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Excitable_Boy, I hate to be argumentative (the only things I enjoy in life are love and peace!!!), but would not logic dictate that you cannot "skip" in the middle of a series (its core), but you can before and after the series.
Shar, please ask your son's teacher for the answer and the proof.
Originally posted by Excitable_Boy
Excitable_Boy, I hate to be argumentative (the only things I enjoy in life are love and peace!!!), but would not logic dictate that you cannot "skip" in the middle of a series (its core), but you can before and after the series.
GT...it appears you are obsessing. No one said this problem was a perfect series. It is simply 5 squares that are all related somehow and we need to figure out what the fifth is. Based, once again, on the multiple choice answers we have to choose from, the answer is 18 because, again, it is a factor of 36 just like all the other squares.
It says NOWHERE that this is a perfect series we are working on. And....it also doesn't matter what the 6th square is. There is no sixth square. This puzzle has 5 squares.
The problem is set up to make one think, at first glance, that the answer is 13. Also, the 4 is there to throw things off. The problem is not a perfect series and was never said to be.
You can spend days working out various ways to come up with the various multiple choice answers. The fact is, none of them are logicial except the one I came up with!
[edit on 26-3-2007 by Excitable_Boy]
Originally posted by GreatTech
Excitable_Boy, I believe that you have the best proof of 18 (maybe I am wrong???) in a finite series.
I believe I have the best proof of 18 (maybe I am wrong???) in an infinite series.
Way to go, Excitable_Boy!!!
Originally posted by GreatTech
The sequence is 3, 4, 6, 9, 18, 36, 108, 324, 1944, 11664...
The two keys are:
1) The second square (4) is the numerical square of 2. The fourth square (9) is the numerical square of 3. The sixth square (36) is the numerical square of 6, derived from the numerical square of square 2 (2) multiplied by the numerical square of square 4 (3), or (2*3)^2 = 36. The eighth square (11664) is the numerical square of 108, derived from the numerical square of square 4 (3) multiplied by the numerical square of square 6 (36), or (3*36)^2 = 11664. This can continue on indefinitely.
2) The second key is much simpler. An alternating odd sequence can be partly proven since the first square (3) times the third square (6) equals one of the answer choices (18). This can continue on indefinitely. This second key combined with the first key provides a logical answer of 18.
Originally posted by GreatTech
Please attempt to disprove the logic in my quote above that proves that 18 is the correct answer in an infinite series.
The four squares are also all factors of 72, as is answer C (24). I believe the fact that the series adds in a pattern of +1, +2, +3 is too much to ignore. My vote is still for a misprinted answer key.
A. A logical answer to the problem is not one of the choices
B. Tests are not always going to be perfect
The most logical assumption here would be that it is a misprint.
Now even if we were to use your method, which doesn't really make sense in the first place because of how the question is presented, the next number in the series would be 12, not 18. This has been pointed out previously in the thread. It is not logical to skip a number when you are working with a series. Again 18 being there is just a coincidence, do you really think you would have put 18 as an answer if you were taking this test and it wasn't multiple choice?
A big part of the problem IS that it is multiple choice. It takes away the OBVIOUS answer of 13 and forces the test taker to think harder and outside the box.
It wants YOU to look at the 4 choices for answers and find the one that RELATES to the others