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# There are 5 integers such that the difference of the biggest number an

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There are 5 integers such that the difference of the biggest number an  [#permalink]

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Updated on: 05 Mar 2019, 21:24
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Question Stats:

39% (02:52) correct 61% (02:33) wrong based on 31 sessions

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There are 5 integers such that the difference of the biggest number and the median is 4. Is the average (arithmetic mean) of them less than the median of them?

(1) The sum of biggest numbers and the median is 34.
(2) The difference of median and the smallest number is 10

Originally posted by rawat2583 on 05 Mar 2019, 13:16.
Last edited by Bunuel on 05 Mar 2019, 21:24, edited 1 time in total.
Renamed the topic and edited the question.
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There are 5 integers such that the difference of the biggest number an  [#permalink]

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Updated on: 09 Mar 2019, 17:05
We have 5 integers such that:

$$n_1 , n_2 , n_3 , n_4 , n_5$$

where $$n_3$$ is the median.

We know that $$n_5 - n_3 = 4$$.

$$1. n_5 + n_3 = 34$$. We could find $$n_5$$ and $$n_3$$ but are useless: we can infer nothing about the average.

$$2. n_3 - n_1 = 10$$. Take $$n_3$$ as reference point. On the left, difference is 10. On the right, 4. So, $$10 + 4 = 14$$. It is the range from $$n_1$$ to $$n_5$$. Since $$14 : 2 = 7$$ and $$n_3 = n + 10$$, we conclude that the average is less than the median.

Correct answer is B.

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Originally posted by lucajava on 05 Mar 2019, 16:24.
Last edited by lucajava on 09 Mar 2019, 17:05, edited 1 time in total.
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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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05 Mar 2019, 21:24
rawat2583 wrote:
There are 5 integers such that the difference of the biggest number and the median is 4. Is the average (arithmetic mean) of them less than the median of them?

(1) The sum of biggest numbers and the median is 34.
(2) The difference of median and the smallest number is 10

Similar question to practice: https://gmatclub.com/forum/there-are-5- ... 37063.html
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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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09 Mar 2019, 15:34
lucajava wrote:
We have 5 integers such that:

$$n_1 , n_2 , n_3 , n_4 , n_5$$

where $$n_3$$ is the median.

We know that $$n_5 - n_3 = 4$$.

$$1. n_5 + n_3 = 34$$. We could find $$n_5$$ and $$n_3$$ but are useless: we can infer nothing about the average.

$$2. n_3 - n_1 = 10$$. Take $$n_3$$ as reference point. On the left, difference is 10. On the right, 4. So, $$10 + 4 = 14$$. It is the range from $$n_1$$ to $$n_5$$. Since $$14 : 2 = 7$$ and $$n_3 = 10$$, we conclude that the average is less than the median.

Correct answer is B.

Hi lucajava ,
How did you conclude n3=10? and 14:2 = 7? what is this for?

Thanks.
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Re: There are 5 integers such that the difference of the biggest number an  [#permalink]

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09 Mar 2019, 17:03
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Hi Doer01, you're right, my conclusion was too hasty and I should've explained more. What i meant to say was that you do care only about deviations from the mean. So, $$10$$ will be the deviation from the mean as we consider the median; $$\frac{14}{2}$$ is the average deviation from the mean (i took the extreme values: $$\frac{n + (n + 14)}{2}= n + 7$$). Hope it's clear.
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Re: There are 5 integers such that the difference of the biggest number an   [#permalink] 09 Mar 2019, 17:03
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