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

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Math Revolution GMAT Instructor
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If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink]

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30 Jun 2017, 01:04
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25% (medium)

Question Stats:

77% (01:15) correct 23% (02:13) wrong based on 70 sessions

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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

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"Only $99 for 3 month Online Course" "Free Resources-30 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 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: 700 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI 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 GMAT 1: 800 Q59 V59 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$99 for 3 month Online Course"
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Re: If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink]

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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?
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Joined: 02 Sep 2009
Posts: 46251
Re: If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink]

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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.
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VP
Joined: 07 Dec 2014
Posts: 1018
If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink]

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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
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Re: If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink]

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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.
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Manager
Joined: 30 May 2012
Posts: 215
Location: United States (TX)
Concentration: Finance, Marketing
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Re: If x=2y=4z for positive integers x, y, and z, which of the following c [#permalink]

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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
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