Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 168
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
Updated on: 30 Oct 2018, 01:09
Question Stats:
57% (01:28) correct 43% (01:39) wrong based on 436 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The proof of understanding is the ability to explain it.
Originally posted by GMATD11 on 01 May 2012, 10:03.
Last edited by pushpitkc on 30 Oct 2018, 01:09, edited 1 time in total.
Edited question




Math Expert
Joined: 02 Sep 2009
Posts: 59129

Re: If x is the average (arithmetic mean) of 5 consecutive even
[#permalink]
Show Tags
01 May 2012, 14:41
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}. Answer: A. Hope it's clear. P.S. In your example if n=4 then x=n+4=0, so II is not always true.
_________________




Senior Manager
Joined: 23 Oct 2010
Posts: 319
Location: Azerbaijan
Concentration: Finance

Re: If x is the average (arithmetic mean) of 5 consecutive even
[#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: 59129

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
_________________



Intern
Joined: 06 May 2014
Posts: 6
Concentration: Marketing, Technology

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: 9789
Location: Pune, India

Re: If x is the average (arithmetic mean) of 5 consecutive even
[#permalink]
Show Tags
14 Jul 2014, 22:19
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 ... eticmean/http://www.veritasprep.com/blog/2012/04 ... questions/http://www.veritasprep.com/blog/2012/05 ... eviations/http://www.veritasprep.com/blog/2012/05 ... ticmeans/http://www.veritasprep.com/blog/2012/05 ... onmedian/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



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}.
Answer: A.
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: 6
Concentration: Marketing, Technology

Re: If x is the average (arithmetic mean) of 5 consecutive even
[#permalink]
Show Tags
Updated on: 17 Jul 2014, 23:00
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
Originally posted by ayushee01 on 17 Jul 2014, 22:06.
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: 6
Concentration: Marketing, Technology

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: 116

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 x4, 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 Hence I is the answer.
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views
Perfect Scores http://perfectscores.org http://www.youtube.com/perfectscores



Intern
Joined: 16 May 2015
Posts: 14

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: 59129

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: numberpropertiestipsandhints174996.html
_________________



Current Student
Joined: 12 Aug 2015
Posts: 2549

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
_________________



Intern
Joined: 31 May 2017
Posts: 1

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 So answer is A



Manager
Joined: 08 Sep 2016
Posts: 100

Re: If x is the average (arithmetic mean) of 5 consecutive even
[#permalink]
Show Tags
28 Jun 2018, 15:23
Nice Question
X = avg of 5 consecutive even integers *no restriction on sign
Pick numbers to try.
4 + 2 + 0 + 2 +4 > fits question
X= 0
Statements 1. True > 0 is neither positive nor negative but it's even 2. False  could be true. But we proved wrong with statement 1 3. False  could be true. Try a different set such as 8 + 6+ 4 + 2 +0 /5 = 4
Answer A



NonHuman User
Joined: 09 Sep 2013
Posts: 13609

Re: If x is the average (arithmetic mean) of 5 consecutive even
[#permalink]
Show Tags
11 Oct 2019, 09:01
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.
_________________




Re: If x is the average (arithmetic mean) of 5 consecutive even
[#permalink]
11 Oct 2019, 09:01






