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# A set has N distinct integers. Is the sum of all these N integers nega

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A set has N distinct integers. Is the sum of all these N integers nega  [#permalink]

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13 Mar 2019, 12:11
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A set has N distinct integers. Is the sum of all these N integers negative?

(1) These N integers are all consecutive.
(2) Exactly half of these N integers are positive.
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Joined: 24 Jun 2008
Posts: 1881
Re: A set has N distinct integers. Is the sum of all these N integers nega  [#permalink]

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14 Mar 2019, 07:11
Each statement is clearly insufficient alone. Using both, if the numbers are consecutive, and exactly half of them are positive, then one of them must be zero, and the rest (less than half) are negative. So the sum is going to be positive, because we're going to have a set something like this:

-2, -1, 0, 1, 2, 3

where all of the positive values besides the largest one have a negative 'twin', and so each positive value will sum with its negative twin to zero. So the sum of all of the values will just equal whatever the largest value is in the set -- in this example, 3.
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Re: A set has N distinct integers. Is the sum of all these N integers nega  [#permalink]

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18 Mar 2019, 00:02
amanvermagmat wrote:
A set has N distinct integers. Is the sum of all these N integers negative?

(1) These N integers are all consecutive.
(2) Exactly half of these N integers are positive.

#1
N integers are all consective , but no range or limit of series is given so in sufficeint

#2
Exactly half of these N integers are positive
so if N = 4 integers
-8-4+3+1 = -ve sum
-2-1+5+9 = +ve sum
insufficient
from 1&2
-3,-2,-1,0,1,2 ; -ve sum sufficeint
IMO C
Re: A set has N distinct integers. Is the sum of all these N integers nega   [#permalink] 18 Mar 2019, 00:02
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