Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5593
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
Question Stats:
77% (01:15) correct 23% (02:13) wrong based on 70 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2831
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: 293
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: 974
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
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/howtoget60awamyguide64327.html#p470475



Director
Joined: 04 Dec 2015
Posts: 700
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: 3511
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: 5593
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 oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Senior Manager
Joined: 06 Jan 2015
Posts: 388
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: 46251

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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



VP
Joined: 07 Dec 2014
Posts: 1018

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



Senior Manager
Joined: 06 Jan 2015
Posts: 388
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: 215
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






