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Adding y on both sides of the in-equality

by gmattesttaker2 » Mon Sep 30, 2013 6:07 pm
Hello,

I was wondering if you can please assist with this:

Is x - y + 1 greater than x + y - 1?

1) x > 0
2) y < 0

OA: B

My approach:

Is, x - y + 1 > x + y - 1
i.e. -y + 1 > y - 1

I was wondering if it is correct here to add y on both sides?
i.e. -y + 1 + y > y - 1 + y
i.e. 1 > 2y - 1

I was not sure if this is correct since we don't know whether y is positive or negative. Can you please clarify? Thanks a lot.

Best Regards,
Sri
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by theCodeToGMAT » Mon Sep 30, 2013 7:11 pm
x - y + 1 > x + y - 1
=> -2y > -2
=> y < 1 ??

Statement 1:
No info of Y..
INSUFFICIENT

Statement 2:
y<0
every value of y <0 will definitely be less than <1.
SUFFICIENT

Answer {B}

No, you should NOT add the variables like that; I remember I solved one question wherein I reached Answer {D} by applying a similar approach but the actual answer was {B}
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by vinay1983 » Mon Sep 30, 2013 8:00 pm
Statement 2 is sufficient by itself
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by gmattesttaker2 » Mon Sep 30, 2013 8:36 pm
theCodeToGMAT wrote:x - y + 1 > x + y - 1
=> -2y > -2
=> y < 1 ??

Statement 1:
No info of Y..
INSUFFICIENT

Statement 2:
y<0
every value of y <0 will definitely be less than <1.
SUFFICIENT

Answer {B}

No, you should NOT add the variables like that; I remember I solved one question wherein I reached Answer {D} by applying a similar approach but the actual answer was {B}

Hello,

I had a question here:
x - y + 1 > x + y - 1
=> -2y > -2
=> y < 1 ??
So I guess what we are doing is first subtracting x from both sides i.e.

x - y + 1 - x > x + y - 1 - x

But then if x is negative here, will the sign change?

Thanks,
Sri
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by theCodeToGMAT » Mon Sep 30, 2013 8:47 pm
gmattesttaker2 wrote:
So I guess what we are doing is first subtracting x from both sides i.e.

x - y + 1 - x > x + y - 1 - x

But then if x is negative here, will the sign change?

Thanks,
Sri
No, that logic is for Multiplication

For example:
a/b > c/d
If "b" is negative.. then sign will change as we multiply both sides by "-1"
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by gmattesttaker2 » Mon Sep 30, 2013 10:30 pm
theCodeToGMAT wrote:
gmattesttaker2 wrote:
So I guess what we are doing is first subtracting x from both sides i.e.

x - y + 1 - x > x + y - 1 - x

But then if x is negative here, will the sign change?

Thanks,
Sri
No, that logic is for Multiplication

For example:
a/b > c/d
If "b" is negative.. then sign will change as we multiply both sides by "-1"
Hi Rahul,

Thanks a lot for clearing my doubt.

Best Regards,
Sri
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by theCodeToGMAT » Mon Sep 30, 2013 10:37 pm
gmattesttaker2 wrote: Hi Rahul,

Thanks a lot for clearing my doubt.

Best Regards,
Sri
You are welcome
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by rakeshd347 » Tue Oct 01, 2013 10:12 pm
gmattesttaker2 wrote:Hello,

I was wondering if you can please assist with this:

Is x - y + 1 greater than x + y - 1?

1) x > 0
2) y < 0

OA: B

My approach:

Is, x - y + 1 > x + y - 1
i.e. -y + 1 > y - 1

I was wondering if it is correct here to add y on both sides?
i.e. -y + 1 + y > y - 1 + y
i.e. 1 > 2y - 1

I was not sure if this is correct since we don't know whether y is positive or negative. Can you please clarify? Thanks a lot.

Best Regards,
Sri
Hi Sri,

You can add the same variable to both the sides of an inequality. It will not affect the answer what so ever. I don't agree with thecodeTogmat.
Its wrong to advice that you can't add the same variable to both sides.
Suppose 5>3 if you add 2 on both sides 7>5 its still bigger.....now for argument sake say you add the negative number as you are not sure about the sign of Y. then say add -2 on both sides..... 2>1 now let us try the bigger number -100 then -95>-97.
So in all you can add the same variable to both sides and I can assure you that the result won't change.
When you are multiplying you need to be careful of the sign of the variable. If the variable is positive then the inequality sign remains in the same direction if the variable is negative with whom you are multiplying then the inequality sign will change.

