Well... I'm happy about this test. I'm finally starting to see some marked improvement in my score. This test wasnt an easy one either, so yeah! But of course... I have a few questions.
20) 61 x 18 x 49 = __________________________.
I did 60*20*50 and got 60,000 which is out of range by a few thousand, so I was wondering how you estimate this correctly.
33) If 17 = x^2 - y^2 and x,y are both positive integers then x = ________________.
I guessed and checked my way to 9, but it cost me 30 seconds and 4 or 5 more problems, so whats the fast way?
Thats it. I got a 142 on this one. My score is steadily increasing thanks to you guys! I've gone from the 80s to the 130s -140s in just a few weeks! And I still have yet to memorize the crud that I'm supposed to have memorized for NS. Thanks again, Sam, Brad, and whoever else have been answering my questions!
20) I would have done the same thing as you on this one, but looking at it closely, the 18 is what makes the difference. *20 instead of *18 is more of a difference than *50 vs. *49. So chop off a few thousand at the end
33) I don't know if you run into them yet, but NS tests use difference of squares a lot. So often times you'll see:
On 61*18*49, I rather do 18*50 = 900, and 61*900 =54900 is just piece of cake.
It's right to factor a square minus b square but if you see a prime number as the difference, you should realized that the only way to factor a prime number is 1*that number. Thus a shortcut is born. If the difference of the two squares is a prime, k, add 1 to k and divide by 2 for the bigger of the number squared, and minus 1 divide by 2 for the smaller one. The two numbers are consecutive.
Cool! I didn't think about it that way. Thanks agian for the great insight. The estimation method you showed seemed kinda arbitrary though... I mean, how do you know exactly when to not over approximate, like I did?
I would have to say it's one of things on NS that truly tests your number SENSE. For example on the last one I did, you know your answer are in the right range because even if you do multiply 18 by 50 is just 2 percent off the exact answer.
What I'd do when I see 3 numbers multiplying is first see if there's any special numbers, like if it's 27*77*37, I would combine 27 and 37 because they make 999. And if there are no special numbers, estimate real quick which combination will get you prettier numbers, like near hundreds, number that roughly fit some shortcuts(like 1248 ->1250, 253 -> 250, and be creative), or that their products will connect with the 3rd number(like when you can do a^2-b^2 or such). Then estimate that will your answer give you more/less, is it <5%, how much more/less, then how much to add/subtract, how many digits and zeros should the answer have? I know it sounds like a lot of work, but it is feasible to be accomplished in a few seconds as proven by many NSers. The key is don't lose your head, and don't get frustrated. If you got lost really bad, skip and proceed because there will be a lot more wonderful things ahead that will make you forget that freakin problem in a blink.
Practice is the only way. To do'em fast you have to first encounter enough of them. You've just brought up one problem. So every time you see a problem, tell us about it, and each of us will I guess after a few more problem you'll have a better idea.
