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# The sum of seven consecutive integers is equal to 7. What is the avera

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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05 Nov 2017, 02:07
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The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

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Joined: 10 Apr 2017
Posts: 38
Schools: Kelley '20
Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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05 Nov 2017, 02:16
1
Here, Seven consecutive number is -2, -1, 0, 1 , 2, 3, 4
So, Average of highest and least number is 1
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Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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05 Nov 2017, 03:12
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

As its an AP.. a-3d + a-2d+a-d+a+a+d+a+2d+a+3d = 7
a=1

a-3d+a+3d/2= 1
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Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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05 Nov 2017, 05:29
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

Let the 7 consecutive integers be a-3d , a-2d , a-d , a , a+d , a+2d and a+3d
Sum = 7a = 7
=> a = 1
Least term = a-3d = 1-3 = -2
Greatest term = a+3d = 1+3 = 4
Average = (-2+4)/2 = 1

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Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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05 Nov 2017, 05:47
1
Let the first term be x

Sum of seven consecutive numbers = 7x+21
Now 7x+21=7

x=-2

Hence average of first & last term is (-2+4)/2=1

Option D
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The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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05 Nov 2017, 09:25
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

7 sum/7 integers=1 average
D
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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12 Nov 2017, 07:49
1
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

Since 7 consecutive integers sum to 7, we can let x = the first integer and create the following equation:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7

7x + 21 = 7

7x = -14

x = -2

Thus, the first integer is -2 and the seventh integer is 4. The average of those integers is (-2 + 4)/2 = 1.

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The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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22 Nov 2017, 21:56
let the lowest no be x
since the set contains subsequent integers we have
x, x+1, x+2,x+3,x+4,x+5,x+6=7(sum of consequtive integers)
7x+21=7
7x=7-21=-14
x=-14/7=-2
lowest number is -2 other numbers are -1,0,1,2,3,4
lowest+highest/2=-2+4/2=1=average.
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Joined: 28 Aug 2016
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The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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23 Nov 2017, 03:51
Sum of consecutive values= n*Average of the first and the last term
7= 7(First+last)/2
1=(First+Last)/2

D
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Joined: 16 Oct 2010
Posts: 8792
Location: Pune, India
Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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23 Nov 2017, 05:06
1
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

Sum of 7 consecutive integers is 7. But if you try to add numbers such as 1, 2, 3,... the sum will be much higher. Hence, there must be some negative integers to cancel off some positive integers and get a sum as low as 7.

A little bit of thought will show that the integers must be -2, -1, 0, 1, 2, 3, 4
So sum = 3+4 = 7

Average of least and greatest numbers = (-2 + 4)/2 = 1

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Math Expert
Joined: 02 Aug 2009
Posts: 7202
Re: The sum of seven consecutive integers is equal to 7. What is the avera  [#permalink]

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23 Nov 2017, 06:16
2
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the sequence?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

Hi..

since the terms are CONSECUTIVE, the average of all 7 is EQUAL to average of the largest and smallest integer..
average of all 7 $$= \frac{7}{7} =1 =$$ average of the largest and smallest integer..
ans 1...D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: The sum of seven consecutive integers is equal to 7. What is the avera &nbs [#permalink] 23 Nov 2017, 06:16
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