The sum of 28 consecutive odd, positive integers is a perfect cube. If p and q are the least and greatest of these intergers, the average of the least possible value of p and the least possible value of q is between
(A)80 and 90
(B)90 and 100
(C)100 and 110
(D)110 and 120
(E)120 and 130
i bet you cant solve it HA
show your work if you do =D
2006-11-26 17:02:00 · 11 answers · asked by joker92 2 in Science & Mathematics ➔ Mathematics
Lets call the numbers 2a-27, 2a-25, 2a-23, ..., 2a+23, 2a+25, 2a+27. Thats 28 numbers, and since all the constant terms cancel out, their sum is 28*2a = 56a = 7a*2^3.
Since we already have a factor of 2^3 in there, all we need for the entire thing to be a cube is a = 7*7*cube.
The smallest value of a gives the smallest p and the smallest q, so a = 7*7 = 49.
That gives p = 71, q = 125, average = 98, ie B.
2006-11-26 17:17:21 · answer #1 · answered by stephen m 4 · 1⤊ 1⤋
The answer is B. Use an excel spreadsheet. In the first column, put odd numbered values in sequence. In the second column, beginning at row 28, put in the function that adds the 28 cells to the left and above the reference cell. In the third column, put in the cube root of the cell to the left. Cell C63 gives an answer. The odd integers are 71 through 125. their sum is 2744, which is the cube of 14. The average of 71 and 125 is 93.
Note for stephen m: Your formula works, but the math you did may not be correct. If p is 83, and q is 125, that is only 22 consecutive odd numbers.
2006-11-26 17:32:52 · answer #2 · answered by _Bogie_ 4 · 0⤊ 0⤋
q = p + 27*2 = p + 54
S = 28 (2*p + 54) / 2 = 14 (2p +54)
= 2^2 * 7 * (p+ 27)
hence, p + 27 = 2 * 7^2
or p = 71
Hence average = p + 27 = 98
ans is B
Now, where's my prize for doing ur homework?
2006-11-26 17:14:06 · answer #3 · answered by placebo 2 · 1⤊ 2⤋
Well, I got as far as 28x + 702 = perfect cube and x+26 is the average. Lol
2006-11-26 17:11:10 · answer #4 · answered by crage_ralius 3 · 0⤊ 1⤋
Dewd..... If you really don't see this one, you need to go back and learn something about the other math classes you had before this. You remember those? The ones where you screwed around and didn't learn anything?
Doug
2006-11-26 17:10:28 · answer #5 · answered by doug_donaghue 7 · 0⤊ 2⤋
I bet you can't solve it either !
2006-11-26 17:07:07 · answer #6 · answered by mathlete1 3 · 0⤊ 2⤋
O and R
2006-11-26 17:10:44 · answer #7 · answered by visyboy 3 · 0⤊ 2⤋
I challenge you to DO YOUR OWN HOMEWORK!
2006-11-26 17:03:37 · answer #8 · answered by The Nag 5 · 1⤊ 2⤋
are you high?
2006-11-26 17:05:52 · answer #9 · answered by obsidian_elegance 1 · 0⤊ 2⤋
um...no one cares.
2006-11-26 17:05:24 · answer #10 · answered by laura 4 · 0⤊ 2⤋