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# M70-29

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Math Expert
Joined: 02 Sep 2009
Posts: 59675

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04 Sep 2018, 01:31
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Difficulty:

35% (medium)

Question Stats:

67% (01:16) correct 33% (01:34) wrong based on 12 sessions

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Set A consists of $$n$$ consecutive integers, denoted from $$Q_1$$ to $$Q_n$$. What is the median of Set A?

(1) $$\frac{Q_1+Q_2+Q_3+...+Q_n}{n}=13$$

(2) $$Q_1=7$$ and $$Q_n=19$$

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Math Expert
Joined: 02 Sep 2009
Posts: 59675

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04 Sep 2018, 01:31
Official Solution:

We’ll go for LOGICAL because we can use the logic of median and average.

In a set of consecutive integers, the average and the median are the same. Therefore, (1) is sufficient to give us the median. (B), (C) and (E) are eliminated.

(2) is also sufficient on its own, as we know that the set of consecutive integers goes from 7 to 19: if we know all the numbers in set A, that’s enough in order to find its median. (A) is also eliminated.

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Intern
Joined: 20 Dec 2018
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25 Dec 2018, 22:29
I dont understand s1, we dont have the value of n, so how can u solve it? Pls clarify this more.
Manager
Joined: 12 Mar 2019
Posts: 158

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10 Aug 2019, 10:05
vando wrote:
I dont understand s1, we dont have the value of n, so how can u solve it? Pls clarify this more.

It doesn't matter if you have value of n or not, what matter is rule,
In a set of consecutive integers, the average and the median are the same.

you can check it for some no.'s and see
Intern
Joined: 15 Oct 2018
Posts: 2

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23 Oct 2019, 07:42
Sorry but I think it's not always be the case that the average and the median are the same for a set of consecutive integers. This is true only when there is an odd number of items in the data set. For data set with even number of items, the media is the average of the two most middle numbers.
Math Expert
Joined: 02 Sep 2009
Posts: 59675

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23 Oct 2019, 07:47
ltkngoc222 wrote:
Sorry but I think it's not always be the case that the average and the median are the same for a set of consecutive integers. This is true only when there is an odd number of items in the data set. For data set with even number of items, the media is the average of the two most middle numbers.

{2, 3, 4, 5}

Median = (3 + 4)/2 = 3.5
Average = (2 + 3 + 4 + 5)/4 = 3.5.

For evenly spaced set, median always equals to the mean (average).
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Intern
Joined: 15 Oct 2018
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23 Oct 2019, 07:48
Oh I see, thanks so much!
Re: M70-29   [#permalink] 23 Oct 2019, 07:48
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# M70-29

Moderators: chetan2u, Bunuel