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vietst
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Post subject: f the terms of a sequence t1, t2, ....tn, what is  Posted: Fri Jan 04, 2008 5:52 pm |
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If the terms of a sequence t1, t2, ....tn, what is the value of n?
1. The sum of the n terms is 3,124.
2. The average (arithmetic mean) of the n terms is 4.
OA is C
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RonPurewal
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Post subject: Posted: Sun Jan 06, 2008 2:44 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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you should start this question the same way you start all questions involving averages: by using the 'magic formula'
average = sum / number of data points
or
(average)(number of data points) = sum
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note that the desired quantitiy in this problem is number of data points in the above formula.
examining the answer choices:
(1) alone
we only have one of the three quantities in the formula (i.e., sum). this is insufficient to determine either of the other two.
insufficient
(2) alone
we only have one of the three quantities in the formula (i.e., average). this is insufficient to determine either of the other two.
insufficient
together
we have sum and average, so the formula will yield number of data points.
sufficient
answer = c
**note that, had the problem contained a particular number in the place of 'n' (like t1, t2, ..., t8), then that would implicity give a value for number of data points. be careful!
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Maverick
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Post subject: Posted: Sun Jun 15, 2008 5:29 am |
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The question has one small problem. It talks about sequence, but does not clarify whether it is an arithmetic sequence.
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Success
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Post subject: Posted: Sun Jun 15, 2008 7:06 pm |
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I assume it is arithmetic becaues it says T1, T2,.....Tn; my guess is that you add '1' to the next term, making it arithmetic.
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RonPurewal
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Post subject: Posted: Wed Jun 18, 2008 5:23 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Maverick wrote: The question has one small problem. It talks about sequence, but does not clarify whether it is an arithmetic sequence.
whether this sequence is arithmetic is actually irrelevant; the facts above, concerning the relationship between sum, average, and number of data points, are true for any set or sequence.
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imanemekouar
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Post subject: Re: f the terms of a sequence t1, t2, ....tn, what is Posted: Mon Jan 18, 2010 5:46 pm |
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Hi Ron , I did not get the last part of your explanation. you find the number of term which is equal average*sum. But number of term is not equal of n. The number of term is equal to the last term -first/2. something that we don t have?
Maybe i m understanding the relation in wrong way, but what do we means exactly by numbers of terms
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aravindc78
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Post subject: Re: f the terms of a sequence t1, t2, ....tn, what is Posted: Wed Jan 20, 2010 2:20 pm |
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imanemekouar wrote: Hi Ron , I did not get the last part of your explanation. you find the number of term which is equal average*sum. But number of term is not equal of n. The number of term is equal to the last term -first/2. something that we don t have?
Maybe i m understanding the relation in wrong way, but what do we means exactly by numbers of terms We know the sum of terms is equal to 3124. And 3124/number of terms is equal to arithmetic mean/average Average = 4. So number of terms = 3124/4 = 781 and n is the 781st term. Sequence does not imply anything. There can be numbers that repeat etc. No need to consider the sequence as an arithmetic progression or anything of that sort. Sum of n terms/number of terms = Average.
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RonPurewal
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Post subject: Re: f the terms of a sequence t1, t2, ....tn, what is Posted: Tue Feb 09, 2010 6:50 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Quote: Hi Ron , I did not get the last part of your explanation. you find the number of term which is equal average*sum. But number of term is not equal of n. the sequence is represented as "t1, t2, ..., tn". this representation means exactly one thing: that the total number of terms in the sequence is "n". it does not mean anything else; in particular, we know nothing whatsoever about the terms themselves or about the pattern in which they are arranged (if, indeed, there is a pattern at all). Quote: The number of term is equal to the last term -first/2. something that we don t have? where did you get this formula? i could concoct an example in which it would be true, but it would only be true for certain very specialized sequences. for commonly seen types of sequences, such as arithmetic sequences, this formula will pretty much always be wrong.
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subbiah1.an
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Post subject: Re: Posted: Sat Nov 12, 2011 1:35 pm |
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How do arrive that the series will not contain any negative number? If there were any negative numbers in the series, the negative numbers might cancel with the equivalent positive number in the series. Thanks. RonPurewal wrote: you should start this question the same way you start all questions involving averages: by using the 'magic formula'
average = sum / number of data points
or
(average)(number of data points) = sum
--
note that the desired quantitiy in this problem is number of data points in the above formula.
examining the answer choices:
(1) alone
we only have one of the three quantities in the formula (i.e., sum). this is insufficient to determine either of the other two.
insufficient
(2) alone
we only have one of the three quantities in the formula (i.e., average). this is insufficient to determine either of the other two.
insufficient
together
we have sum and average, so the formula will yield number of data points.
sufficient
answer = c
**note that, had the problem contained a particular number in the place of 'n' (like t1, t2, ..., t8), then that would implicity give a value for number of data points. be careful!
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RonPurewal
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Post subject: Re: Re: Posted: Wed Nov 23, 2011 6:28 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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subbiah1.an wrote: How do arrive that the series will not contain any negative number? If there were any negative numbers in the series, the negative numbers might cancel with the equivalent positive number in the series. the equation "average * count = sum" is true for all sets of numbers, regardless of the signs of the numbers themselves. so, this would change nothing about the analysis above.
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