If the range of the set containing the numbers x, y, and z : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 09 Dec 2016, 12:57

### 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

# If the range of the set containing the numbers x, y, and z

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Oct 2011
Posts: 191
Location: United States
Concentration: Finance, Strategy
GMAT 1: Q V
GPA: 3.7
WE: Account Management (Consumer Products)
Followers: 5

Kudos [?]: 146 [0], given: 4

If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

05 Feb 2012, 15:31
3
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (03:01) correct 37% (01:51) wrong based on 176 sessions

### HideShow timer Statistics

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5.
(2) The mean and the median of the set containing the numbers x, y, and z are equal.
[Reveal] Spoiler: OA

_________________

DETERMINED TO BREAK 700!!!

Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90091 [1] , given: 10413

### Show Tags

05 Feb 2012, 15:58
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

Let the numbers in ascending order be {x, y, z} (it really doesn't matter how we group them).

The range of a set is the difference between the largest and smallest elements in the set.
Given: $$z-x=8$$. Question: $$x=?$$

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5 --> $$x+y+z+8=4*12.5=50$$ --> $$x+y+z=42$$: 2 distinct linear equations 3 with unknowns. Not sufficient.

(2) The mean and the median of the set containing the numbers x, y, and z are equal --> $$mean=\frac{x+y+z}{3}=y=median$$ --> $$x+z=2y$$: 2 distinct linear equations with 3 unknowns. Not sufficient.

(1)+(2) 3 distinct linear equations with 3 unknowns --> we can solve for $$x$$. Sufficient.

_________________
Manager
Status: exam is close ... dont know if i ll hit that number
Joined: 06 Jun 2011
Posts: 206
Location: India
GMAT Date: 10-09-2012
GPA: 3.2
Followers: 2

Kudos [?]: 22 [0], given: 1

Re: If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

14 Jul 2012, 02:38
hello sir..

here when you have calculated the mean .. as per the data in 1st option mean should include 8 in the set and its value is 12.5

but you have excluded it...
can you just let me know where i am goin wrong

_________________

just one more month for exam...

Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90091 [0], given: 10413

Re: If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

14 Jul 2012, 02:45
mohan514 wrote:
hello sir..

here when you have calculated the mean .. as per the data in 1st option mean should include 8 in the set and its value is 12.5

but you have excluded it...
can you just let me know where i am goin wrong

I don't understand what you mean.

(1) says: The average of the set containing the numbers x, y, z, and 8 is 12.5. So, $$\frac{x+y+z+8}{4}=12.5$$ --> $$x+y+z+8=4*12.5=50$$ --> $$x+y+z=42$$.
_________________
Manager
Status: faciendo quod indiget fieri
Joined: 13 Mar 2012
Posts: 88
Followers: 0

Kudos [?]: 32 [0], given: 4

if the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

15 Sep 2012, 06:47
if the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5.
(2) The mean and the median of the set containing the numbers x, y, and z are equal.
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90091 [0], given: 10413

Re: if the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

15 Sep 2012, 07:00
if the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5.
(2) The mean and the median of the set containing the numbers x, y, and z are equal.

Merging similar topics. Please refer to the solution above.
_________________
Manager
Status: faciendo quod indiget fieri
Joined: 13 Mar 2012
Posts: 88
Followers: 0

Kudos [?]: 32 [0], given: 4

Re: If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

15 Sep 2012, 07:10
I had a doubt regarding option A:

In that we are given that x + y+ z = 42 and also that range is 8.

Now lets say smallest number is x and largest is z then equation is (x) + (x+n) + (x+8). Where 0<n<8 .

isnt this constraint enough to give us the required answer? Since we are just looking for the smallest number, for finding the middle number we will need another equation.
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90091 [1] , given: 10413

Re: If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

15 Sep 2012, 07:20
1
KUDOS
Expert's post
I had a doubt regarding option A:

In that we are given that x + y+ z = 42 and also that range is 8.

Now lets say smallest number is x and largest is z then equation is (x) + (x+n) + (x+8). Where 0<n<8 .

isnt this constraint enough to give us the required answer? Since we are just looking for the smallest number, for finding the middle number we will need another equation.

From (1) we can have many options, for example: {10, 14, 18} or {11, 12, 19}, therefore this statement is not sufficient.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Re: If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

21 Sep 2014, 17:41
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.
_________________
Manager
Joined: 22 Jan 2014
Posts: 138
WE: Project Management (Computer Hardware)
Followers: 0

Kudos [?]: 51 [0], given: 135

If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

22 Sep 2014, 08:26
calreg11 wrote:
If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5.
(2) The mean and the median of the set containing the numbers x, y, and z are equal.

C.

did it like this

1) x+y+z+8 = 50
=> x+y+z = 42
and |x-z| = 8
so, sets can be: {8,16,16}, {9,15,17}, {10,14,18}, {11,13,19}, and {12,12,20}
A is insufficient.

2) (x+y+z)/3 = y
=> x+z = 2y
and |x-z| = 8
B is insufficient.

(1)+(2)
among the sets in (1) the sets which have x+z = 2y is {10,14,18}
hence C.
_________________

Illegitimi non carborundum.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Re: If the range of the set containing the numbers x, y, and z [#permalink]

### Show Tags

17 May 2016, 05:05
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: If the range of the set containing the numbers x, y, and z   [#permalink] 17 May 2016, 05:05
Similar topics Replies Last post
Similar
Topics:
23 If S is a set of four numbers w, x, y, and z, is the range o 7 17 Jan 2014, 01:27
12 If set S consists of the numbers w, x, y, z is the range of 3 01 Sep 2013, 04:21
8 The range of the numbers in set S is X, and the range of the 5 10 May 2012, 06:57
2 If S is a set of four numbers w, x, y and z, is the range of 1 24 Apr 2012, 08:17
6 If S is a set of Four numbers w,x,y, and z, is the range of 6 24 Aug 2010, 18:33
Display posts from previous: Sort by