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# M19-26

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Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135295 [0], given: 12686

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16 Sep 2014, 01:06
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Difficulty:

95% (hard)

Question Stats:

35% (00:54) correct 65% (00:59) wrong based on 156 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
[Reveal] Spoiler: OA

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Kudos [?]: 135295 [0], given: 12686

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135295 [3], given: 12686

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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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Kudos [?]: 135295 [3], given: 12686

Intern
Joined: 14 Jun 2015
Posts: 17

Kudos [?]: [0], given: 46

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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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Intern
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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Intern
Joined: 25 Jan 2017
Posts: 5

Kudos [?]: 1 [0], given: 99

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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.

Kudos [?]: 1 [0], given: 99

Senior Manager
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 369

Kudos [?]: 133 [0], given: 370

Location: India
GPA: 3.64

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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.

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Kudos [?]: 133 [0], given: 370

M19-26   [#permalink] 12 Sep 2017, 12:09
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# M19-26

Moderators: chetan2u, Bunuel

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