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# If R is a set of 9 consecutive odd integers, what is the median of R?

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If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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14 Sep 2016, 05:02
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81% (01:15) correct 19% (01:35) wrong based on 203 sessions

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If R is a set of 9 consecutive odd integers, what is the median of R?

(1) The difference between the highest and the lowest elements of R is 16.

(2) The average (arithmetic mean) of R is 9.

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Re: If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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14 Sep 2016, 06:19
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Bunuel wrote:
If R is a set of 9 consecutive odd integers, what is the median of R?

(1) The difference between the highest and the lowest elements of R is 16.

(2) The average (arithmetic mean) of R is 9.

Stat 1 : Last - first = 16...here we can any numbers for the first and last...no clear information...Insufficient.

Stat 2: We know that In any evenly spaced set the arithmetic mean (average) is equal to the median( since the numbers are consecutive, difference is just 1)..

Mean = Median..Sufficient.

IMO option B.
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Re: If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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14 Sep 2016, 23:18
If R is a set of 9 consecutive odd integers, what is the median of R?

(1) The difference between the highest and the lowest elements of R is 16.

1,3,5...17 or 55, 57, 59 ... 71. Two different medians - insufficient

(2) The average (arithmetic mean) of R is 9.

Since n is odd, mean=median

B
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Re: If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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15 Sep 2016, 14:20
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Bunuel wrote:
If R is a set of 9 consecutive odd integers, what is the median of R?

(1) The difference between the highest and the lowest elements of R is 16.

(2) The average (arithmetic mean) of R is 9.

The two posters above have already provided nice solutions, so I won't add another one.
However, I thought I'd make a small point.

Notice that we could have deduced statement 1 from the information that we were already given.
That is, for ANY 9 consecutive odd integers, the difference between the highest and the lowest numbers will ALWAYS BE 16.
Here's why:
Let x = first odd integer
So, x + 2 = 2nd odd integer
x + 4 = 3rd odd integer
x + 6 = 4th odd integer
.
.
.
x + 16 = 9th odd integer.
As we can see, the difference between the highest and the lowest numbers = (x + 16) - x = 16

Since statement 1 provides NO ADDITIONAL INFORMATION, there's no way that it can play any role in answering the target question.
So, we can automatically eliminate answer choices A, C and D, leaving us with B or E.

Cheers,
Brent
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Re: If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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15 Sep 2016, 16:12
9n is the sum of the 9 numbers considering the middle term n. So, n is the mean and it will be the median too. Hence, B

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Re: If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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21 Dec 2016, 23:21
Nice Question.
Here is my solution to this one =>
Let the consecutive odd inters be =>
n
n+2
n+4
n+6
n+8
n+10
n+12
n+14
n+16

It is an evenly spaced set => Mean = Median

Statement 1=>
Different will always be 16
Hence Not sufficient

Statement 2=>
Mean = Median = 9
Hence Sufficient

Hence B

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Re: If R is a set of 9 consecutive odd integers, what is the median of R?  [#permalink]

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30 Mar 2018, 07:19
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Re: If R is a set of 9 consecutive odd integers, what is the median of R?   [#permalink] 30 Mar 2018, 07:19
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