Starting at the end. You're
averaging a minute longer on PS than DS. So you aren't actually doing "better" on PS. You're spending a lot more time...and of course that's going to make a difference. Meanwhile, you're potentially sacrificing DS as a result (possibly causing more errors there due to speed?).
I see this all the time: people spend more time on PS, then rush DS to make up the time and fall into traps and miss things they could've gotten. But DS is awesome because it doesn't make you do all the annoying math that PS makes you do! So stop rushing it just to spend more time on annoying stuff.
General rule: don't artificially rush your strengths in order to devote more time to your weaknesses. If a strength naturally takes less time to solve, great. But don't risk losing that point when you know how to get it.
Those 3 fast quadratics...why were they so fast? Did you know how to do them and make some kind of mistake? Did you know you didn't know how to do them? When you look at the explanation, does it make sense / do you think, "Yes, I can totally learn how to do that?" Or does even the explanation seem like gobbledy-gook?
What you do to remedy the issue depends entirely on the answers to those questions.
Re: the NP problem, what are you using to study? Are you using our books? If so, look at the Test Cases strategy chapter. You'll need to test cases on this problem to see whether you can get a definitive answer.
n = + int
n / 6 = something remainder something
(2) n is a multiple of 12.
Now, test cases. You're only allowed to pick cases that make statement (2) true. (See book for full details on this strategy.)
If n = 12, then 12 / 6 = 2 remainder 0. In this case, the remainder is 0.
If n = 24, then 24 / 6 = 4 remainder 0. In this case, the remainder is 0.
If n = 36, then 36 / 6 = 5 remainder 0. In this case, the remainder is 0.
In fact, in any case you try, the remainder will be 0 if n is a multiple of 12. So this statement is sufficient because it gives a definitive answer: the remainder must be 0 (even though you don't know what n actually is).
My guess is that you were trying to solve for n? And if n could be 12 or 24, that would be two different answers?
That would be the case IF the problem asked for n, but it didn't. It asked for the remainder when n is divided by 6.
So this might be a broader DS issue: you have to make sure that you are investigating
exactly what they asked you. Don't make any assumptions / don't fall into the trap of just solving for the variable because that's what we had to do in school.
Next, regarding how to increase your level on the ones that you can't do (and that are more than just careless mistakes or not reading carefully), have you read this yet?
http://tinyurl.com/2ndlevelofgmatIf not, give it a try. Don't try it on every problem. If you read the explanation and you're like, "Uh...what?!?" then just decide how to get that one wrong fast. (ie, how you're going to know to make the decision to move on)
But where there's some opportunity, learn:
- You got it right but took longer than you could have; is there a different, more efficient path?
- You legitimately got it wrong, but the explanation makes complete sense; how can you learn to recognize something similar next time? What skills do you need to learn in order to be able to execute on that solution process, whatever it is? Then go practice / make that happen.
That sort of thing. What do you think about all of that?