcomes.

Otherwise when it comes to adding variable to both sides of the inequality it is absolutely fine.

Thanks,
Rakesh
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by theCodeToGMAT » Tue Oct 01, 2013 11:51 pm
The problem here is :

I have mistakenly changed the sign in the solution mentioned in the post

w - y < - (x + y)

If x+y<0

that means w - y "<" and NOT w - y ">"
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by GMATGuruNY » Wed Oct 02, 2013 2:28 am
theCodeToGMAT wrote:If w + x < 0, is w - y > 0?
(1) x + y < 0
(2) y < x < w

My Steps to Solutions:
w + x < 0
w + x < y - y
w - y < - y - x
w - y < - (x + y)
The reasoning above is valid.
Statement 1 says x + y < 0 ... So, w - y > 0 ... Sufficient
This reasoning is not valid.
Since x+y < 0, -(x+y) > 0.
Since -(x+y) is POSITIVE, w-y < - (x + y) can be rephrased as follows:
w-y < POSITIVE.

This tells us nothing about the relationship between w and y.
It's possible that w<y, that w=y, or that w>y.

To illustrate:
If x+y = -10, then -(x+y) = 10.
In this case, w-y < 10.
Here, it's possible that w=1 and y=2, that w=1 and y=1, or that w=2 and y=1.

Thus, statement 1 is INSUFFICIENT.
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by gmattesttaker2 » Wed Oct 02, 2013 4:30 pm
Hello,

I was just wondering why this would be wrong since I thought that we can add/subtract in-equalites as long as they have the same sign:

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

So, w + x < 0
& y + x < 0

So, w - y < 0


Thanks,
Sri
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by rakeshd347 » Wed Oct 02, 2013 6:26 pm
gmattesttaker2 wrote:Hello,

I was just wondering why this would be wrong since I thought that we can add/subtract in-equalites as long as they have the same sign:

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

So, w + x < 0
& y + x < 0

So, w - y < 0


Thanks,
Sri
Hi Sri,

Have a look at my explanation above and you will understand.
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by Mike@Magoosh » Wed Oct 02, 2013 7:32 pm
gmattesttaker2 wrote:Hello,

I was wondering why this would be wrong since I thought that we can add/subtract inequalites as long as they have the same sign:

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

So, w + x < 0
& y + x < 0

So, w - y < 0

Thanks,
Sri
Sri,
I'm responding to your private message. Sometimes the best way to think about what's true for inequalities is to think in terms of ordinary numbers.

Inequality A: 15 < 17
Inequality B: 3 < 100
Both true. Both are in the same direction.

If we add them, all is well,
A + B: 18 < 117

BUT, if we subtract them ....
A - B: 12 > -83
Here, the direction of inequality reverses when we subtract (A - B). Notice that the direction wouldn't reverse if we subtracted (B - A). There's no predictable pattern --- subtracting inequalities is trouble!

It's NEVER a good idea to subtract two inequalities. Again, adding them is perfectly legit. You are also allowed to add or subtract any constant to both sides, and the inequality would still work. BUT, subtracting one inequality from another is just asking for big problems. That's what's so tempting about this brilliantly designed DS ---- it just lures the unsuspecting test taker into making a very predictable mistake. It's so good for you to learn about these predictable mistakes, so you can learn to avoid them.

Does all this make sense?
Mike :-)
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by rakeshd347 » Wed Oct 02, 2013 8:01 pm
gmattesttaker2 wrote:Hello,

I was just wondering why this would be wrong since I thought that we can add/subtract in-equalites as long as they have the same sign:

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

So, w + x < 0
& y + x < 0

So, w - y < 0


Thanks,
Sri
Hi Sri,

Here is the golden rule of inequality:

A>C and B>D then you can add both inequality: A+B>C+D.
However you can't subtract both inequality A-B>C-D....this is wrong.
If you want to subtract then you have to have the opposite sign.

Let me explain you here:

A>C and B>D...or we can say A>C and D<B....one and same thing right.
Now you can subtract A-D>C-B ( now the main point here to note is inequality sign will take the sign of the inequality from which we are subtracting)

A>C and D<B now suppose you want to get D-A<B-C....in this case it will take the sign of D inequality because you are subtracting from D. In the above inequality you were subtracting from A.

Suppose
3>2 and 3>1...now if you subtract 3-3>2-1 or 0>1 no this is wrong
but if you were to do.

3>2 and 1<3 then you can do 3-1>2-3 which is 2>-1

This Rule will always hold true. Not many people know it but this is a good tool to tackle inequality questions.
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