GRE Fast Math Week 5 Handout

[kent8402]

I am having a hard time with the last four problems of this handout.

To be more clear, the first of the four problems is posted below:

"If m/3 > n/12, is 12m > 3m?"

While I realize that the answers to these questions have been posted, I am specifically interested in what steps need to be taken to solve these problems.

Thanks!

[tommywallach]

Hey Kent,

If you have multiple questions, it's best to post each question as a separate thread, only because the threads get really confusing and convoluted when they take on multiple questions and issues at once. However, I'm happy to talk about the question you have posted.

m/3 > n/12

Whenever you're given a piece of information, make sure you get everything out of it you can before you move onto the question itself (because often the question itself will confuse you). In this case, we're way better off looking at non-fractions than fractions, so let's transform these by multiplying both sides by 12 (because that will get rid of BOTH denominators):

4m > n

Now look at the question. If we multiply both sides of our new manipulated equation, we end up with 12m > 3n, which was the original question (though you posted it as 12m > 3m, I assume that was a typo).

Let me know if that makes sense!

-t

[jen]

Hi there! Tommy is correct, of course, but figured I'd throw in my two cents! The key to all of those problems as a group is this:

DON'T MULTIPLY OR DIVIDE A VARIABLE ACROSS AN INEQUALITY UNLESS YOU KNOW WHETHER IT'S POSITIVE OR NEGATIVE!

Pardon the all-caps, but I really mean it ;)

So, in this case, you CAN cross-multiply:

a/2 > b/6

... because the variables are on the TOP, so we don't care about their signs.

But, in this case, you CANNOT cross-multiply...

4/x < 7/y

... because the variables are on the BOTTOM. So, when we cross-multiply (which is really just multiplying both sides by both denominators), we don't know whether to flip the sign! So, don't cross-multiply!

Now, if I TOLD you the signs of x and y (or even just something like "one is pos and one is neg, but we don't know which one is which" -- that is, "xy<0"), we'd be in business again -- we just need enough info to know whether to flip the sign when we cross- multiply.

Sincerely,
Jen

[anindita.dc]

Hi there. I have same problem with handout week 5 fast math. I understand Jen's explanation , infact i solve that way for that perticular problem then why next problem ans is CBD. Is that for presence of variable.problem is:
1. If 3/m>12/n is 3n>12m?

then why nxt qs ans is mention as "No". PROBLEM IS
2) IF xy<0 and4/y>9/x,is 4x>9y if that then this ans also be CBD.

3) if y> 0 and 5/x^2> 7/y, is 5y> 7x^2?

if I solve like multiply both side by x^y. then i get 5y>7x^2. but here y >0 but nothing mention about x so ans would be CBD. I am total confused why ans is YES.

[tommywallach]

why next problem ans is CBD. Is that for presence of variable.problem is:
1. If 3/m>12/n is 3n>12m?

Question #2 differs from Question #1 in that, in #1, you're cross-multiplying up KNOWN POSITIVE values. This means that the inequality sign will not change. In Question #2, you're multiplying up UNKNOWN variables. They could be either positive or negative, meaning the sign could flip, so the answer is CBD.

For question #3, the issue is that they tell you xy<0. That means that EITHER x is positive and y is negative OR y is positive and x is negative. That means that when you multiply up the two variables, you KNOW that the sign will flip ONCE (either for the x or the y, depending on which is negative). So you can actually determine the final equation. You KNOW the sign will flip.

Finally, for question #4, remember that x^2 is always positive, and they tell you that y is positive. That means you cross-multiply without ANY fear that you're multiplying by something negative. Remember, you only care about the sign insofar as it affects the inequality symbol.

Hope that helps!

-t