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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) Please explain your steps.

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.

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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KUDOS me if you feel my contribution has helped you.

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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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.
_________________

KUDOS me if you feel my contribution has helped you.

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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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!

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?

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.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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