It is currently 22 Jan 2018, 00:39

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 + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43361
If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme [#permalink]

Show Tags

New post 28 Dec 2017, 20:38
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

85% (02:13) correct 15% (02:05) wrong based on 33 sessions

HideShow timer Statistics

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 627
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge
Re: If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme [#permalink]

Show Tags

New post 29 Dec 2017, 05:07
Bunuel wrote:
If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithmetic mean) of x, y, and z?

A. 2
B. 3
C. 4
D. 5
E. 6


z = 8-x = 11-2y
x-2y = -3
3x+y = 19

6x+2y = 38
x-2y = -3
Adding
7x = 35
x = 5
y=4
z=3
Mean of x,y,z (5,4,3) = 4
C
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

BSchool Forum Moderator
User avatar
D
Joined: 26 Feb 2016
Posts: 1816
Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme [#permalink]

Show Tags

New post 29 Dec 2017, 06:14
Bunuel wrote:
If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithmetic mean) of x, y, and z?

A. 2
B. 3
C. 4
D. 5
E. 6


Since x + z = 8, z = 8 - x -> (1)

2y + 8 -x = 11 -> -x + 2y = 3 -> (2)

3x + y = 19
Multiplying this equation by 2, 6x + 2y = 38 -> (3)

Solving equation (2) and (3), -7x = - 35 -> x = 5
Using value of x=5 in equation (3), we get y = 4
Similarly using the value of x in equation (1), we get z = 3

Therefore, the average of x,y, and z is \(\frac{3+4+5}{3}\) = 4(Option C)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Intern
Intern
avatar
B
Joined: 28 Dec 2017
Posts: 26
Re: If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme [#permalink]

Show Tags

New post 29 Dec 2017, 09:38
Subtract 2y + z = 11 from x + z = 8 to get 2y - x = 3 (equation 1). This eliminates one equation already.

Multiply 3x + y = 19 by 2 to get 6x + 2y = 38 (equation 2).

6x + 2y = 38 (equation 2) minus 2y - x = 3 (equation 1) is 7x = 35 because y cancels out. Hence, x = 5.

If x = 5, then z = 3 and y = 4. The average of x, y and z is 4, which is C.
VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1259
Premium Member CAT Tests
If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme [#permalink]

Show Tags

New post 30 Dec 2017, 09:09
Bunuel wrote:
If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithmetic mean) of x, y, and z?

A. 2
B. 3
C. 4
D. 5
E. 6

1) Pick two equations, eliminate one variable

With three equations and two variables, usually, you can eliminate only one variable at first.

Look for a pair in which one variable has the same coefficient (not always possible).

x + z = 8 (P)
2y + z = 11 (Q)
3x + y = 19 (R)

P and Q: z's coefficient is 1 in both. Use (Q - P)

2y + z = 11 (Q)
(-)x + z = 8 (P)___
2y - x = 3 (S)

2) Pair new equation with an original that has the same two remaining variables

Pair (S) with (R). Both have x and y only.
3x + y = 19 (R), rewritten to line up x and y

y + 3x = 19 (R)
2y - x = 3 (S)

x- and y-coefficents do not match. Multiply bottom equation (S) by 3, then add (R + S)

y + 3x = 19 (R)
6y - 3x = 9__ (S\(_1\))
7y . . . = 28
y = 4

3) Find other variables. Substitute known value(s) into other equation(s)

Find x: y + 3x = 19 (S)
4 + 3x = 19
3x = 15
x = 5

Find z: x + z = 8 (P)
5 + z = 8
z = 3

4) Average of x + y + z?
3, 4, 5 are consecutive integers. Median = mean
Mean = 4

OR \(\frac{3 + 4 + 5}{3} =\frac{12}{3}=4\)

Answer C
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme   [#permalink] 30 Dec 2017, 09:09
Display posts from previous: Sort by

If x + z = 8, 2y + z =11, and 3x + y= 19, what is the average (arithme

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


cron

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®.