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

 It is currently 12 Dec 2019, 20:16 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the average of x, y, and z?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59712
What is the average of x, y, and z?  [#permalink]

### Show Tags

1
3 00:00

Difficulty:   25% (medium)

Question Stats: 65% (01:01) correct 35% (01:22) wrong based on 164 sessions

### HideShow timer Statistics

What is the average of x, y, and z?

(1) 2x + y + 4z = 23
(2) 3x + 4y + z = 22

_________________
Verbal Forum Moderator V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2435
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: What is the average of x, y, and z?  [#permalink]

### Show Tags

1
we need to find (x+y+z)/3

(1) 2x + y + 4z = 23
Not sufficient
(2) 3x + 4y + z = 22
Not sufficient

Adding 1 and 2 , we get
5x+5y+5z = 45
=> x+y+z = 9
Average (x+y+z)/3 = 3

_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4145
Re: What is the average of x, y, and z?  [#permalink]

### Show Tags

2
Top Contributor
Bunuel wrote:
What is the average of x, y, and z?

(1) 2x + y + 4z = 23
(2) 3x + 4y + z = 22

Target question: What is the average of x, y, and z?

NOTE: the average of x, y and z = (x + y + z)/3

Statement 1: 2x + y + 4z = 23
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 0, y = 23 and z = 0. In this case, the average of x, y and z = (0 + 23 + 0)/3 = 23/3
Case b: x = 11, y = 1 and z = 0. In this case, the average of x, y and z = (11 + 1 + 0)/3 = 12/3 = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: 3x + 4y + z = 22
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 0, y = 0 and z = 22. In this case, the average of x, y and z = (0 + 0 + 22)/3 = 22/3
Case b: x = 0, y = 5 and z = 2. In this case, the average of x, y and z = (0 + 5 + 2)/3 = 7/3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2x + y + 4z = 23
Statement 2 tells us that 3x + 4y + z = 22
ADD the two equations to get: 5x + 5y + 5z = 45
Divide both sides by 5 to get: x + y + z = 9
Since the average of x, y and z = (x + y + z)/3, we can see that the average of x, y and z = 9/3 = 3
So, the average = 3
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13740
Re: What is the average of x, y, and z?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the average of x, y, and z?   [#permalink] 08 Feb 2019, 23:56
Display posts from previous: Sort by

# What is the average of x, y, and z?  