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# M19-26

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:06
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Difficulty:

95% (hard)

Question Stats:

40% (00:59) correct 60% (01:00) wrong based on 192 sessions

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What is the sum of four consecutive odd integers?

(1) The product of the four integers is 105

(2) The median of the four integers is 4

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Math Expert
Joined: 02 Sep 2009
Posts: 47945

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16 Sep 2014, 01:06
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Official Solution:

Statement (1) by itself is insufficient. Both $$\{-1, -3, -5, -7\}$$ and $$\{1, 3, 5, 7\}$$ are possible sets.

Statement (2) by itself is sufficient. The median of four consecutive odd integers always equals their mean, therefore, the sum of the integers is $$4*4 = 16$$.

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Joined: 14 Jun 2015
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10 Nov 2016, 14:20
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi,

Are negative integers considered for odd and even? I have this doubt because Prime numbers don not include negative numbers, and i believe that same rule holds for odd/even as well. Please help me with this. Thanks.
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Joined: 10 Jun 2016
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10 Nov 2016, 19:20
@Saurav Arora
(1). It is not written in the question that we have to take prime numbers.
(2). 3, 5 and 7 are prime numbers, but 1 is not a prime number.
(3). These terms exist, such as negative odds/evens and positive odds/evens. So, it is right.

I hope you'll find this useful.

Sent from my LS-5016 using GMAT Club Forum mobile app
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Joined: 25 Jan 2017
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28 Aug 2017, 17:15
Bunuel wrote:
Official Solution:

Statement (2) by itself is sufficient. The median of four consecutive odd integers always equals their mean, therefore, the sum of the integers is $$4*4 = 16$$.

Can someone explain why the bolded part is true? I tried using numbers and it is indeed the case, but I am curious as to why it's true and how I can predict similar patterns.
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Joined: 25 Nov 2015
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12 Sep 2017, 12:09
mba.2020 wrote:
Bunuel wrote:
Official Solution:

Statement (2) by itself is sufficient. The median of four consecutive odd integers always equals their mean, therefore, the sum of the integers is $$4*4 = 16$$.

Can someone explain why the bolded part is true? I tried using numbers and it is indeed the case, but I am curious as to why it's true and how I can predict similar patterns.

The median of 4 terms will be average of 2nd and 3rd term.
Since the numbers are evenly spaced i.e. consecutive odd numbers, average of middle 2 numbers or last 2 terms will give the mean hence, it is same as median.

Please give kudos, if u find this post useful.
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Joined: 29 Nov 2016
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16 Feb 2018, 14:30
We can assume the numbers are x-3,x-1,x+1,x-3.
Therefore sum=4x
Median of these numbers=Mean of x-1 and x+1=x

Statement 1, the numbers can be 1,3,5,7 or -1,-3,-5,-7. Not sufficient
Statement 2 If median is 4, x=4 and the sum is 4x=16. Sufficient.
M19-26 &nbs [#permalink] 16 Feb 2018, 14:30
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# M19-26

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