It is currently 22 Jan 2018, 00:36

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is the average of three integers a, b, and c, is x a multiple of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5537
If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 06 Jan 2018, 05:30
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (01:05) correct 50% (01:55) wrong based on 74 sessions

HideShow timer Statistics

If x is the average of three integers a, b, and c, is x a multiple of 4?

(1) a, b, and c are consecutive even integers.
(2) a is multiple of 4.


New question on average
[Reveal] Spoiler: OA

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

2 KUDOS received
Intern
Intern
avatar
B
Joined: 30 May 2017
Posts: 42
CAT Tests
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 06 Jan 2018, 06:06
2
This post received
KUDOS
If x is the average of three integers a,b, and c, is x a multiple of 4?

(1) a, b, and c are consecutive even integers.
(2) a is multiple of 4.

Hi,
(a+b+c)/3=x

1.
Let a be the first even integer.Then b=a+2 and c= a+4
therefore (3a+6)/3=x
or a+2=x

Now if a= 2 then x is 4which is a multiple of 4
However if a=4 then x is 6.. not a multiple of 4
BCE

2. Insufficient on it's own

CE
Now after combining both 1 & 2 we get

a+2=x and a=4k

therefore a+2=4k+2 which will never be a multiple of 4.
Hence C is sufficient.

Let me know if there's a flaw
DS Forum Moderator
avatar
G
Joined: 21 Aug 2013
Posts: 677
Location: India
Premium Member CAT Tests
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 06 Jan 2018, 09:44
chetan2u wrote:
If x is the average of three integers a,b, and c, is x a multiple of 4?

(1) a, b, and c are consecutive even integers.
(2) a is multiple of 4.


New question on average


Is (a+b+c)/3 = 4k, where k is a non negative integer. So the question is basically asking whether a+b+c = 12k, where k is a non negative integer.

(1) Lets look at various cases of consecutive even integers. If we take a set of 0, 2, 4 then the sum = 0+2+4 = 6, is NOT a multiple of 12. But if we take a set of 2, 4, 6 then the sum = 2+4+6 = 12, which IS a multiple of 12. So cant say. Not Sufficient.

(2) a is a multiple of 4, but if (b+c) gives us an odd number, then the sum will not be a multiple of 12. If b & c are both multiples of 4, then the average can be a multiple of 4. Not Sufficient.

Combining the two statements, a has to be a multiple of 4 and a,b,c are consecutive even integers. If we take a,b,c as (4,6,8) respectively then the sum = 4+6+8 = 18, is NOT a multiple of 12. If we take a,b,c as (4,2,6) respectively then the sum = 4+2+6 = 12, which IS a multiple of 12. So both cases are possible (we are given that a,b,c are consecutive even integers but we are not given that they are so in ascending order).
So Insufficient.

Hence E answer
Intern
Intern
avatar
Joined: 06 Oct 2017
Posts: 10
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 06 Jan 2018, 09:52
amanvermagmat wrote:
chetan2u wrote:
If x is the average of three integers a,b, and c, is x a multiple of 4?

(1) a, b, and c are consecutive even integers.
(2) a is multiple of 4.


New question on average


Is (a+b+c)/3 = 4k, where k is a non negative integer. So the question is basically asking whether a+b+c = 12k, where k is a non negative integer.

(1) Lets look at various cases of consecutive even integers. If we take a set of 0, 2, 4 then the sum = 0+2+4 = 6, is NOT a multiple of 12. But if we take a set of 2, 4, 6 then the sum = 2+4+6 = 12, which IS a multiple of 12. So cant say. Not Sufficient.

(2) a is a multiple of 4, but if (b+c) gives us an odd number, then the sum will not be a multiple of 12. If b & c are both multiples of 4, then the average can be a multiple of 4. Not Sufficient.

Combining the two statements, a has to be a multiple of 4 and a,b,c are consecutive even integers. If we take a,b,c as (4,6,8) respectively then the sum = 4+6+8 = 18, is NOT a multiple of 12. If we take a,b,c as (4,2,6) respectively then the sum = 4+2+6 = 12, which IS a multiple of 12. So both cases are possible (we are given that a,b,c are consecutive even integers but we are not given that they are so in ascending order).
So Insufficient.

Hence E answer

Answer should be C.

You did a mistake! On combining you took a case where you got X as a multiple when you considered numbers as
4+2+6 = 12
You should check again that the *statement1* says that they are even consecutive integers.

