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Greatest Possible Integer

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Manager
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Joined: 28 Jul 2004
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Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Greatest Possible Integer [#permalink]

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New post 29 Jan 2009, 05:34
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A set of 15 different integers has a median of 25 and range of 25. What is the greatest possible integer that could be in this set?

a) 32
b) 37
c) 40
d) 43
e) 50
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kris

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Re: Greatest Possible Integer [#permalink]

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New post 29 Jan 2009, 08:04
krishan wrote:
A set of 15 different integers has a median of 25 and range of 25. What is the greatest possible integer that could be in this set?

a) 32
b) 37
c) 40
d) 43
e) 50



x1..x7.. 15 x8.. x15

to get the higest x15 x1 to x7 must be close to 25

x1.. x7 are 18..24 25.. x15

max possible value = 18+25 = 43

D
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Manager
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Joined: 28 Jul 2004
Posts: 136

Kudos [?]: 73 [1], given: 2

Location: Melbourne
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Re: Greatest Possible Integer [#permalink]

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New post 29 Jan 2009, 19:51
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thanks. I will just explain for others.

x2suresh wrote:
krishan wrote:
A set of 15 different integers has a median of 25 and range of 25. What is the greatest possible integer that could be in this set?

a) 32
b) 37
c) 40
d) 43
e) 50



x1..x7.. 15 x8.. x15

to get the higest x15 x1 to x7 must be close to 25

x1.. x7 are 18..24 25.. x15

max possible value = 18+25 = 43

D


To get the greatest the number in the set, we will be adding the range value (25) to the smallest element in the set.

i.e. Greates number (G)= Least number (L) + 25

In order to maximize G, we have ot find the maximum possible value of L.

Are you thinking, why L can't be 25 (same as the median) and in this case the value of G would be = 25+25 = 50 and the answer should be (e). This is wrong !

THe question stem says , "A set of 15 different integers ". So we have to find the number closest to 25 and that number would be 25-7 = 18 (remember the median is the 8th digit and hence we have subtracted 7 here)

So, Now L = 18

Hence, G = 18+25 = 43 and (d) is the answer
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kris

Kudos [?]: 73 [1], given: 2

Re: Greatest Possible Integer   [#permalink] 29 Jan 2009, 19:51
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