Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

I read somewhere that whenever you see the expression |x+y|= [#permalink]

Show Tags

31 Jul 2008, 02:07

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I read somewhere that whenever you see the expression |x+y|= |x| + |y|, then it means that both x and y have the same sign. So can someone then please explain what it means when you see the expression |x+y|< |x| + |y| and |x+y|> |x| + |y|?

I read somewhere that whenever you see the expression |x+y|= |x| + |y|, then it means that both x and y have the same sign. So can someone then please explain what it means when you see the expression |x+y|< |x| + |y| and |x+y|> |x| + |y|?

thanks

If you see the expression |x+y| > |x| + |y|, that means you're in an alternate universe. This can never be true for real numbers x and y. If you see the expression |x+y| < |x| + |y|, then x and y have opposite signs. Lastly I'd note that if you see the expression |x+y| = |x| + |y|, that doesn't guarantee that x and y have the same sign- one of them could be equal to zero.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

I read somewhere that whenever you see the expression |x+y|= |x| + |y|, then it means that both x and y have the same sign. So can someone then please explain what it means when you see the expression |x+y|< |x| + |y| and |x+y|> |x| + |y|?

thanks

If you see the expression |x+y| > |x| + |y|, that means you're in an alternate universe. This can never be true for real numbers x and y. If you see the expression |x+y| < |x| + |y|, then x and y have opposite signs. Lastly I'd note that if you see the expression |x+y| = |x| + |y|, that doesn't guarantee that x and y have the same sign- one of them could be equal to zero.

That really cleared things up....thanks a lot! |x+y| = |x| + |y| would suggest that x and y have the same sign if only we were given an expression xy doesn't equal to zero.

however, if we were give |x+y| is less than or equal to |x| + |y|, then that would mean that either both have the same sign, or both have different signs, or one of them could be zero....correct?

Last edited by tarek99 on 31 Jul 2008, 06:30, edited 1 time in total.

I read somewhere that whenever you see the expression |x+y|= |x| + |y|, then it means that both x and y have the same sign. So can someone then please explain what it means when you see the expression |x+y|< |x| + |y| and |x+y|> |x| + |y|?

thanks

the expr(1) : |x+y|= |x| + |y| means that mod of sum is equal to sum of mods. When we say mod it means magnitude or abolute value irrespective of sign of a number in expr (1) is true when both x and y are of same sign since value on LHS and RHS are equal => magnitude of -(x+y) = x+y sum of magnitudes : |-x| +|-y| = x+y again hence LHS RHS same

now say in expr (1) ,x and y have opp signs then in LHS : magnitude of x+y < x+y when both have same signs i.e < |x|+|y|

|x+y|< |x| + |y| => this implies x,y have opp signs

|x+y|>|x| + |y| => there is no condition called this one since sum of the magnitudes can never be greater than RHS of this expr,Value of RHS is independent of sign.

Also, what does this expression mean when we have a minus sign?

|x-y| = |x| - |y| or

|x-y| = |y| - |x|

or, when we use the greater or less sign? for example:

|x-y| < |x| - |y|

|x-y| > |x| - |y|

I would really appreciate your input! thanks

consider : |x-y| = |x| - |y| or |x-y| = |y| - |x| we are just taking difference in magnitudes or simple value (irrespective of sign ) if both x and y have same signs then above equation is true ,since the operation subtraction is subtraction if both variabl;es are of same sign. |x-y| = |x| - |y| => this implies x,y same sign and x>y since LHS is +ve and hence RHS is +ve similarly : |x-y| = |y| - |x|=> this implies x,y same sign and y>x since LHS is +ve and hence RHS is +ve

consider eqn: |x-y| > |x| - |y| this says mod of difference > diff of modes now diff of mods is least always since max of x and max of y are subtracted. if in case x and y have opp signs then subtraction operation becomes addition hence mod of diff of x,y with opp signs is > than actual diff of mods.

hence |x-y| > |x| - |y| => this implies x,y opp sign and x>y since LHS is +ve and hence RHS is +ve

similarly

|x-y| > |y| - |x| => this implies x,y opp sign and y>x since LHS is +ve and hence RHS is +ve

|x-y| < |x| - |y| => this conmdition is not feasible since minimum diff between two numbers is the diff(in magnitude) between their mods.INVALID CONDN. _________________

Also, what does this expression mean when we have a minus sign?

|x-y| = |x| - |y| or

|x-y| = |y| - |x|

or, when we use the greater or less sign? for example:

|x-y| < |x| - |y|

|x-y| > |x| - |y|

I would really appreciate your input! thanks

consider : |x-y| = |x| - |y| or |x-y| = |y| - |x| we are just taking difference in magnitudes or simple value (irrespective of sign ) if both x and y have same signs then above equation is true ,since the operation subtraction is subtraction if both variabl;es are of same sign. |x-y| = |x| - |y| => this implies x,y same sign and x>y since LHS is +ve and hence RHS is +ve similarly : |x-y| = |y| - |x|=> this implies x,y same sign and y>x since LHS is +ve and hence RHS is +ve

consider eqn: |x-y| > |x| - |y| this says mod of difference > diff of modes now diff of mods is least always since max of x and max of y are subtracted. if in case x and y have opp signs then subtraction operation becomes addition hence mod of diff of x,y with opp signs is > than actual diff of mods.

hence |x-y| > |x| - |y| => this implies x,y opp sign and x>y since LHS is +ve and hence RHS is +ve

similarly

|x-y| > |y| - |x| => this implies x,y opp sign and y>x since LHS is +ve and hence RHS is +ve

|x-y| < |x| - |y| => this conmdition is not feasible since minimum diff between two numbers is the diff(in magnitude) between their mods.INVALID CONDN.

great explanation. Just what do you mean by RHS and LHS? thanks