the question is (Find three, consecutive numbers in G.P whose sum is 26 and their product is 216?)
133389
the numbers are \n 2+6+18= 26\n 2*6*18= 216
139902
You have to graph them and find the corner points.  One of the corner points will be the answer.\nI found the corner points to be\n(28,52) and (40,40)\nPlug each point into g = 3x+y \nFor (28,52): g = 3(28) + 52 = 136\nFor (40,40): g = 3(40) + 40 = 160\n136 is the smaller value, so (28,52) is the answer.
189302
Problem #1:  Four consecutive integers have sum of -34.  Let the first integer be x.  The next three must be x+1, x+2, and x+3.  This gives you the equation\n\n-34 = x + x+1 + x+2 + x+3\n-34 = 4x + 6\n-40 = 4x\nx = -10\n\nSo, the 4 consecutive integers are -10, -9, -8, and -7.\n\nProblem #2:  Again, four consecutive integers can be written as x, x+1, x+2, and x+3.  This time the equation is:\n\n4(x + x+3) = 24 + 6(x+2)\n4(2x + 3) = 24 + 6x + 12\n8x + 12 = 6x + 36\n2x = 24\nx = 12\n\nSo, the 4 integers are 12, 13, 14, and 15.  \n\nIt pays to check your answers:  The sum of the first and fourth is 12+15=27.  Four times this sum is 108.  6 times the third integer is 6*14=84.  108 is 24 greater than 84.
62491
The problem asks for:\na natural number n wich: n = k*3+1, n=q*5+1, n=r*7+1, n=p*9+1, n=m*11. => n = cM(3,5,7,9)+1 and 11 divides n. (cM(3,5,7,9) = a common multiple of 3,5,7,9). \nYou take the less cM(3,5,7,9) of all, wich is 945, add 1, and you find out that 11 divides it.\nAnswer is:\n\n-- 946 --
356414
4w - 24 = 3w + 3 (multiplying out the brackets)\n4w-3w = 24 + 3 (moving the 'w's and numbers to seperate sides)\n\ntherefore we are left with\nw = 27\n\nAnd to check\n4(27-6) = 4(21) = 84 = 3(27 + 1) = 3*28 = 84
157415
your answer is 255.  I believe it works something like this (look at the one integer gaps), remove them at one integer spaces (2,4) (3, 15) (4,16) what do these have in common?  Whats the next chain to follow?  4 is divisible by 2, step up 15 is divisible by 3, step up 16 is divisible by 4 step up and the next number divisible must be whatever is divisible by 15, the only answer which is given and fits that description is D 255.  I hope you can follow the logic :)  I dont see any relation where three numbers can be sequenced in relation here.  I know that next you could say 224 is divisible by 16 but there is nothing left after that for a third answer to form a chain with what is left to choose from (19 and 20)  Note also that by using this method the number which divides into 255 by 15 is in fact 17 to continue your string 15,16,17.
552267
Use binomial coefficients to solve this.\n\n| n |           n!\n|    |   =  ----------\n| k |        (n-k)!k!\n\nn is the number of possibilities and k is the number of unordered outcomes.\n\nCombination of six numbers from ten possibilities.\n\n| 10 |       10!          3628800         \n|      | = ------------ = --------------- = 210\n|   6 |    (10-6)!6!     (24)(720)\n\nCombination of four numbers from ten possibilities.\n\n| 10 |\n|      |\n|   4 |\n\nYou should be able to figure out the second one on your own.\nHere's a link on factorials, just in case you don't know what they are.\n\nhttp://mathworld.wolfram.com/Factorial.html
284555
n + (n+1) + (n+2) = 102\n3n + 3 = 102\n3n = 99\nn = 33\nn+1 = 34\nn+2 = 35\nsecond integer = 34
418474
Let x = the number you are looking for.\n\nSo, 3x + 7 = 52, which is easily solvable for x as follows:\n\n3x + 7 = 52\n\n3x = 45\n\nx = 15\n\n~ ♥ ~
532311
2L + 2w = p\n2L + 2(8) = 22\n2L + 16 = 22\n2L = 6\nL = 3
431951
Consecutive integers are n, n + 1, n + 2, n + 3\n\nThe sum of the second and fourth equals the third increased by 17.\n\n(n + 1) + (n + 3) = (n + 2) + 17
523766
The answer is 72.  You multiply the three numbers together.
103730
Hi there,\nWe will always be guaranteed a period of consecutive days when exactly 129 books are sold. The reason the number 129 is important is clear below. The proof uses what is known as the pigeonhole principle. [If n>m pigeons are put into m pigeonholes, then there exists a hole with more than one pigeon.] As usual, the trick is in constructing the "pigeons" and the "pigeonholes".\n\nLet B_i (for i=1,2,...,365) be the number of books sold during the period from the first day to the ith day inclusive (for example, B_3 represents the number of books sold in the first three days). Then we have:\n1 <= B_1 < B_2 < ... < B_365 = 600\nWe have strict inequalities inbetween as at least one book is sold each day. Now for the trick. Add 129 to this sequence of numbers to get:\n130 <= B_1 + 129 < B_2 + 129 < ... < B_365 + 129 = 729.\n\nWe choose B_1, B_2, ..., B_365, B_1 + 129, B_2 + 129, ..., B_365 + 129 as our pigeons. There are 730 of them, each being a positive integer between 1 and 729 inclusive. The numbers from 1 to 729 will be our pigeonholes. Thus by the pigeonhole principle, two of the numbers in our sequence of 730 numbers must be the same. As B_1, B_2, ..., B_365 are distinct, and B_1 + 129, B_2 + 129, ..., B_365 + 129 are distinct, one of the B_i's must be equal to one of the B_i + 129.\n\nSuppose that B_n = B_k + 129, where 1 <= k < n <= 365. Then we have B_n - B_k = 129. So between the (k+1)th day and the nth day inclusive, exactly 129 books were sold.\n\nCheerios,\nMike
440680
To get you started:\n1. 17, 32, 47, 62, 77.\na = 17, b = 15
329935
the sum of the two smallest numbers must be higher than the third one so your answer is d)
479820
3p + 2w = 462\nand \np - 24 = w\n\n3p + 2(p - 24) = 462\n3p + 29 - 48 = 462\n5p = 462 + 48 = 510\np = 102\n\n3x102 + 2w = 462\n306 + 2w = 462\n2w = 462 - 306 = 156\nw = 78\n\n102 boxes of pecans and 78 boxes of walnuts
378216
The answer is 78:\n\n1² + 2² + 3² + 8² = 1 + 4 + 9 + 64 = 78\n2² + 3² + 4² + 7² = 4 + 9 + 16 + 49 = 78\n1² + 4² + 5² + 6² = 1 + 16 + 25 + 36 = 78\n\nI did this creating a spreadsheet with the first 9 squares.  There were 126 ways (9 choose 4) ways to pick the four squares which then resulted in a sum.  I sorted the sums and found the one that repeated itself 3 times (78).\n\nThe answer is 78.