Manhattan method produces a wrong ANSWER.

[dddanny2006]

Is x ≥ 0?

1) x^2 = 9x

2) |x| = -x

Statement 1 is absolutely sufficient.So the answer is A or D.When it comes to statment 2,this is my way of solving it and it contradicts with the real answer.

|x|=-x => x=+(-x)=-x,this is true when x>0, and x=-(-x),this is true when x<0
Therefore statement 2 gives us 2 conditions x=x and x=-x.Now since x=-x when x>0 ,x can never be equal to -x when x>0.So I dont know what I can call this condition.Now,we also have x=x when x<0,so -5=-5,-6=-6,these dont satisfy the condition in the question stem and hence No.ThereforeStatement 2 gives us 2 conditions of which one condition gives us a _________(I dont know what to call it because it cant be tested due to x>0) and the other condition gives us a No(-1,-2... are not greater than or equal to 0).When we have a statement that has 2 sub statements,and one of those sub statements(x=-x and x=x subjected to x>0 for the former and x<0 for the latter) cant be tested,but the other one gives us a No.What bearing does this have on that statement?Is it a Yes or a No for Statement 2?Please help me solve this on the basis of the Manhattan article here.

In which way is my understanding of the question wrong?

I have followed this technique from here--
http://www.manhattangmat.com/strategy-s ... -value.cfm

Absolute value expressions start to become difficult when variable expressions are placed inside the bars. For example, /x/. Upon a cursory examination, the expression /x/ seems like it should be equal to x. Since there is no sign in front of the x, the absolute value bars should be able to be removed without jeopardizing the "guarantee of positive." What this line of reasoning fails to account for, however, is that x itself could be negative! When dealing with absolute value expressions that contain variables, two scenarios must be considered: (1) the scenario whereby the expression inside the bars is positive and (2) the scenario whereby the expression inside the bars is negative.

In this example, for scenario (1) if x > 0, the expression /x/ can simply be represented as x; for scenario (2) if x < 0, the expression /x/ must be represented as (-x). Notice that in the negative scenario, we don't simply remove the absolute value bars. We remove the absolute value bars and negate the entire expression within.

Let's look at a more complicated example: the expression /x - 3/. As always, we must consider both the positive and negative scenarios. When is the expression inside the absolute value bars positive? Not simply when x > 0, but when x - 3 > 0 or when x > 3. Likewise the expression will be negative when x < 3.

To recap, the two scenarios are:
(1) /x - 3/ can be rewritten as x - 3 when x > 3
(2) /x - 3/ can be rewritten as -(x - 3) or 3 - x when x < 3

One more for the road: /3x + y/.
(1) /3x + y/ can be rewritten as 3x + y when 3x + y > 0
(2) /3x + y/ can be rewritten as -(3x + y) when 3x + y < 0

[StaceyKoprince]

Please read (and follow!) the forum guidelines before posting.

This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). If you are a course student, you can also ask about other problems or issues before or after class or during section.

Please also note that sources MUST be cited before we answer, so that's another reason I actually shouldn't be answering your question here...

You have, however, pointed out to me an error in something on our site, so I am going to answer you here as thanks. :) Just note that you do need to post in the right folder for additional / future qustions. (And: thanks!)

The explanation you quoted should say "positive or zero" for the "positive" case. In both of those cases (positive or zero), the number stays the same once the absolute value signs are removed.

In that case, your first scenario is x = -x when x is zero or positive. It can't be true for any positive number, but it is true for 0. In this scenario, yes, x > 0.

Your second scenario (x = x when x is negative) works for all negatives. In this scenario, no, x is not > 0.

Does that make sense?

[dddanny2006]

Well,I did get your point.And thanks for responding in-spite of me not following the rules.I was very stressed because different things were spoken in different places regarding the concept and I expected the Manhattan to be very transparent and easy to understand which the article failed to do,not only that it even got me confused as to where I may test that -0 due to the boundary conditions .I did post in the other folders too,but you did not respond to them rather overlooked them I should say because you did respond to other questions during that time on that day,and I thought I needed to make multiple entries for your response.Millions around the world read the article and the subject matter should be very understandable and complete,and that too its a strategy-based article,and had I given my GMAT on that day,I would have answered the question wrongly and lost valuable points.Since I alerted you'll on this,I think I do stand a chance to win goodies from you'll in the form of a book,or anything else that you could arrange for :)

Thanks again

Please read (and follow!) the forum guidelines before posting.

