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

ANSWER IS C

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