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# find number, given median

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Manager
Joined: 24 Nov 2010
Posts: 212
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 32 [1] , given: 7

find number, given median [#permalink]  18 Sep 2011, 19:02
1
KUDOS
00:00

Difficulty:

(N/A)

Question Stats:

11% (00:00) correct 89% (00:46) wrong based on 17 sessions
A set of 25 different integers has a median of 50 and a range of
50. What is the greatest possible integer that could be in this
set?
(A) 62
(B) 68
(C) 75
(D) 88
(E) 100
Intern
Joined: 06 May 2011
Posts: 13
Followers: 0

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

Re: find number, given median [#permalink]  18 Sep 2011, 19:43
dreambeliever wrote:
A set of 25 different integers has a median of 50 and a range of
50. What is the greatest possible integer that could be in this
set?
(A) 62
(B) 68
(C) 75
(D) 88
(E) 100

I go for D

Given Median = 50
Range = 50

Let Numbers be x1 , x2 , x3 ,.....,x13, .....x24, x25
x13 = 50
x25 - x1 = 50
E : let x25 = 100
=> x1 = 50
Not possible as we need atleast a difference of 12 between x13 and x1.

Applying the same for all the answer choices we get A, B, C, D are possible.
As we are asked abt max possible Ans is D.
Manager
Joined: 04 Jun 2011
Posts: 193
Followers: 0

Kudos [?]: 32 [2] , given: 21

Re: find number, given median [#permalink]  18 Sep 2011, 21:29
2
KUDOS
yes.. i think D too...

i have a different solution though... without looking at the answers...

the total set contains 25 numbers... and the mid-value (median) is 50
which implies the 13th value is 50.

For range to remain 50 and the last digit to be maximum, the first digit must be as close to 50 as possible...
the greatest possible number is x1 is 38 (only then will the 13th number be 50)

if x1 = 38, x25 = 38+50 = 88
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2047
Followers: 128

Kudos [?]: 903 [2] , given: 376

Re: find number, given median [#permalink]  18 Sep 2011, 23:26
2
KUDOS
dreambeliever wrote:
A set of 25 different integers has a median of 50 and a range of
50. What is the greatest possible integer that could be in this
set?
(A) 62
(B) 68
(C) 75
(D) 88
(E) 100

Sol:

50 is the 13th number in the set.

Smallest integer closest to 50= 50-12=38 {: "minus 12" because there must be exactly 12 unique integers smaller than 50(median=50):}

Range=50; Greatest number=smallest+range=38+50=88

Ans: "D"
_________________
Manager
Joined: 24 Nov 2010
Posts: 212
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 32 [0], given: 7

Re: find number, given median [#permalink]  19 Sep 2011, 05:51
i got D too.

Just wanted to double check in the forum as i can't find the OA/source of the problem anymore .
Manager
Status: Essaying
Joined: 27 May 2010
Posts: 156
Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE: Accounting (Education)
Followers: 1

Kudos [?]: 7 [0], given: 8

Re: find number, given median [#permalink]  20 Sep 2011, 02:26
Fluke really knows his math.
Re: find number, given median   [#permalink] 20 Sep 2011, 02:26
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