### Diagnostic Math Drill #3

Here's another drill for you to use to isolate problem areas. Please remember: When you're practicing, the time you spend reviewing your mistakes is arguably more important than the time you spend doing the problems in the first place. This drill will be most useful to you if you spend some real time with the answer key and technique guide afterwards. If you just mark the drill, shrug off your mistakes as "silly" ones, and move on, you're dooming yourself to repeat them. It's important to LEARN from your mistakes.

I should also restate something I've said before: These drills of mine are not exhaustive. I'm trying to write questions that cover a broad range of possible SAT questions, but in no way can these 20 questions (or these 60 questions, if you count the first two drills too) encompass every kind of question that will be thrown your way. I'm trying to help you work out a few specific kinks, but the bulk of your work should be in the Blue Book.

The answer key, as always, is linked from the end of the drill so that you can work through the drill without peeking, but you can also access it directly here.

Feel free to print, share, etc.

--OR--

Good luck!

1. I'm in....Can't wait. Printing out now....
Company will be here momentarily.  Can't wait till they leave ;)

2. WOO HOO WOO HOO!

guess whatttt? i only missed like 1 or 2! the last 10 or so I aced yeahhhh.

are these easier than diagnostic test 2? i got more wrong on that one than this.

3. Nice work! Yes, this one is slightly easier than the 2nd drill. :)

4. ah okay... well, i think it's time to take a full math portion soon! i've reviewed for the whole month, after all!

5. Yeah, I'd say so. Good luck with it!

6. Could you tell me how you did #8? I solved for y using the first equation then plugged it in to find x, and then plugged that in to find y. I'm sure there's a faster way though, perhaps using elimination?

7. Ah, yes. There is a MUCH faster way! :)

Just add the two equations together!

You should get 3y + 2y + 8x - 3x = 19 + 11. That simplifies to:

5y + 5x = 30

Now divide both sides by 5, and you get y + x = 6.

8. Cheers. Thanks for all your help.

9. I don't get #13 and #2... Can you please explain to me?

10. Sure. I recently explained #3 here.

#13 is a problem that's well-suited for backsolving, but to set it up you should create a Venn diagram. Make one circle for king beds and one for bathtubs. You know the TOTAL number of king beds (86) and the TOTAL number of bathtubs (57). But don't write those in your circles. Write them right below, just to remind yourself what the totals should be.

Choice (C) says there are 36 guests with both amenities, so fill that in the overlap of your Venn diagram. Now, if 36 are there, how many go in the non-overlapping parts? To make your totals, you need 50 in just king, and 21 in just bathtub. But those add up to 71, and the question said a total of 83 guests had only one amenity. So we need FEWER people with both.

So try (D). 30 guests with both means 56 with only king and 27 with only bathtub. Total guests with only one amenity? 56 + 27 = 83. Bingo.

11. Can you please explain #14?

12. For a question like this, focus on one point on each graph. I think in this case the most obvious point is the minimum of each one. Note that the lower graph is 4 down and 1 to the right of the upper graph.

It's important to know your graph translation rules. A shift of one to the right is going to mean a "–1" inside the function's argument, and a shift of 4 down will mean a "–4" outside. That's why it's (B).

13. #2 !! I don't understand how to interpret what f(6) means?

14. Is there any other method to solve instead of resorting to backsolving?

15. I've got a whole post on function notation here: http://blog.pwnthesat.com/2011/03/plain-old-non-symbol-function-questions.html

16. Yes. Using the Venn diagram you can also solve algebraically.

17. This website's organization is kind of throwing me off :/

18. Could i PLEASE email you the couple of questions i have?

19. I provide all these services for free because I want them to help everyone. So you can email me your questions, but I will probably take longer to respond than I would if you posted them to the Q&A. And I will still post their answers to the Q&A page in addition to responding.

20. I understand that, and i did attempt to post them. I'll try again and if i still don't get the hang of it I will email you, and, by all means, post the answers as you wish! Thank you!

21. OK, sounds good. :)

22. ... Email sent :) i have 4 questions.

23. Question #1? :s

24. First, note that the median of a set with an even number of elements is the average of the middle two elements. If the median of this set is 0, then the average of l and m must be 0. The only way that happens is if their sum is also 0, so II must be true.

The best way to eliminate the others is to plug in some values. Start with {–3, –2, –1, 1, 2, 3}. That's enough to eliminate roman numeral I.

What if the set changed to {–100, –99, -1, 1, 2, 3}. Then the sum of all the elements would be less than j, so you can eliminate III.