If the sum of 6 consecutive integers is x, which of the must be true?

Question

I. x is even
II. x is odd
III. x is a multiple of 3

A) I only
B) II only
C) III only
D) I and III
E) II and III

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • Sum of 6 consecutive integers is x

To find:  
 • Which of the given options is true

Approach and Working:   
If we assume the first of the 6 consecutive numbers are n, then the next numbers are n+1, n+2, n+3, n+4, and n+5
 • Therefore, the sum of them = x = 6n + 15

Now, for any value of n, 6n is always even.
 • So, x = even + odd = odd.

Also, both 6 and 15 are divisible by 3.
 • So, x is a multiple of 3.

Hence, the correct answer is option E.

Answer: E

Note: The question can also be solved assuming any numerical value of n.

saisiddharth · Answer

sum of n consecutive numbers n/2*(2a+(n-1)d
d=1 n =6 a is the first umber
3*(2a+5)
so odd and multiple of 3 as 2a is multiple of 2 and adding even and odd gives odd

KSBGC · Answer

Test the numbers :

x = 2 +3 + 4 + 5 + 6 + 7 =27

x = 3 + 4 + 5 + 6 + 7 + 8 = 33

So, x is odd and multiple of 3.

The best answer is E.

Bismarck · Answer

OA: E 
Let first integer be  a 
Then list of 6 consecutive integers would be  a, a+1,a+2,a+3,a+4,a+5 
Sum of first n terms of an AP: S =(n/2)  
here d = 1 and n =6,
Sum of first 6 terms of AP: S = (\frac{6}{2})* =3(2a+5) 
So S is multiple of 3.
 2a  is always even, S =odd(even+odd)=odd*odd =odd 
and S is also odd.

CounterSniper · Answer

six consecutive int will always have 3 odd and 3 even 
odd+odd=even
we are now left with all even and an odd
and even +odd=odd
so x will always be odd !!

also , six consecutive int will always have one int that is a multiple of 3 , and any number*(3p) will be a multiple of 3

so E

JeffTargetTestPrep · Answer

The sum of 6 consecutive integers will be the sum of 3 odd numbers and 3 even numbers, which results in an odd sum.

The sum of any 3 consecutive integers is a multiple of 3. Since 6 consecutive integers consist of two (disjoint) sets of 3 consecutive integers, thus the sum of 6 consecutive integers is also a multiple of 3.

Answer: E

gracie · Answer

x=3 times the odd sum of 2 middle odd-even integers
so x must be odd and a multiple of 3
E

bumpbot · Answer

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If the sum of 6 consecutive integers is x, which of the must be true?

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If the sum of 6 consecutive integers is x, which of the must be true?

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