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What is the smallest of six consecutive odd integers whose average (ar

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What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 09 Jun 2016, 02:49
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Re: What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 09 Jun 2016, 03:08
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Bunuel wrote:
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?

A. x - 5
B. x - 3
C. x - 1
D. x
E. x + 1


Assume the integers to be
n - 5, n - 3, n- 1, n+1, n + 3, n + 5
AM = 6n/6 = n

Given n = x + 2
Therefore, smallest term = n - 5 = x + 2 - 5 = x - 3

Correct Option: B

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Re: What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 09 Jun 2016, 03:19
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No. of terms = 6 (Even). So, the AM will be the average of 3rd & 4th term.
For Mean to be 'x+2' the terms would be 'x+1' & 'x+3'. (Check: ((x+1)+(x+3))/2 = (2x+4)/2 = x+2).
We can obtain the remaining terms by adding 2 to 'x+3' & by subtracting 2 from 'x+1' & so on.
The series becomes: x-3, x-1, x+1, x+3, x+5, x+7.
Thus, smallest odd integer is: x-3 (Option B).
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Re: What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 09 Jun 2016, 08:14
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Bunuel wrote:
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?

A. x - 5
B. x - 3
C. x - 1
D. x
E. x + 1


Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2

And 1st integer= 3rd integer- 4

let's say 3rd integer = n and 4th integer = n+2

2n+2/2= x+2

n= x+1

1st integer= x+1-4= x-3

B is the answer
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Re: What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 04 Oct 2017, 21:53
Algebra solution
We have to find a
Set =(a ,a+2,a+4……..a+10)
Sum = 6a + 30 ----------------------[1]
Also Given average = x+2
Sum by average = 6X+12 ----------------------- [2 ]
Equating 1 and 2
6a +30 =6X +12
Solve for a = X-3
Sol ..B

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What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 05 Oct 2017, 01:02
To get a "+2" in average of 6 terms, we need sum of 12 other than x for all the terms. (Since x is common)
now substituting the options for 6 terms.
a. -5, sum of 6 terms, we will have -5,-3-,1,1,3,5 = 0 NOT CORRECT (we can ignore x as it is common)
b. -3, sum of 6 terms, we will have -3,-1,1,3,5,7 = 12 CORRECT

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Re: What is the smallest of six consecutive odd integers whose average (ar [#permalink]

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New post 09 Oct 2017, 15:52
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Bunuel wrote:
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?

A. x - 5
B. x - 3
C. x - 1
D. x
E. x + 1


We can let the first (or smallest) odd integer = n, and thus we have:

n, n + 2, n + 4, n + 6, n + 8, and n + 10 as the six consecutive odd integers.

Since the average of terms in an evenly spaced set is (first number + last number)/2:

(n + n + 10)/2 = x + 2

2n + 10 = 2x + 4

2n = 2x - 6

n = x - 3

Answer: B
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Re: What is the smallest of six consecutive odd integers whose average (ar   [#permalink] 09 Oct 2017, 15:52
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