Conclusion: YOU CAN ADD OR SUBTRACT THE SAME VARIABLE FROM AN INEQUALITY FROM BOTH SIDE WITHOUT AFFECTING THE OUTCOME OF THE INEQUALITY.

I hope that clarifies.
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by theCodeToGMAT » Tue Oct 01, 2013 10:44 pm
rakeshd347 wrote: Hi Sri,

You can add the same variable to both the sides of an inequality. It will not affect the answer what so ever. I don't agree with thecodeTogmat.
Its wrong to advice that you can't add the same variable to both sides.
Suppose 5>3 if you add 2 on both sides 7>5 its still bigger.....now for argument sake say you add the negative number as you are not sure about the sign of Y. then say add -2 on both sides..... 2>1 now let us try the bigger number -100 then -95>-97.
So in all you can add the same variable to both sides and I can assure you that the result won't change.
When you are multiplying you need to be careful of the sign of the variable. If the variable is positive then the inequality sign remains in the same direction if the variable is negative with whom you are multiplying then the inequality sign will change.

Conclusion: YOU CAN ADD OR SUBTRACT THE SAME VARIABLE FROM AN INEQUALITY FROM BOTH SIDE WITHOUT AFFECTING THE OUTCOME OF THE INEQUALITY.

I hope that clarifies.
Rakesh, i don't agree with your justification.

Kindly go through the link : https://www.beatthegmat.com/if-w-x-0-is- ... tml#693234
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by rakeshd347 » Tue Oct 01, 2013 10:55 pm
theCodeToGMAT wrote:x - y + 1 > x + y - 1
=> -2y > -2
=> y < 1 ??

Statement 1:
No info of Y..
INSUFFICIENT

Statement 2:
y<0
every value of y <0 will definitely be less than <1.
SUFFICIENT

Answer {B}

No, you should NOT add the variables like that; I remember I solved one question wherein I reached Answer {D} by applying a similar approach but the actual answer was {B}
Let me ask you one thing.

In your solution in this question what have you done:
x - y + 1 > x + y - 1
=> -2y > -2 (You subtracted X from both sides and subtracted Y on both sides)
=> y < 1 ??
What you have recommended above to Sri you have done yourself. Now you might argue that you have not subtracted or added but you have cancelled out X. that is one and same thing cancelling out or subtracting is same thing.
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by theCodeToGMAT » Tue Oct 01, 2013 11:14 pm
rakeshd347 wrote: Let me ask you one thing.

In your solution in this question what have you done:
x - y + 1 > x + y - 1
=> -2y > -2 (You subtracted X from both sides and subtracted Y on both sides)
=> y < 1 ??
What you have recommended above to Sri you have done yourself. Now you might argue that you have not subtracted or added but you have cancelled out X. that is one and same thing cancelling out or subtracting is same thing.
Rakesh, you cannot simply add variables on the inequalities by adding both the variable on both sides are replacing 0 by "x - x"

THe GMAT Instructor has also clearly stated that it's always a big risk involved when you are trying to do that. Also, the outcome is that my Answer turned out to be "D" rather than "B". It's correct to add definite numeric number but playing with Variables can be very risky.

The point which you are raising is a simple mathematic concept; if you apply the same method in inequality then your are going to get many incorrect inequalities answers simply because you can introduce any variable from anywhere you want and prove the inequality as per the desired motive. Also, I dint introduce any new variable in my solution; I have simply eliminated and elimination is very different from addition of new variables. If you apply a similar approach then I can give you many such question wherein you can get Answers as {A} but infact the OA won;t be {A}

The question put up by "Sri" is very clear.. he wants to know whether we can play with variables ..
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by rakeshd347 » Tue Oct 01, 2013 11:22 pm
theCodeToGMAT wrote:
rakeshd347 wrote: Let me ask you one thing.

