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jan
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LT GT switch in answer on optimization problem

by jan Fri Feb 21, 2014 11:21 pm

In ch 4 of the Algebra Strategy guide, I am not clear on when to switch the GT to a LT in a problem. On page 89-90, I follow the explanations on how to find a range with the largest and smallest values for a variable, but when they change from using Less Than or Equal to OR Greater than or Equal To...to just Less Than or just Greater than (LT or GT), I am not clear.

For example, on page 90, in the box, you have m Min is -4, n min is GT(-3) and then the problem m-n is shown as (-4)- GT(-3)=LT(-1).

On a GMAT Manhattan Prep site I found that sometimes you can substitute LESS or MORE for the < or >, and sometimes that helps you know the sign of the answer (i.e., Less - Less = Less, so -4 - LT-2 = LT-6

But there were some exceptions and I didn't follow the logic.

Is there an explanation somewhere, and will I need this for the GRE, since I found a partial answer on the GMAT prep page, but can't seem to find anyone who understands it either.

Thank you.
tommywallach
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Re: LT GT switch in answer on optimization problem

by tommywallach Sat Feb 22, 2014 6:27 pm

Hey Jan,

The truth is that I recommend you simply "think" about it logically, as opposed to trying to come up with a formulaic way of trading things.

For example, if you have 4 - GT3, you can just think that 4 - 3 = 1, while 4 - 4 = 0, so now we know the answer is LT1. There are rules, but they are different for subtraction, addition, multiplication, and division, and they're also different based on order (the difference between GT3 - 4 as opposed to 4 - GT3). So I encourage just thinking about it/trying a couple actual numbers, and derive it on the fly.

Let me know if that makes sense!

-t
jan
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Re: LT GT switch in answer on optimization problem

by jan Fri Feb 28, 2014 12:25 am

Well, ...not really, actually. I get the subtracting the numbers. I'm not a mathematical thinker, and it's been 30 years since I did math. I'm studying Arabic--a bit of a different thing than math. I'm trying to visualize on a numberline. I understand that 4-3=1. That I get. It's whether it makes it a LT or a GT that for whatever reason I am stuck on. For some reason, that is not computing for me.

I also understand that 4 is greater than 3, so you picked 4 to subtract from 4 (and got zero). But I still don't follow why that has to be a Less than 1...

I probably sound stupid, but oh well. If there is a way you can think of to explain it to me, I'd appreciate it. I was pretty much whipping through the Algebra book, remembering things and understanding what I didn't remember...until that part.

I guess I don't get how to visualize the Greater than 3, if that makes sense. And how to determine the resulting inequality sign.

Thanks.
jan
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Re: LT GT switch in answer on optimization problem

by jan Fri Feb 28, 2014 12:37 am

Oh, and as a note...before I asked you guys, I had my husband look at it (he is an engineer) and my friend who teaches math (albeit to junior high and below) and neither of them could follow it either. There is an assumption in thinking that is not immediately obvious. Thank you for clarifying. I'm sure the logic will be needed for the GRE.

Thanks,
Jan
jan
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Re: LT GT switch in answer on optimization problem

by jan Mon Mar 03, 2014 11:33 am

Are you there...? Or maybe just not on the weekend?

Thanks for more clarification.

Jan
tommywallach
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Re: LT GT switch in answer on optimization problem

by tommywallach Mon Mar 03, 2014 11:38 pm

Hey Jan,

What I'm telling you is to just try it with numbers, on the fly. You will never have to do this in some conceptual way. So if a question asks you:

What is 4 - GT 3?

You: Try the first legal thing you could try

4 - 3.00001 = .99999

Then you: Try some other legal number

4 - 4 = 0

We can see that the result is getting SMALLER, and our outer limit was 1, so the answer is:

LT 1

Make sense? There's no assumptions being made in our book at all. We're simply showing you what the rules are. You can simply memorize them as rules, but as I said, there are a lot of them, which is why I recommend you just try out a couple numbers each time (I certainly don't have all of the "rules" memorized; I just work it out with some numbers when it's necessary to do so).

Hope that helps!

-t