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# The mean of fourteen consecutive integers is 27 1/2. If the integers a

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The mean of fourteen consecutive integers is 27 1/2. If the integers a  [#permalink]

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10 Jul 2020, 03:41
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The mean of fourteen consecutive integers is $$27 \frac{1}{2}$$. If the integers are arranged in increasing order. what is the mean of the largest seven integers?

A. 24
B. 25
C. 31
D. 34
E. 35

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The mean of fourteen consecutive integers is 27 1/2. If the integers a  [#permalink]

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Updated on: 10 Jul 2020, 04:29
Mean = 27.5
Since number of elements is even and elements are consecutive integers, the mean will the average of 7th and 8th integers => 7th element = 27
=> first element = 21
=> 4th element = 24

Edited: mean of largest 7 numbers will be the 11th integer
11th integer = 31
Ans: C

Originally posted by Lipun on 10 Jul 2020, 03:45.
Last edited by Lipun on 10 Jul 2020, 04:29, edited 1 time in total.
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Re: The mean of fourteen consecutive integers is 27 1/2. If the integers a  [#permalink]

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10 Jul 2020, 03:47
because they are Even numbers the mean is between 7th and 8th items so 27 an 28

28 is the smallest of the largest seven numbers and 34 is the largest, so 28+34/2= 31
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Re: The mean of fourteen consecutive integers is 27 1/2. If the integers a  [#permalink]

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10 Jul 2020, 03:51
(C). mean = 55/2. Since there are 14 consecutive numbers, mean 55/2 is also mean of 7th and 8th numbers. Therefore 7th number is 27 and 8th is 28.
So, largest 7 numbers are - 28, 29, 30, 31, 32, 33, 34. And mean of these 7 numbers would be 4th number - 31.
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Re: The mean of fourteen consecutive integers is 27 1/2. If the integers a  [#permalink]

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10 Jul 2020, 05:50
Bunuel wrote:
The mean of fourteen consecutive integers is $$27 \frac{1}{2}$$. If the integers are arranged in increasing order. what is the mean of the largest seven integers?

A. 24
B. 25
C. 31
D. 34
E. 35

As it is mentioned that the integers are consecutive

Let the first integer be a, the 14th integer will be a+13d, where d = 1

Average of the 14 integers = {[a+(a+13)]}/2 = 27.5

=> a+6.5 = 27.5

=> a = 21

Finally, 8th integer = a+7d = 28
And, 14th integer = a+13d = 34

Mean of last 7 integers = (28+34)/2 = 31

OA: C

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Re: The mean of fourteen consecutive integers is 27 1/2. If the integers a   [#permalink] 10 Jul 2020, 05:50

# The mean of fourteen consecutive integers is 27 1/2. If the integers a

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