Which of the following cannot be expressed as the sum of three or more

Question

Which of the following cannot be expressed as the sum of three or more consecutive integers?

A. 0 
B. 1 
C. 2 
D. 3 
E. 4

KSBGC · Answer

Note :  Sum of 3 or more CONSECUTIVE integers

Option A) -1 + 0 +1 = 0............possible

Option B) impossible

option c) -1 + 0 +1 +2 = 2.............possible

Option D) -2 -1 +0 +1+2 +3 =3...........possible

Option E) -3 -2 - 1 +0 +1+2+3+4 = 4........possible

Option B is the correct answer.

yoannnesme · Answer

We can get there with a little bit of trial and error.

It is easy to prove that we can discard answer A with the 3 consecutive integers which add up to 0:
-1;0;1

We can add consecutive numbers to the right and left to see if we can discard more answers.

-1;0;1;2 add up to 2. Discard answer C.
-2;-1;0;1;2;3 add up to 3. Discard answer D.
-3;-2;-1;0;1;2;3;4 add up to 4. Discard answer E.

We haven't so far discarded option B so that will be our answer.

dave13 · Answer

(n)+ (n+1) +(n+2) = 3n=3 n = 1 is it valid solution

Bunuel · Answer

Unfortunately not. It does not make sense.

(n)+ (n+1) +(n+2) = 3n + 3 not 3n. Also, it's not clear as to why you are equating 3n to 3...

yoannnesme · Answer

As Bunuel pointed out, you should get (n)+(n+1)+(n+2)=3n+3.

Also, the stem says "3 or more consecutive numbers" so you could also have: 
(n)+(n+1)+(n+2)+(n+3)
or
(n)+(n+1)+(n+2)+(n+3)+(n+4)
etc.

Prep Toolkit