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# What is the sum of the terms in a sequence of consecutive integers?

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What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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25 Jun 2015, 12:15
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What is the sum of the terms in a sequence of consecutive integers?

(1) Exactly half of the terms in the sequence are non-negative.

(2) There are 16 terms in the sequence.
[Reveal] Spoiler: OA

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Re: What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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25 Jun 2015, 12:21
reto wrote:
What is the sum of the terms in a sequence of consecutive integers?

(1) Exactly half of the terms in the sequence are non-negative.

(2) There are 16 terms in the sequence.

1) From this statement we can infer that sum of this sequence will be equal to minimal negative number of this sequence (because 0 is non-negative integer)
So answer depends on how many numbers in this sequence.
Insufficient

2) From this information any number is possible.
Insufficient

1+2) We know that non-negative numbers are from 0 to 7 and negative from -1 to -8 so sum is equal to -8
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Re: What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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25 Jun 2015, 13:00
Harley1980 wrote:
reto wrote:
What is the sum of the terms in a sequence of consecutive integers?

(1) Exactly half of the terms in the sequence are non-negative.

(2) There are 16 terms in the sequence.

1) From this statement we can infer that sum of this sequence will be equal to minimal negative number of this sequence (because 0 is non-negative integer)
So answer depends on how many numbers in this sequence.
Insufficient

2) From this information any number is possible.
Insufficient

1+2) We know that non-negative numbers are from 0 to 7 and negative from -1 to -8 so sum is equal to -8

Hi,
I don't agree with your analysis if statement [1]....You said "0" is non-negative.
We know that Zero is not positive, nor negative!
So when [1] says that "Exactly half of the terms in the sequence are non-negative." we should conclude that total negative numbers in the sequence is one less than the non-negatives and hence the sum of this series can't be = the minimal negative number.
Hoewver, I agree that the statement is Insufficient since we don't know "n" for this series.

[1] + [2] tells us:
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
thus the sum = 8

Please let me know if I wrong.

Thanks

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Re: What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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25 Jun 2015, 13:54
rohitd80 wrote:
Harley1980 wrote:
reto wrote:
What is the sum of the terms in a sequence of consecutive integers?

(1) Exactly half of the terms in the sequence are non-negative.

(2) There are 16 terms in the sequence.

1) From this statement we can infer that sum of this sequence will be equal to minimal negative number of this sequence (because 0 is non-negative integer)
So answer depends on how many numbers in this sequence.
Insufficient

2) From this information any number is possible.
Insufficient

1+2) We know that non-negative numbers are from 0 to 7 and negative from -1 to -8 so sum is equal to -8

Hi,
I don't agree with your analysis if statement [1]....You said "0" is non-negative.
We know that Zero is not positive, nor negative!
So when [1] says that "Exactly half of the terms in the sequence are non-negative." we should conclude that total negative numbers in the sequence is one less than the non-negatives and hence the sum of this series can't be = the minimal negative number.
Hoewver, I agree that the statement is Insufficient since we don't know "n" for this series.

[1] + [2] tells us:
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
thus the sum = 8

Please let me know if I wrong.

Thanks

Hello rohitd80
You are right that 0 is not positive and not negative.
But when tasks says something about all non negative numbers then you should take 0 in these numbers because 0 it is non negative number.
Non negative doesn't mean positive it is mean non-negative.
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Re: What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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25 Jun 2015, 14:40
WOW..... That's a valuable tip....
I concluded that 0 is not part of the "exactly half of the non-negative population in the series" and thus concluded that there can only be even number of numbers in the series....based on [1]

Thanks again.

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What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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16 Jul 2016, 03:22
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reto wrote:
What is the sum of the terms in a sequence of consecutive integers?

(1) Exactly half of the terms in the sequence are non-negative.

(2) There are 16 terms in the sequence.

From question stem :-
i) We know that all elements will be consecutive.

ii) Since the stem talks about half of them being non negative, then the other half must be negative. There will be 8 consecutive -ve numbers.
ALSO important to note is that in this set 0 must be one of the element. To pass from -ve to +ve in a number line we have to include 0.

iii) Now the set will have a unbalanced polarity because 0 has no polarity and no magnitude; so the sum of -ve numbers will have a greater magnitude.

iv) Since the set is almost symmetrical except for the inclusion of 0, all +ve number will cancel all -ve numbers, except for one -ve number that will also be first element of the set. All other elements starting from 2nd term to the last term will cancel each other and 0 will contribute no numeric or polar value. It will be there just to make up the number of total elements in the set.

NOW WE ARE READY TO ATTACK THE QUESTION

(1) Exactly half of the terms in the sequence are non-negative.
Total number of elements in the set can be any even integer . Set can have 10 elements, 390 elements, 2 elements
S={-4,-3,-2,-1,0,1,2,3,}==> SUM =-4
S={-2,-1,0,1}==> SUM = -2
INSUFFICIENT
we do not know how many total elements are in the set. Sum will keep changing as the number of elements keep changing.

(2) There are 16 terms in the sequence.
S= {any 16 consecutive numbers}
S= {1,2,3.........16} OR {-11,-10,..........4} {-16,-15............-1} ==> Sum will keep changing

INSUFFICIENT

Merging BOTH
S={16 consecutive numbers and half of them should be negative}
Only one such set exist
S={-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}
SUFFICIENT
The sum of the set will be the first term =-8
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Re: What is the sum of the terms in a sequence of consecutive integers? [#permalink]

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12 Sep 2017, 18:05
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Re: What is the sum of the terms in a sequence of consecutive integers?   [#permalink] 12 Sep 2017, 18:05
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