when to change the LT or GT sign in the answer

[jan]

I'm going to post this again. It was answered, but basically I was told to just "think logically." I don't follow the logic. That is the issue. I would appreciate an answer, so maybe someone else could try to help me. Thank you.
In ch 4 of the Algebra Strategy guide, I am not clear on when to switch the GT to a LT in the answer to 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, having asked my husband who is an engineer, and my friend who tutors math to younger students (but who has not had Algebra 2--is this algebra 2 that is in this problem?).

This is probably not that hard. I'm just missing a piece somewhere.
Thanks.

Thank you.

[tommywallach]

Hey Jan,

I apologize that my answer wasn't satisfactory to you, but I promise you that it was the correct answer. You seem to be misunderstanding me. I'm not telling you to think logically as in "This should be obvious to you, just think about it logically and you'll have the answer."

What I meant was that this is too complicated to attempt to memorize, which seems to be what you're looking for (i.e. you want to know when you can simply translate one thing into another thing). The issue is that there are many many things you'd have to learn. If you really want to memorize it would look like this

The sum of two things where one of them is GT than an integer keeps the GT.

4 + GT 5 = GT 9

The difference between two things where one of them is GT than an integer trades the GT for LT.

4 - GT 5 = LT -1

The difference between two things where one of them is LT an integer trades the LT for GT.

4 - LT 5 = GT -1

The sum of two things where one of them is LT an integer keeps the LT.

4 + LT 5 = LT 9

The product of two things where one of them is GT than an integer keeps the GT.

4 * GT 5 = GT 20

The product of two things where one of them is LT an integer keeps the LT.

4 * LT 5 = LT 20

If you'd like to memorize all those, you certainly can. My recommendation remains that you should TRY a few number (that is not the same as "thinking about it logically") and use the results to work out what the new range is.

-t

[jan]

Thanks for getting back to me. Actually, I did finally just figure it out. I'll post this in case it randomly helps someone who thinks like me.

The issue was that it is thinking in terms of a number line. That's what I meant by I needed help on the thinking about _how_ to think about it? I understood you that you weren't just trying to tell me to be logical, but I did not follow the reasoning of what was happening.

So, thinking in terms of a number line, an answer that is LT 3 is to the left on the number line, a number that is GT than -3 is to the right on the number line. When solving a problem, such as -4 - GT(-3) = ?, then I could do the math to get -4 +3 = 1, but it wasn't until I started thinking in terms of well, if the second number there is 'Greater than -3' and substituted a number that was actually 'Greater than -3' such as -2.8 (notice, NOT -3.5 -- it is NOT greater in number, but in position on the number line), and I would get the answer -4 - (-2.8) = -1.2, and I could see that -1.2 was to the Left of the number line of 1.0 (the answer to the first problem of -4 +3 =1). So then I would know that the answer was Less Than -1 (LT-1). Not Greater than -1, although the words 'greater than' were used in the problem.

Convoluted, maybe. But I now get it. Not sure if I can do this fast enough for a 2 minute GRE problem. But we'll see.

Bottom line. Need to think of the number line and not get confused by the words 'greater' or 'less than' AND substitute appropriately.

[tommywallach]

Cool! Well I'm glad it got sorted out! : )

-t