This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). If you are a course student, you can also ask about other problems or issues before or after class or during section.

Please also note that sources MUST be cited before we answer, so that's another reason I actually shouldn't be answering your question here...

You have, however, pointed out to me an error in something on our site, so I am going to answer you here as thanks. :) Just note that you do need to post in the right folder for additional / future qustions. (And: thanks!)

The explanation you quoted should say "positive or zero" for the "positive" case. In both of those cases (positive or zero), the number stays the same once the absolute value signs are removed.

In that case, your first scenario is x = -x when x is zero or positive. It can't be true for any positive number, but it is true for 0. In this scenario, yes, x > 0.

Your second scenario (x = x when x is negative) works for all negatives. In this scenario, no, x is not > 0.

Does that make sense?

[StaceyKoprince]

Thanks for your reply. We've fixed the article, by the way - take a look!

I'll ask our Student Services department whether they can't rustle up something for you as a thank you. My guess is that they'll be happy to offer you a free e-book of your choice. (Note: "of your choice" is limited to our own books, of course - not any book in the world! :)

I've already sent an email to explain the situation. Send an email to gmat@manhattanprep.com and tell them your forum username. Mention my name and say that I told you to write in about catching a mistake on our site and ask them to forward the email to me. We'll verify your identity (so, others reading this, don't write in and say that you're dddanny2006!!).

Note to others reading this: we don't give rewards for reporting minor errors / typos (beyond the satisfaction of knowing that you helped make the world a little better!). In this case, dddanny2006 spotted a pretty significant error.

Thanks Danny!

[dddanny2006]

Hey Stacey.
I did get a ebook.It would have been nice if I could atleast get one more as I deserved it.They told me that it was you who decide on the number of books.Can I have the Word-translation book too.I'd be happy if I get that and Im sure you'll oblige since I helped you'll in fixing the error.Facebook does have a Bug-detection program with a $500 minimum pay-out.Im just asking for another book. :)

Thanks
Danny

Well,I did get your point.And thanks for responding in-spite of me not following the rules.I was very stressed because different things were spoken in different places regarding the concept and I expected the Manhattan to be very transparent and easy to understand which the article failed to do,not only that it even got me confused as to where I may test that -0 due to the boundary conditions .I did post in the other folders too,but you did not respond to them rather overlooked them I should say because you did respond to other questions during that time on that day,and I thought I needed to make multiple entries for your response.Millions around the world read the article and the subject matter should be very understandable and complete,and that too its a strategy-based article,and had I given my GMAT on that day,I would have answered the question wrongly and lost valuable points.Since I alerted you'll on this,I think I do stand a chance to win goodies from you'll in the form of a book,or anything else that you could arrange for :)

Thanks again

Please read (and follow!) the forum guidelines before posting.

This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). If you are a course student, you can also ask about other problems or issues before or after class or during section.

Please also note that sources MUST be cited before we answer, so that's another reason I actually shouldn't be answering your question here...

You have, however, pointed out to me an error in something on our site, so I am going to answer you here as thanks. :) Just note that you do need to post in the right folder for additional / future qustions. (And: thanks!)

The explanation you quoted should say "positive or zero" for the "positive" case. In both of those cases (positive or zero), the number stays the same once the absolute value signs are removed.

In that case, your first scenario is x = -x when x is zero or positive. It can't be true for any positive number, but it is true for 0. In this scenario, yes, x > 0.

Your second scenario (x = x when x is negative) works for all negatives. In this scenario, no, x is not > 0.

Does that make sense?

[StaceyKoprince]

That's news to me - I've never been the one with the power to decide that before! (And I don't think I have that power now - I think the person was mistaken.)

I'd be happy to ask our Director of Student Services whether an exception can be made in your case, but just FYI - in every case I've ever heard of in the past, it has always been just one book.

[dddanny2006]

Oh yea,please have a word and get back to me. Thank you again

That's news to me - I've never been the one with the power to decide that before! (And I don't think I have that power now - I think the person was mistaken.)

I'd be happy to ask our Director of Student Services whether an exception can be made in your case, but just FYI - in every case I've ever heard of in the past, it has always been just one book.

[StaceyKoprince]

no worries - thanks!