Which of the following CANNOT be zero?

Question

I. The sum of 7 consecutive integers 
II. The sum of 10 consecutive even integers 
III. The product of 13 consecutive integers

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

randomavoidplease · Answer

1. Since it is consecutive sum, I think there has to be a series from negative to positive for it to turn zero. 
2. Since even numbers are positive, it can't be zero.
3. Well, in any number of ways it can contain zero which will lead to zero.

Ans: A

fmcgee1 · Answer

#2 - Even numbers can definitely be negative. #1 - nowhere in the question stem does it state that the series can't start negative.

randomavoidplease · Answer

Ah, wasn't sure of that. The answer still remains A though. Thanks for pointing this out.

Archit3110 · Answer

On a number line for integers which are consecutive i.e both along 0 can have sum 0 if the count is odd
Eg -2,-1,0,1,2
And even count would give non zero term eg
-3,-2,-1,0,1,2 
Option A is correct

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livfcind · Answer

Which of the following CANNOT be zero?

I. The sum of 7 consecutive integers
II. The sum of 10 consecutive even integers
III. The product of 13 consecutive integers

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

Explanation-

I. The sum of 7 consecutive integers
Take mirror no. around zero(-3,-2,-1,0,1,2,3)
Sum=0  (False )

II. The sum of 10 consecutive even integers
10 consecutive even numbers will never add up to zero in any kind of distribution.  (True)

III. The product of 13 consecutive integers
if any of the no . is zero product will be zero  (False)

Thus only II is right and  A is the correct answer.

NdGoyal · Answer

IMO A.
Sum of number in the set = (no of digits)* (Avg of digits) eg A={1,2,3,4,5,6}, No of digit (A) = 6, Avg of (A) = 3.5, thus Sum of digits = 6*3.5= 21
Using this principle =

I. The sum of 7 consecutive integers- 
Since avg of 7 consecutive integers is middle 4th term. Thus if 0 is 4th term, Sum = 0. Eg. -3,-2,-1,0,1,2,3; then sum=0 (False)

II. The sum of 10 consecutive even integers
Sum of 10 consecutive even digit = 10*Avg of (5th and 6th Digits) = alway a odd number between 5th & 6th digit (since digits are EVEN & consecutive) which cannot be ≠ 0 (as 0 is even)
Eg. B={-8,-6,-4,-2, 0, 2, 4, 6,8,10} Sum(B) = 1 (Avg of 0,2)*10 =10 OR C={-10,-8,-6,-4,-2, 0, 2, 4, 6,8} Sum(C)= -1(Avg of -2,0)*10 =-10

Thus, 10 consecutive even numbers will never add up to zero in any kind of distribution. (True)

III. The product of 13 consecutive integers
if any of the no . is zero product will be zero (False)

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ananya3 · Answer

IMO A

I. The sum of 7 consecutive integers - 
odd number of integers => sum = middle number(same as avg) * n 
middle number can be 0 if we consider negative and positive numbers {-3,-2,-1,0,1,2,3} - so this is 0 - possible

II. The sum of 10 consecutive even integers
even number of integers => sum = avg(middle two numbers) * n
so it can be either {-2,0} or {0,2} none of which would result in zero - not possible

III. The product of 13 consecutive integers
if the consecutive integers contain 0 the product will be 0 - possible

hopefulmba2021 · Answer

For II,
we take, -10,-8,-6,-4,-2,2,4,6,8,10
this has 10 consecutive even integers. We cannot consider 0 because 0 is neither even nor odd. So the sum of this set will also result in 0.

Where am I going wrong?

erv20 · Answer

I don't see why A cannot be 0...basically if we take   --> wouldn't the sum of these consecutive integers be 0? it doesn't say anywhere the consecutive numbers cannot be negative...

MathRevolution · Answer

Case I: The sum of 7 consecutive integers: (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 = 0. 
 
Case II: The sum of 10 consecutive even integers:

Case III: The product of 13 consecutive integers

Answer A

hopefulmba2021 · Answer

Can someone please explain/correct this reasoning?
In an even consecutive series, 2 should come after -2, right? Since 0 is neither even nor odd, we should not consider 0 in an even series.

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Bunuel · Answer

ZERO:  
1. 0 is an integer.
 2. 0 is an even integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 
3. 0 is neither positive nor negative integer (the only one of this kind).
4. 0 is divisible by EVERY integer except 0 itself.

Which of the following CANNOT be zero?

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Which of the following CANNOT be zero?

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