as state is approaching, i've gone back to my old ways... taking lots of practice tests and asking you all for the answers to the ones i didn't know how to do!
So, without further ado, i present to you... more questions!
50. sheesh, uhmm....I guess just about 18 * 5.5 * 1.8 * 1.8 is about 20*5*2*1.5 is 300? could be way off here
51. think of it this way....the first 2 points form a line with each other. Every line thereafter forms a line with every other point, so we have 2p = 1 line, 3p = 3 lines, 4p = 6 lines, etc...
So, we have the number of lines that are determined by n points, no three of which are collinear is the (n-1)th triangular number.
70. 21 is pretty close to 11*2, so replace 31*21 with 11*62, giving 11*190 = 2090
8. That's an exact problem? hmm...a slow way would be to divide 1158 by 4 giving 289.5 * 30 giving 2895 * 3 giving 8685...is that right? check it
20. 613957/434, I would just divide to find 2 digits,estimate the 3rd, then add zeros...1450
im not that big on ns, but i think i might be able to help you on a few of these... and i apologize for working them out of order...
35. 122 *123 - 122 = 14884 if you think about it, subtracting the 122 would make the problem 122*122. as for the multiplying, i FOIL it, but then again i FOIL anything i cant remember the trick for...
58. 1+3-5+7...+61 = 1 each 'pair' of numbers (+x-y) gives -2. since the last term is +61, subtract one (to get an even number of pairs) and divide by two (to determine how many pairs there are.) multiply the answer (30) by -2 and add 61.
36. (n*((n+i)/2))/2 = 650 where n = the final number (50) and i = the initial number (2)
74.(1+3+5+...+29)/30 = 7.5 the way i would do it: pair up the numbers that add up to 30: (1,29) (3,27) etc... you see you have 7 pairs, with the number 15 left over. divide 15 by 30 (you already know that the 7 pairs have been divided) the *most likely* more ns-like way to do it: ((n+1)^2) * 1 4 30 since (n+1) = 30, and (n+1)^2 = (30)(30), you can cancel out one of the 30s, and youre left with 30/4, or 7.5.
48. the next term of -1,4,21,56,115 = 204 the only way i know how to do this would be hard for me, but you guys could do it easily. look at the differences in the numbers. -1 4 21 56 115 5 17 35 59 now look at the differences in the differences. -1 4 21 56 115 5 17 35 59 12 18 24 you see the 2nd difference is increasing by 6 each time. so, you would add 6 to 24 (30), add THAT to 59 (89) and add THAT to 115 (204)
21. 1/8 + 1/9 + 1/10 = 40/119 find a common denominator (720) since you multiplied each number by the other two, to get the numerator you just multiply all 3 combinations of numbers and add them together (8*9)+(9*10)+(8*10)=242. 242/720 reduces to 40/119.
69. 216^2 = 46656 i would have to FOIL this one...
33. the square root of 6084 is.... 78 i would have to factor it. 6084= 2*2*3*3*13*13. so the square root of 6084 would be 2*3*13, or 78.
i apologize for the childishness of most of my solutions... i thought i would try to help
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i was going to conquer the world... but i got distracted by something sparkly!
#50) Think of this as being sqrt(314 x 31.4 x 3.14 x 3.14) which is the same as saying
sqrt(31.4 x 31.4 x 3.14 x 3.14 x 10) = 31.4 x 3.14 x sqrt(10) which is approximately 100 x 3 which is 300....pretty dang close. Notice I rounded up a lot though. This is a key to this problem.
51) (n-1) triangular number
70) 31 x 21 + 11 x 121 is approximately 600 + 1331 (you should know 11^3 or 11 x 11^2) which is basically 2000 since we rounded down.
8) This has to be a misprint, especially if this is number 8. But I would do 15 x 1158/2 = 15 x 579 = 15 x 580 - 15 = 8700 - 15 = 8685. Still don't think this is what he intended.
20) This is not very mathematical but to me it looks like what is leftover from the 6 will cancel out what is left over from the 4. In other words, 613957 / 434 would become 600000/400 which comes out to 1500. Now I know I fudged a lot, and I know the real answer is between 1400 and 1500, so I would just go with the middle and say 1450. When I saw the problem this is what I immediately saw and came up with without doing any hard or complicated math. The actual answer is 1414... which should be within range. Grant it most people have a hard time generalizing this much, but it almost always worked for me and it is very fast.
21) I don't know of any trick but I would just find the common denominator and reduce. It is pretty easy to find 242/720 and dividing by 2 we will get 121/360. This is in simplest terms since we know 121 = 11^2, and 360 is not divisible by 11.
33) sqrt (6084) = ? The way I do square roots is get it between a multiple of 5. I know 75^2 = 5625 and 80^2 = 6400. So the answer is 75<x<80. It must end in an 8 now so the answer is 78. Pretty easy since squaring numbers ending in 5 is easy. Look on my website under square roots for more examples.
35) Square 122. You can do this easily by using the square numbers trick and using the tens humber as 12. So it would end up being (12 2)^2. The ones digit is 2^2 or 4. The next digit is 2 x (12 * 2) or 48. Write 8 carry the 4. The next is 12^2 or 144. Adding 4 we get 148. The answer is 148 8 4 or 14484.
36) This is how I would do it. Dividing everything by 2 we get 1+2+...+25 which is 26*25/2. Since we divided everything by 2 we have 2 x (26*25) / 2 = 26 X 25 = 650. Or you could do what FHT did.
49) This problem is difficult. If you don't recognize the formula almost immediately (which most of the time you should be able to) skip it and return if you have more time. It took me awhile to recognize this one when first seeing it, so I would have skipped it instead of wasting time on it. But FHT is right on this one as well.
58) Again, FHT nailed this one
69) Same concept as using 122^2. I wouldn't foil, just use the squaring method, although technically there is very little difference. But this is a little faster for me.
