It is currently 18 Nov 2017, 20:47

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the average (arithmetic mean) of x, y and z?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132626 [1], given: 12326

What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

07 Sep 2015, 04:28
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:57) correct 28% (01:07) wrong based on 186 sessions

### HideShow timer Statistics

What is the average (arithmetic mean) of x, y and z?

(1) 3x – 2y + 7z = 23

(2) 4x – 3y + 5z = 5 and –x + 6y – 2z = 58

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132626 [1], given: 12326

Manager
Joined: 10 Aug 2015
Posts: 98

Kudos [?]: 84 [1], given: 20

Re: What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

07 Sep 2015, 06:19
1
KUDOS
Bunuel wrote:
What is the average (arithmetic mean) of x, y and z?

(1) 3x – 2y + 7z = 23

(2) 4x – 3y + 5z = 5 and –x + 6y – 2z = 58

Kudos for a correct solution.

Solution: We need to find mean i.e $$\frac{x+y+z}{3}$$.
In order to find this we need either values of x,y and z or value of x+y+z

Statement1 : We have 3 variables and 1 equation. So, we cannot find x,y and z. Finding x+y+z is also impossible here.
So, insufficient.

Statement2 : There is a small trap here. We have 3 variables and 2 equations,we cant find x,y and z individually. But adding those two equations we get the value of x+y+z. This is enough to find the mean.
So, sufficient.

Option B

Kudos [?]: 84 [1], given: 20

Intern
Joined: 12 Nov 2013
Posts: 44

Kudos [?]: 121 [1], given: 141

Re: What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

07 Sep 2015, 06:32
1
KUDOS
Bunuel wrote:
What is the average (arithmetic mean) of x, y and z?

(1) 3x – 2y + 7z = 23

(2) 4x – 3y + 5z = 5 and –x + 6y – 2z = 58

Kudos for a correct solution.

Basically, we need to find x + y + z

Statement 1) Insufficient. We cannot find the sum of x + y + z through any mathematical operation.

Statement 2 ) Add both the equations and you get x + y + z = 21 . Sufficient
_________________

Kindly support by giving Kudos, if my post helped you!

Kudos [?]: 121 [1], given: 141

Intern
Joined: 03 Feb 2014
Posts: 38

Kudos [?]: 10 [1], given: 208

Location: United States
Concentration: Entrepreneurship, General Management
WE: General Management (Other)
What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

07 Sep 2015, 21:50
1
KUDOS
Arithmetic Mean = (x+y+z)/3
From 1:
3x-2y+7z=23; Insufficient
From 2:
4x-3y+5z=5 & -x+6y-2z=58
3x+3y+3z=63
x+y+z=21 --> (x+y+z)/3=7; Sufficient
_________________

--Shailendra

Kudos [?]: 10 [1], given: 208

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4318

Kudos [?]: 3037 [0], given: 0

GPA: 3.82
What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

08 Sep 2015, 07:48
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

What is the average (arithmetic mean) of x, y and z?

(1) 3x – 2y + 7z = 23

(2) 4x – 3y + 5z = 5 and –x + 6y – 2z = 58

Transforming the original condition and the question, (x+y+z)/3=? and we just need to know x+y+z. Looking at 2) we have 4x – 3y + 5z = 5 and –x + 6y – 2z = 58, so adding them gives us 3x+3y+3z=63. The condition is sufficient, therefore B is the answer.
_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 3037 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132626 [0], given: 12326

Re: What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

14 Sep 2015, 07:40
Bunuel wrote:
What is the average (arithmetic mean) of x, y and z?

(1) 3x – 2y + 7z = 23

(2) 4x – 3y + 5z = 5 and –x + 6y – 2z = 58

Kudos for a correct solution.

KAPLAN OFFICIAL SOLUTION:

In this data sufficiency question we are asked to find the average of three unknowns. Remember that when asked to find an average, you need to find the sum of the terms divided by the number of terms. In this case we would need to know the sum of x + y + z and divide it by 3. The key to remember, is that we do not need to know x, y and z individually, only their sum. As long as we can do this, we will be able to find the average.

Statement 1 tells us 3x – 2y + 7z = 23. From this statement we are unable to determine x, y and z individually and we are also unable to find the sum of x, y and z directly. Statement 1 is, therefore, insufficient.

Statement 2 tells us 4x – 3y + 5z = 5 and –x + 6y – 2z = 58. At first this statement looks insufficient, as we have three equations and two variables, meaning that we are unable to solve for x, y and z. However, if we add these two equations together we get:

If we divide 3x + 3y + 3z = 63 by 3, we are left with x + y + z = 21. As we know the sum of x, y and z, statement 2 is sufficient.

Since statement 2 is sufficient and statement 1 is not, we do not need to check if the statements are sufficient together. Our answer must be (B).

[Reveal] Spoiler:
Attachment:

Screen-shot-2010-11-09-at-12.28.24-PM.png [ 9.96 KiB | Viewed 5618 times ]

_________________

Kudos [?]: 132626 [0], given: 12326

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 869 [0], given: 602

Re: What is the average (arithmetic mean) of x, y and z? [#permalink]

### Show Tags

21 Dec 2016, 17:20
Nice one.
Here is my solution to this one =>
Mean = Sum/#

Hence to get the mean we need the sum x+y+z

Statement 1=>
clearly not sufficient

Statement 2=>
Adding the two equations we get => 3x+3y+3z=63
Hence x+y+z = 21
Hence Sufficient

Hence B

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 869 [0], given: 602

Re: What is the average (arithmetic mean) of x, y and z?   [#permalink] 21 Dec 2016, 17:20
Display posts from previous: Sort by