Set A consists of a set of n consecutive integers. Is the sum of all t

Question

Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?

(1) If -5 is added to set A, the set would become symmetric about 0

(2) If the largest integer of set A is removed, the sum of the remaining integers is even

IanStewart · Answer

If a set is symmetric, its mean equals its median. Statement 1 tells us that by inserting "-5" in the set, we get a symmetric set with a median of 0, which thus has a mean of 0, and therefore a sum of 0. Since by inserting "-5" in the set we reduce the sum by 5, the original set must sum to 5, so its sum is odd, and the information is sufficient to give a "no" answer to the question. (I haven't even used the fact that the integers are consecutive, but another way to do this is to notice that the only set of consecutive integers that becomes symmetric around 0 when you insert "-5" is the set -4, -3, -2, -1, 0, 1, 2, 3, 4, 5).

Statement 2 tells us that the sum of all but one of the elements is even, but we don't know if the largest element is even or odd, so we have no way to tell if the sum of every element is even or odd. So the answer is A.

Statement 2 tells us that the sum of all but one of the elements is even, but we don't know if the largest element is even or odd, so we have no way to tell if the sum of every element is even or odd. So the answer is A.

Archit3110 · Answer

#1
by symmetric it means that count of integers on both sides of 0 i.e + & -ve are equal
so 
-5,-4,-3,-2,-1,0,1,2,3,4,5
so sum = 0
sufficient
#2
largest integer of set A is remove , sum is even
so we can have
-3,-2-1 ,0,1 so 1 is removed ; -6 
or
-3,-2,-1,0,1,2,3,4,5 ,; 5 is removed ; sum is 4 
or 
-3,-2,-1,0,1,2,3,4; 4 is removed ; sum = 0
in sufficient 
IMO A

nick1816 · Answer

Statement 1-
 If -5 is added to set A, the set would become symmetric about 0.
Sum of all the elements of the set that is symmetric about 0 is 0.

Hence, sum of all the integers in set A= 0-(-5)=5

Sufficient

Statement 2- 
 Case 1 
Set A= {1,2,3,4).....Sum of all integers=10
After the largest integer removed, sum of all integer= 6

Case 2 
Set A= {1,2,3,4,5).....Sum of all integers=15
After the largest integer removed, sum of all integer= 10

Insufficient

samubel · Answer

I'm confused, the question is asking if set A is even, therefore it shouldn't matter whether we know the exact sum of the set as long as we know if it's even or not. I think the answer should be D for either option is sufficient.

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Set A consists of a set of n consecutive integers. Is the sum of all t

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Set A consists of a set of n consecutive integers. Is the sum of all t

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