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find number, given median

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Manager
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Joined: 24 Nov 2010
Posts: 212
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
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find number, given median [#permalink] New post 18 Sep 2011, 19:02
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A
B
C
D
E

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
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Joined: 06 May 2011
Posts: 13
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Re: find number, given median [#permalink] New post 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
Now From answer choices,
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.
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Manager
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Re: find number, given median [#permalink] New post 18 Sep 2011, 21:29
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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
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Re: find number, given median [#permalink] New post 18 Sep 2011, 23:26
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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"
_________________

~fluke

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

Kudos [?]: 35 [0], given: 7

GMAT ToolKit User
Re: find number, given median [#permalink] New post 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
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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 [?]: 8 [0], given: 8

GMAT ToolKit User
Re: find number, given median [#permalink] New post 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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