And statement 2 says a is multiple of 4

So numbers can be 4,6,8 or 8,10,12 or, 12,14,16 and so on.. The sum of all of them in the form of 3X doesn't make X as multiple of 4

So OA should be C

Sent from my vivo 1609 using GMAT Club Forum mobile app
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 827
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If x is the average of three integers a,b, and c, is x a multiple of 4 [#permalink]

Show Tags

New post 06 Jan 2018, 09:56
chetan2u wrote:
If x is the average of three integers a,b, and c, is x a multiple of 4?

(1) a, b, and c are consecutive even integers.
(2) a is multiple of 4.


New question on average


Statement 1: as \(a\), \(b\) & \(c\) are consecutive even integers so we we have \(b=a+2\) & \(c=a+4\)

So average \(=\frac{a+a+2+a+4}{3}=a+2=x\)

if \(a=2\), then \(x=4\), a multiple of \(4\) but if \(a=4\), then \(x=6\), not a multiple of \(4\). Insufficient

Statement 2: \(a=4k\). But we do not know about other integers. Insufficient

Combining 1 & 2: we have \(x=a+2=4k+2\). Hence \(x\) will not be a multiple of \(4\). Sufficient

Option C
Intern
Intern
avatar
Joined: 06 Jan 2018
Posts: 3
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 07 Jan 2018, 07:36
stmt 1: let 3 consecutive integers be 2n-2, 2n , 2n+2. So (avg) x = [(2n-2) + (2n) + (2n+2)]/3 => x = 2n. x is even for sure but not definitely a multiple of 4 (put x = 1,3,5 etc). stmt 1 alone not enough

stmt 2: it says a is a multiple of 4, let's wrint a as 4k. Now the avg is (4k + b + c)/3. Does not give anything. stmt 2 not enough

now combine stmt 2 and 1.

From stmt 1 -> x = 2n
From stmt 2 -> 2n-2 multiple of 4 => 2(n-1) = 4k => n-1 = 2k => n = 2k - 1.
put the value of n in stmt 1, we get
x = 2(2k -1)
x = 4k - 2

Now we can definitely say x is not a multiple of 4. Hence C
Intern
Intern
avatar
B
Joined: 30 Jul 2017
Posts: 14
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 07 Jan 2018, 09:01
Hi,

Can someone verify if the above answers are correct?

Since X is the average of a+b+c, then a+b+c= 3x (since the average is calculated as a+b+c/3 = x).

Now, if you use both statements and plug in for example 10+12+14, you have 3x = 36, thus x=12, which is a multiple of 4.

Then there are plenty examples where x is not a multiple of 4, therefore using this logic E should be the answer.

Regards.
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 827
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 07 Jan 2018, 09:35
krikre wrote:
Hi,

Can someone verify if the above answers are correct?

Since X is the average of a+b+c, then a+b+c= 3x (since the average is calculated as a+b+c/3 = x).

Now, if you use both statements and plug in for example 10+12+14, you have 3x = 36, thus x=12, which is a multiple of 4.

Then there are plenty examples where x is not a multiple of 4, therefore using this logic E should be the answer.

Regards.


Hi krikre

if you are using both the statements, then the highlighted portion is incorrect. it is mentioned that "a" is a multiple of 4 and 10 is not a multiple of 4. try using any multiple of 4 and then see if you are getting C or E
Intern
Intern
avatar
B
Joined: 28 Jan 2015
Posts: 3
Location: Brazil
GMAT ToolKit User
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 17 Jan 2018, 11:46
Hi everyone,

I have a doubt about statement 1.

When it says "a, b, and c are consecutive even integers.", can I assume that a < b < c or this relation has to be explicit in the statement?

Could anyone clarify this issue?

Thanks!
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 827
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If x is the average of three integers a, b, and c, is x a multiple of [#permalink]

Show Tags

New post 17 Jan 2018, 12:10
kdgodoy wrote:
Hi everyone,

I have a doubt about statement 1.

When it says "a, b, and c are consecutive even integers.", can I assume that a < b < c or this relation has to be explicit in the statement?

Could anyone clarify this issue?

Thanks!


Hi

For this question you can assume any order because ultimately you are taking summation of the 3 variables. But for other question types you must not assume the order unless stated even if the variables are consecutive.


Sent from my iPhone using GMAT Club Forum mobile app
Re: If x is the average of three integers a, b, and c, is x a multiple of   [#permalink] 17 Jan 2018, 12:10
Display posts from previous: Sort by

If x is the average of three integers a, b, and c, is x a multiple of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.