It is currently 26 Jun 2017, 08:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is the average (arithmetic mean) of 5 consecutive even

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Nov 2010
Posts: 262
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

01 May 2012, 10:03
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:59) correct 45% (00:58) wrong based on 401 sessions

### HideShow timer Statistics

If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

x= n+(n+2)+(n+4)+(n+6)+(n+8)/5

x = n+4

IMO I & II is correct
[Reveal] Spoiler: OA

_________________

The proof of understanding is the ability to explain it.

Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: x is a nonzero integer [#permalink]

### Show Tags

01 May 2012, 11:28
İİ is not correct, since nowhere mentioned that even integers MUST BE positive
I is true, since the avrg sum= (sum of even integers)/ 5 (odd integer)=even/odd=even

III is also out. u can check it , if u pick some integers
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Math Expert
Joined: 02 Sep 2009
Posts: 39697
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

01 May 2012, 14:41
4
KUDOS
Expert's post
If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

First of all notice that we are asked which of the following MUST be true, not COULD be true.

Also notice that the average of 5 consecutive even integers equals to the median, so it's just a middle term. So, I must always be true: {even, even, even, even, even}

Next:
II. x is a nonzero integer. Not necessarily true, consider: {-4, -2, 0, 2, 4};
III. x is a multiple of 5. Not necessarily true, consider: {0, 2, 4, 6, 8}.

Hope it's clear.

P.S. In your example if n=-4 then x=n+4=0, so II is not always true.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39697
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

19 Jun 2013, 04:52
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All Must or Could be True Questions to practice: search.php?search_id=tag&tag_id=193

_________________
Intern
Joined: 06 May 2014
Posts: 8
Concentration: Marketing, Technology
GMAT 1: 660 Q49 V31
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

14 Jul 2014, 21:59
consider any even integer , a
we can form a series as a - 4 , a -2 , a , a + 2 , a + 4

average will be 5a/5 = a

so, i) always true , since a is integer

iii) not always true,a can be any integer as we considered, not necessarily multiple of 5

ii) not always true, for -4 -2 0 2 4 , average 0

ans - A
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7443
Location: Pune, India
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

14 Jul 2014, 22:19
Expert's post
1
This post was
BOOKMARKED
GMATD11 wrote:
If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

x= n+(n+2)+(n+4)+(n+6)+(n+8)/5

x = n+4

IMO I & II is correct

Here are some posts on arithmetic mean that you might find helpful.

http://www.veritasprep.com/blog/2012/04 ... etic-mean/
http://www.veritasprep.com/blog/2012/04 ... questions/
http://www.veritasprep.com/blog/2012/05 ... eviations/
http://www.veritasprep.com/blog/2012/05 ... tic-means/
http://www.veritasprep.com/blog/2012/05 ... on-median/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 12 May 2014
Posts: 10
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

17 Jul 2014, 22:00
Bunuel wrote:
If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

First of all notice that we are asked which of the following MUST be true, not COULD be true.

Also notice that the average of 5 consecutive even integers equals to the median, so it's just a middle term. So, I must always be true: {even, even, even, even, even}

Next:
II. x is a nonzero integer. Not necessarily true, consider: {-4, -2, 0, 2, 4};
III. x is a multiple of 5. Not necessarily true, consider: {0, 2, 4, 6, 8}.

Hope it's clear.

P.S. In your example if n=-4 then x=n+4=0, so II is not always true.

Hello Bunuel

I have a dout in this statement that you made :the average of 5 consecutive even integers equals to the median.

How did you establish this ?

Thank you !
Intern
Joined: 06 May 2014
Posts: 8
Concentration: Marketing, Technology
GMAT 1: 660 Q49 V31
If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

17 Jul 2014, 22:06
for evenly spaced numbers , average is same as median

consider 3 integers having common difference d,

a , a+d , a +2d --> average 3a + 3d /3 = a+d
--> median = a+d

hope it helps

Last edited by ayushee01 on 17 Jul 2014, 23:00, edited 1 time in total.
Intern
Joined: 12 May 2014
Posts: 10
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

17 Jul 2014, 22:58
ayushee01 wrote:
for evenly spaced numbers , average is same as mean

consider 3 integers having common difference d,

a , a+d , a +2d --> average 3a + 3d /3 = a+d
--> median = a+d

hope it helps

Hello Ayushee

If I infer correctly, you mean to say that for evenly spaced numbers the average is the same as the median ?

Thank you for the explanation. It's clear now.
Intern
Joined: 06 May 2014
Posts: 8
Concentration: Marketing, Technology
GMAT 1: 660 Q49 V31
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

17 Jul 2014, 23:03
lol yes , i meant median, edited it :D
Manager
Joined: 20 Dec 2013
Posts: 132
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

17 Jul 2014, 23:05
[quote="GMATD11"]If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

x-4, x - 2, x, x+2, x+4

Average = x.

I. x will always be even as they are consecutive even integers.
II. if x = 0 then -4, -2, 0, 2, 4
III. x = 10 is a possibility

_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Intern
Joined: 16 May 2015
Posts: 15
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

23 May 2015, 01:08
Hi Bunuel,

First if all i'd like to Thank you for all the help.
I am deeply appreciate your efforts.

Is zero an even integer ?
Math Expert
Joined: 02 Sep 2009
Posts: 39697
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

23 May 2015, 08:33
shallow9323 wrote:
Hi Bunuel,

First if all i'd like to Thank you for all the help.
I am deeply appreciate your efforts.

Is zero an even integer ?

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: number-properties-tips-and-hints-174996.html
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15982
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

25 Nov 2016, 05:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2185
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

12 Dec 2016, 10:37
Great Question.
Here is my solution to this one ->
Since the consecutive integer set is an arithmetic progression with common difference =2
Mean =Median=Average of the first and the last term.
Clearly 5 is odd
Hence median will be the 3rd term itself.
And since all elements are even => x must be even integer.

Statement 1->
True
Statement 2->
May or may not be true.
E.g => -4,-2,0,2,4 => Mean=0
and 0,2,4,6,8 => Mean ≠0
Hence False

Statement 2->
x Again w can use the some examples =>
6,8,10,12,14 => x=10 i.e multiple of 5
0,2,4,6,8 => Mean = 4 => non multiple of 5
Once False
Hence only 1 must be true.

Thus A

_________________

Give me a hell yeah ...!!!!!

Intern
Joined: 31 May 2017
Posts: 2
Re: If x is the average (arithmetic mean) of 5 consecutive even [#permalink]

### Show Tags

31 May 2017, 22:54
[quote="GMATD11"]If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

Let n is the first integer of the series. So x = (n+n+2+n+4+n+6+n+8)/5 = (5n+20)/5=n+4
Since n is an integer, n+4 must be an integer. Option I is true. It’s never mentioned that the numbers are positive. In that case n might be -4 that will bring x = 0. So option II cannot be true. Option III cannot be true because n+4 is not divisible by 5
Re: If x is the average (arithmetic mean) of 5 consecutive even   [#permalink] 31 May 2017, 22:54
Similar topics Replies Last post
Similar
Topics:
1 If 5w = x+ y, then what is the average (arithmetic mean) of w, x, and 5 24 Apr 2017, 17:15
If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 7 28 Mar 2017, 05:53
5 If the average (arithmetic mean) of six consecutive odd 6 22 Mar 2017, 00:36
2 If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30 4 02 Feb 2017, 11:48
If the average (arithmetic mean) of five consecutive negative integers 4 18 May 2011, 00:00
Display posts from previous: Sort by