In your solution in this question what have you done:
x - y + 1 > x + y - 1
=> -2y > -2 (You subtracted X from both sides and subtracted Y on both sides)
=> y < 1 ??
What you have recommended above to Sri you have done yourself. Now you might argue that you have not subtracted or added but you have cancelled out X. that is one and same thing cancelling out or subtracting is same thing.
Rakesh, you cannot simply add variables on the inequalities by adding both the variable on both sides are replacing 0 by "x - x"

THe GMAT Instructor has also clearly stated that it's always a big risk involved when you are trying to do that. Also, the outcome is that my Answer turned out to be "D" rather than "B". It's correct to add definite numeric number but playing with Variables can be very risky.

The point which you are raising is a simple mathematic concept; if you apply the same method in inequality then your are going to get many incorrect inequalities answers simply because you can introduce any variable from anywhere you want and prove the inequality as per the desired motive. Also, I dint introduce any new variable in my solution; I have simply eliminated and elimination is very different from addition of new variables. If you apply a similar approach then I can give you many such question wherein you can get Answers as {A} but infact the OA won;t be {A}

The question put up by "Sri" is very clear.. he wants to know whether we can play with variables ..
Here is the question asked by Sri:

My approach:

Is, x - y + 1 > x + y - 1
i.e. -y + 1 > y - 1

I was wondering if it is correct here to add y on both sides?
i.e. -y + 1 + y > y - 1 + y
i.e. 1 > 2y - 1

I was not sure if this is correct since we don't know whether y is positive or negative. Can you please clarify? Thanks a lot.

Best Regards,
Sri

He is not doing x-x=0

Now in here can you show me what new variable he has introduced. All he has asked is that is it alright to do this:
-y+1>y-1 ( he is asking is it alright to add Y on both sides and my answer is yes it is absolutely alright to add Y on both side but you said its not)
Now if he add Y on both sides he gets
1>2y-1 or 2>2y or 1>y or Y<1

This is what you calculated in your answer explanation. In your other question what you have done is wrong. But to Sri's answer it is absolutely fine to add the same variable on both sides of the inequality.
If you don't agree with me can you justify your answer in this question. I think you are mixing two different things here. I am directing to Sri's question is that you can add or subtract the same variable from both sides and that is what you have done in your solution.

Thanks,
Rakesh
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by theCodeToGMAT » Tue Oct 01, 2013 11:32 pm
It's the decision of Sri & YOU how you want to take my advise. I have fallen in a pitfall and have learnt my mistake.. The solution i have provided is 100% CORRECT.

Sri, one advise I will definitely give you... Be very careful while determinately adding variables in an inequality.

Good Luck!
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by rakeshd347 » Tue Oct 01, 2013 11:39 pm
theCodeToGMAT wrote:It's the decision of Sri & YOU how you want to take my advise. I have fallen in a pitfall and have learnt my mistake.. The solution i have provided is 100% CORRECT.

Sri, one advise I will definitely give you... Be very careful while determinately adding variables in an inequality.

Good Luck!
Now let me give you a advice and again its up to you to take it or not.

first of all here is the mistake you made in the question which you sent me I have given the explanation.
https://www.beatthegmat.com/if-w-x-0-is- ... tml#695492

I don't know which gmat teacher has advised you not to add the same variable on both sides of the equation but you can do so safely.
Let me know if the mistake that I have pointed out to you make sense or not. But its utter fact that you can add or subtract the same variable from both sides even the way you have done it in the question which you sent me.
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by theCodeToGMAT » Tue Oct 01, 2013 11:43 pm
rakeshd347 wrote:
theCodeToGMAT wrote:It's the decision of Sri & YOU how you want to take my advise. I have fallen in a pitfall and have learnt my mistake.. The solution i have provided is 100% CORRECT.

Sri, one advise I will definitely give you... Be very careful while determinately adding variables in an inequality.

Good Luck!
Now let me give you a advice and again its up to you to take it or not.

first of all here is the mistake you made in the question which you sent me I have given the explanation.
https://www.beatthegmat.com/if-w-x-0-is- ... tml#695492

I don't know which gmat teacher has advised you not to add the same variable on both sides of the equation but you can do so safely.
Let me know if the mistake that I have pointed out to you make sense or not. But its utter fact that you can add or subtract the same variable from both sides even the way you have done it in the question which you sent me.
Rakesh, on same variable; i do agree.. but on playing in different variables.. i don't .. this is what i am insisting from starting.. when in inequalities.. try to solve using simple algebric approach.. similar to the method you say.. BUT, avoid adding variables.. here i meant.. different variables..
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