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04 Dec 2012, 01:11
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This is actually a riddle from some book I had while in the 8th or 9th grade.. I've just tried my best to make it into a DS question... So here goes.. My second question on this forum... No official answer as this is my own question...
If \(0<n\leq{26}\) and n and x are integers, what is the value of \((x-x_1)*(x-x_2)*(x-x_3)........(x-x_n)\)?
1)\(x_1 = a, x_2 = b, x_3 = c\)and so on such that \(x_a = a^{th}\) alphabet when the english alphabet is arranged in alphabetic order and each alphabet represents a unique number.
2) n = 26
If \(0<n\leq{26}\) and n and x are integers, what is the value of \((x-x_1)*(x-x_2)*(x-x_3)........(x-x_n)\)?
1)\(x_1 = a, x_2 = b, x_3 = c\)and so on such that \(x_a = a^{th}\) alphabet when the english alphabet is arranged in alphabetic order and each alphabet represents a unique number.
2) n = 26
My answer is C
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04 Dec 2012, 12:32
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MacFauz
Dear MacFauz,
I don't think this question works as is.
The prompt asks "what is the value" of the expression --- this question typically denotes a numerical value. So, we want a number answer. As it stands, we don't know the numerical value of x, and we don't know the numerical value of any of the alphabetical variables.
Statement #1 tells us the letters we will choose for the variables, but that's not the same as getting values for the variables. We have a bunch of variables, and we know the letter will assign to these variables, but we have no idea what the values will be. Any one of them can be any integer.
Statement #2 just tells us there are 26 variables, so 26 factors in the expression.
Even if we knew that the nth variable equaled n, so that the expression were (x-1)*(x-2)*(x-3)* ....*(x-26), we still wouldn't know the value of x itself, and therefore still would not know the value of the expression. It seems to me the answer should be (E) --- nothing is even close to being determined.
Perhaps I am missing something, or misinterpreting something. I would be intrigued to find out how you are thinking about this question.
Mike
04 Dec 2012, 21:21
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mikemcgarry
Thanks for replying Mike... I should say I was worried whether Statement 1 would be able to convey the meaning properly. The riddle went like this : what is the value of (x-a)*(x-b)-(x-c).....(x-z). The answer was 0. The reason being that this series contains the term (x-x). The logic I used to frame the question was:
Statement 1) The series given becomes (x-a)*(x-b)*(x-c).... etc. But we do not know until which letter this series extends. If it ends before x, we cannot determine the value otherwise the value is zero. Insufficient.
Statement 2) The series given becomes \((x-x_1)*(x-x_2)....(x-x_{26})\). Insufficient.
1 & 2 together the series is (x-a)*(x-b)*(x-c).......(x-w)*(x-x)*(x-y)*(x-z) = 0.
I understand statement 1 is a bit convoluted. Is there a better way for me to express the meaning clearly or is the question itself not salvageable??
