The sum of 3 consecutive numbers is definitely:

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Mon Jun 11, 2018 1:45 am

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The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.
E. Divisible by 5.

[spoiler]OA=C[/spoiler].

I know that the sum will be an odd number, therefore it won't be divisible by 2. But, how can I know that it is divisible by 3? I'd appreciate some help here.

Source: Beat The GMAT — Problem Solving | Mon Jun 11, 2018 1:45 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 11, 2018 1:59 am

Gmat_mission wrote:The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.
E. Divisible by 5.

Try to show that four of the five answer choices are WRONG.
Case 1: -2, -1, 0
Sum = -2 + (-1) + 0 = -3.
The resulting sum is not positive, nor is it divisible by 2, 4 or 5.
Eliminate A, B, D and E.

The correct answer is C.

The sum of 3 consecutive integers can be represented and then simplified as follows:
x + (x+1) + (x+2) = (x+x+x) + (1+2) = 3x + 3 = (3)(x+1) = (3)(integer) = multiple of 3.

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by Jeff@TargetTestPrep » Wed Jun 13, 2018 3:47 pm

Gmat_mission wrote:The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.
E. Divisible by 5.

Lets sum a few consecutive numbers:

1 + 2 + 3 = 6

10 + 11 + 12 = 33

We see that the sum of 3 consecutive integers will always be divisible by 3.

Answer: C

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

The sum of 3 consecutive numbers is definitely:

by Brent@GMATPrepNow » Wed Jun 13, 2018 3:51 pm

Gmat_mission wrote:The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.
E. Divisible by 5.

Another approach:

Let x = the smallest integer
So, x+1 = the next integer
And x+2 = the last integer

Sum of 3 consecutive numbers = x + (x+1) + (x+2)
= 3x + 3
= 3(x+1)

As we can see, the sum MUST be a multiple of 3
Or we can say the sum MUST be a divisible by 3

Answer: C

Cheers,
Brent

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Apr 29, 2019 8:13 am

Gmat_mission wrote:The sum of 3 consecutive numbers is definitely:

A. Positive.
B. Divisible by 2.
C. Divisible by 3.
D. Divisible by 4.
E. Divisible by 5.

[spoiler]OA=C[/spoiler].

We can let n = 1st number, so n + 1 and n + 2 will be the 2nd and 3rd numbers, respectively. We see that n + n + 1 + n + 2 = 3n + 3, which is definitely divisible by 3.

Answer: C

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