Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

## Challenge-statistics

This topic has 3 expert replies and 32 member replies
Goto page

### GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
Joined
08 Jan 2008
Posted:
3156 messages
Followed by:
460 members
Thanked:
1432 times
GMAT Score:
800
Tue May 01, 2012 10:54 am
Hi!

You seem to have misinterpreted the question as "what is the smallest possible number in the set?", when in fact it's simply "what is the smallest number in the set?"

With (1) alone, there's no way to determine the actual value of x, y or z, so (1) is insufficient.

Stuart

shantanu86 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.
This is a great question.. But contrary to popular opinion here, I think the answer is [A]
Lets analyze..

(1) (x+y+z+8) = 4*12.5
=> average of x,y and z is 14

So one of the solution set which satisfies (1) is
(18,14,10)
Now to minimize the smallest number I decrease minimum and balance other two for mean to be 14

(17,16,9).. integral solution with 9 as smallest

(16.66,16.66, 8.66) .. non-integral solution with 8.66 as smallest

Hence (1) alone is sufficient and obviously (2) alone is not sufficient.
Therefore the correct answer is [A].

Hope it helps!!

_________________
Stuart Kovinsky, B.A. LL.B.
Toronto Office
1-800-KAP-TEST
www.kaptest.com

Free GMAT Practice Test under Proctored Conditions! - Find a practice test near you or live and online in Kaplan's Classroom Anywhere environment. Register today!
miteshpant Just gettin' started!
Joined
04 Jun 2012
Posted:
3 messages
Thu Jul 19, 2012 12:28 am
Hi,

No where its said that the numbers are integers. So i think it must be E

optimist Just gettin' started!
Joined
06 Jun 2012
Posted:
15 messages
Thanked:
1 times
Fri Jul 20, 2012 11:34 am
miteshpant wrote:
Hi,

No where its said that the numbers are integers. So i think it must be E
Here, when you combine stmt 1 and stmt 2, you get:
x+y+z=42
assuming 'y' as the median, we get
x+z=42-14=28 ---1
and we know, x-z = 8 ---2

solving 1 and 2 we get x=18 and z=10

So, I don't think there is any question of the numbers being non integers..

Pls let me know if I have missed anything here

Thanks

ashg84 Rising GMAT Star
Joined
09 Jul 2011
Posted:
48 messages
Tue Oct 16, 2012 2:16 am
Hi,

I agree with you.. The question is not asking for smallest possible but the smallest number in the set. Two things are entirely different. In my views the answer should be E as we can not find the smallest number with these two statement. Please suggest if my interpretation of the question is wrong.

What is the OA.

Thanks

Ashish Gupta \

Stuart Kovinsky wrote:
Hi!

You seem to have misinterpreted the question as "what is the smallest possible number in the set?", when in fact it's simply "what is the smallest number in the set?"

With (1) alone, there's no way to determine the actual value of x, y or z, so (1) is insufficient.

Stuart

shantanu86 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.
This is a great question.. But contrary to popular opinion here, I think the answer is [A]
Lets analyze..

(1) (x+y+z+8) = 4*12.5
=> average of x,y and z is 14

So one of the solution set which satisfies (1) is
(18,14,10)
Now to minimize the smallest number I decrease minimum and balance other two for mean to be 14

(17,16,9).. integral solution with 9 as smallest

(16.66,16.66, 8.66) .. non-integral solution with 8.66 as smallest

Hence (1) alone is sufficient and obviously (2) alone is not sufficient.
Therefore the correct answer is [A].

Hope it helps!!

ashg84 Rising GMAT Star
Joined
09 Jul 2011
Posted:
48 messages
Tue Oct 16, 2012 2:23 am
My mistake, answer should be C.

rajeshsinghgmat Really wants to Beat The GMAT!
Joined
08 Jan 2013
Posted:
162 messages
Thanked:
1 times
Wed Feb 20, 2013 2:45 am

### Best Conversation Starters

1 varun289 43 topics
2 greenwich 30 topics
3 sana.noor 21 topics
4 guerrero 20 topics
5 killerdrummer 19 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

202 posts
2 GMATGuruNY

The Princeton Review Teacher

143 posts
3 Anju@Gurome

Gurome

134 posts
4 Jim@StratusPrep

Stratus Prep

86 posts
5 David@VeritasPrep

Veritas Prep

41 posts
See More Top Beat The GMAT Experts