GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 23:52 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x=2y=4z for positive integers x, y, and z, which of the following c

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

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 73% (01:59) correct 27% (03:24) wrong based on 88 sessions

HideShow timer Statistics

If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

_________________
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

Given problem :
If x=2y=4z for positive integers x, y, and z, find the average of x,y,3z?

Since x=2y=4z, assume x=4x,y=2x and z=x
So the average of x,y,3z will be $$\frac{(4x+2x+3x)}{3} = 3x$$
Of the answer options, only 15(Option A) is a multiple of 3 and is our correct answer.
_________________
You've got what it takes, but it will take everything you've got
Senior Manager  G
Joined: 28 May 2017
Posts: 281
Concentration: Finance, General Management
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

MathRevolution wrote:
If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

If x=2y=4z,
x + y + 3z = 4z + 2z + 3z = 9z
Average of 3 numbers =$$\frac{9z}{3}$$ = 3z

Since the average is multiple of 3, answer has to be a multiple of 3 as well.

Only option A is a multiple of 3.

_________________
If you like the post, show appreciation by pressing Kudos button
Retired Moderator P
Joined: 19 Mar 2014
Posts: 922
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

1
MathRevolution wrote:
If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

x = 2y = 4z

x, y, 3z

Average= Sum/Count

Average = (4z+2z+3z)/3

= 9z/3

= 3z

As we can see the answer should be multiple of 3.

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Director  V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

MathRevolution wrote:
If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

Given $$x=2y=4z$$

$$x = 4z$$ --------- (i)

$$2y = 4z$$

$$y = 2z$$ ----------- (ii)

Average of $$x, y$$ and $$3z = \frac{x + y + 3z}{3}$$

Substituting the values of $$x$$ and $$y$$ from (i) and (ii) respectively, we get;

$$\frac{4z + 2z + 3z}{3} = \frac{9z}{3} = 3z$$

Average of $$x, y$$ and $$3z$$ must be a multiple of $$3$$.

Among the options Only (Option A) $$15$$ is multiple of $$3$$.

Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

MathRevolution wrote:
If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

Let, x=2y=4z = 4

So, x = 4 , y = 2 & z = 1

Arithmetic Mean of x, y & 3z is $$\frac{4 + 2 + 3}{3} = 3$$

So, The number must be a multiple of 3, only (A) satisfies, thus answer will be (A) 15
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

==> You get x=4z and y=2z, and the average=$$\frac{(x+y+3z)}{3}=\frac{(4z+2z+3z)}{3}=3z$$, so it always needs to be the multiple of 3.

Therefore, the answer is A.
_________________
Director  V
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

Hi Bunuel, Vyshak,

If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

x=2y ==> y=x/2

x=4z ==> z=x/4

arithmetic mean of x, y and 3z = [x+(x/2)+(3x/4)]/3

=10x/12 ==>5x/6

Can somebody please tell me where am'I going wrong?
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

NandishSS wrote:
Hi Bunuel, Vyshak,

If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

x=2y ==> y=x/2

x=4z ==> z=x/4

arithmetic mean of x, y and 3z = [x+(x/2)+(3x/4)]/3

=10x/12 ==>5x/6

Can somebody please tell me where am'I going wrong?

$$\frac{x+\frac{x}{2}+\frac{3x}{4}}{3}=\frac{\frac{4x+2x+3x}{4}}{3}=\frac{3x}{4}$$, not 5x/6.
_________________
VP  P
Joined: 07 Dec 2014
Posts: 1224
If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

MathRevolution wrote:
If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

A. 15
B. 20
C. 25
D. 40
E. 47

y=x/2
z=x/4
x+x/2+3*x/4=9x/4
mean=(9x/4)/3=3x/4
only 15 is a multiple of 3
A
Director  V
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

Bunuel wrote:
NandishSS wrote:
Hi Bunuel, Vyshak,

If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

x=2y ==> y=x/2

x=4z ==> z=x/4

arithmetic mean of x, y and 3z = [x+(x/2)+(3x/4)]/3

=10x/12 ==>5x/6

Can somebody please tell me where am'I going wrong?

$$\frac{x+\frac{x}{2}+\frac{3x}{4}}{3}=\frac{\frac{4x+2x+3x}{4}}{3}=\frac{3x}{4}$$, not 5x/6.

Tagging VeritasPrepKarishma, Bunuel,

I'm Sorry for very silly mistake.But 3x/4, does ans should be multiple of 3. Can you please explain bit.
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Manager  G
Joined: 30 May 2012
Posts: 198
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

Show Tags

NandishSS wrote:
Bunuel wrote:
NandishSS wrote:
Hi Bunuel, Vyshak,

If x=2y=4z for positive integers x, y, and z, which of the following can be the average (arithmetic mean) of x, y and 3z?

x=2y ==> y=x/2

x=4z ==> z=x/4

arithmetic mean of x, y and 3z = [x+(x/2)+(3x/4)]/3

=10x/12 ==>5x/6

Can somebody please tell me where am'I going wrong?

$$\frac{x+\frac{x}{2}+\frac{3x}{4}}{3}=\frac{\frac{4x+2x+3x}{4}}{3}=\frac{3x}{4}$$, not 5x/6.

Tagging VeritasPrepKarishma, Bunuel,

I'm Sorry for very silly mistake.But 3x/4, does ans should be multiple of 3. Can you please explain bit.

Since the given options are all integers, it needs to be assumed that $$\frac{3x}{4}$$ will be an integer. Therefore, the resultant will 3 * (some number). In the given options, the only option that is a multiple of 3 is Option A. That is why it is the right option. Kapish? Re: If x=2y=4z for positive integers x, y, and z, which of the following c   [#permalink] 07 Aug 2017, 10:12
Display posts from previous: Sort by

If x=2y=4z for positive integers x, y, and z, which of the following c

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

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