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

 It is currently 22 Apr 2019, 07:16

### 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

# 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
Joined: 16 Aug 2015
Posts: 7236
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

30 Jun 2017, 01:04
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:58) correct 28% (03:16) wrong based on 84 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

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3386 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 30 Jun 2017, 01:39 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 Joined: 28 May 2017 Posts: 283 Concentration: Finance, General Management Re: If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink] ### Show Tags 30 Jun 2017, 01:50 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. Hence Answer A _________________ If you like the post, show appreciation by pressing Kudos button Retired Moderator Joined: 19 Mar 2014 Posts: 931 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 30 Jun 2017, 02:16 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. Answer is A _________________ "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 Joined: 04 Dec 2015 Posts: 750 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 30 Jun 2017, 09:35 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 $$3$$. Answer (A)... Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4423 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 30 Jun 2017, 10:42 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 Joined: 16 Aug 2015 Posts: 7236 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 02 Jul 2017, 18:13 ==> 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. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Director
Joined: 06 Jan 2015
Posts: 628
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

23 Jul 2017, 07:27
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
Joined: 02 Sep 2009
Posts: 54434
Re: If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

### Show Tags

23 Jul 2017, 08:16
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
Joined: 07 Dec 2014
Posts: 1179
If x=2y=4z for positive integers x, y, and z, which of the following c  [#permalink]

### Show Tags

23 Jul 2017, 10:55
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
Joined: 06 Jan 2015
Posts: 628
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

24 Jul 2017, 06:58
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
Joined: 30 May 2012
Posts: 201
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

07 Aug 2017, 10:12
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 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®.