2010 PSAT - Saturday - Section 4 (Math)

The following are TestTakers' suggestions for solving the problems on the October 16th, 2010 PSAT, Section 4 (a math section). Click "Read More" to view!

2010 PSAT - Saturday - Section 2 (Math)

The following are TestTakers' suggestions for solving the problems on the October 16th, 2010 PSAT, Section 2 (a math section). Click "Read More" to view!

Test 1 Section 3 - #16 (page 400)

They're asking us to solve for an expression here (6a + 6b, to be precise) so we need to find a way to get from what they gave us to what they ask for.  Here's what we're given:

3a + 4b = b

We're already close.  Multiplying everything by 2 will get us closer (remember, use what they want as a GUIDE...that's what we're aiming for!):

2(3a + 4b) = 2b

6a +8b = 2b

Now, just subtract 2b from both sides, and we're there!

6a + 6b = 0

That's choice (A).

It's important to note that in this particular question, it's impossible to solve for the individual variables a and b. We'd need two equations to do that, and they only gave us one. Doesn't matter, though, since we aren't looking for the individual variables, and don't need them.  If I asked you for a cake, I'd want you to bring me a cake, not the ingredients to make one. Same goes for the SAT: if they ask for an expression, solve directly for the expression, don't try to find the ingredients.

Test 1 Section 3 - #7 (page 398)

Whenever the SAT asks you to solve for an expression (or, anything but a standard single variable), what you want to ask yourself is: "How do I get from what they gave me to what they want?"  Usually once you see the path, it's only a step or two.

The first thing I want to do here is take what they gave me and break it up so it's more useful.
3x² = 4y = 12 can be broken into two equations:

3x² = 12
 4y = 12 *

Note that we have parts of what we want in both equations (our x² is in the first equation, our y is in the second).  Since we're looking for x²y eventually (those two parts multiplied together), let's multiply our entire equations by each other:

(3x²)(4y) = (12)(12)

12x²y = 144

And now we're almost there!  We want to know what x²y is by itself, so just divide both sides by 12:

x²y = 12

That's choice (D).

* Note that from here we COULD just solve: x = 2 (or -2) and y = 3.  HOWEVER, it's better practice to continue to solve directly for the expression x²y because we're not always going to be able to solve for the component parts on questions like this...at least not quickly.