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# A set of 13 different integers has a median of 20 and a range of 20.

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
A set of 13 different integers has a median of 20 and a range of 20.  [#permalink]

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04 Oct 2018, 00:24
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Difficulty:

35% (medium)

Question Stats:

65% (01:32) correct 35% (01:14) wrong based on 62 sessions

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A set of 13 different integers has a median of 20 and a range of 20. What is the greatest possible value of the integer in the set?

(A) 23
(B) 27
(C) 30
(D) 34
(E) 40

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A set of 13 different integers has a median of 20 and a range of 20.  [#permalink]

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Updated on: 04 Oct 2018, 06:08
1
Bunuel wrote:
A set of 13 different integers has a median of 20 and a range of 20. What is the greatest possible value of the integer in the set?

(A) 23
(B) 27
(C) 30
(D) 34
(E) 40

Median of 13 different integers = 7th Term = 20

Range = Highest - Lowest = 20

Sets is { -, -, -, -, -, -, 20, -, -, -, -, -, -)

For Highest value of largest value of set, th elowest value also should be maximized because their difference is constant which is 20 in this case

To maximize the lowest value we can start going backward from median value keeping every previous value highest
Highest value of the 6th term which must be less than 20 is = 19
Highest value of the 5th term which must be less than 19 is = 18
Highest value of the 4th term which must be less than 18 is = 17
Highest value of the 3rd term which must be less than 17 is = 16
Highest value of the 2nd term which must be less than 16 is = 15
Highest value of the 1st term which must be less than 15 is = 14

Lowest value is 14 i.e. highest value = 20+14 = 34

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Originally posted by GMATinsight on 04 Oct 2018, 00:40.
Last edited by GMATinsight on 04 Oct 2018, 06:08, edited 1 time in total.
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Joined: 25 May 2017
Posts: 4
Re: A set of 13 different integers has a median of 20 and a range of 20.  [#permalink]

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04 Oct 2018, 05:23
GMATinsight wrote:
Bunuel wrote:
A set of 13 different integers has a median of 20 and a range of 20. What is the greatest possible value of the integer in the set?

(A) 23
(B) 27
(C) 30
(D) 34
(E) 40

Median of 13 different integers = 7th Term = 20

Range = Highest - Lowest = 20

Sets is { -, -, -, -, -, -, [color=#ffff00]13, -, -, -, -, -, -)[/color]

For Highest value of largest value of set, th elowest value also should be maximized because their difference is constant which is 20 in this case

To maximize the lowest value we can start going backward from median value keeping every previous value highest
Highest value of the 6th term which must be less than 13 is = 12
Highest value of the 5th term which must be less than 12 is = 11
Highest value of the 4th term which must be less than 11 is = 10
Highest value of the 3rd term which must be less than 10 is = 9
Highest value of the 2nd term which must be less than 9 is = 8
Highest value of the 1st term which must be less than 8 is = 7

Lowest value is 7 i.e. highest value = 20+7 = 27

How does the 7th Term become 13?

Im sorry but im having a really hard time understanding answers posted by you on other questions as well. I would like to request to give a detailed analysis. Thanks in advance.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
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Re: A set of 13 different integers has a median of 20 and a range of 20.  [#permalink]

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04 Oct 2018, 06:11
Saundarya wrote:
GMATinsight wrote:
Bunuel wrote:
A set of 13 different integers has a median of 20 and a range of 20. What is the greatest possible value of the integer in the set?

(A) 23
(B) 27
(C) 30
(D) 34
(E) 40

Median of 13 different integers = 7th Term = 20

Range = Highest - Lowest = 20

Sets is { -, -, -, -, -, -, [color=#ffff00]13, -, -, -, -, -, -)[/color]

For Highest value of largest value of set, th elowest value also should be maximized because their difference is constant which is 20 in this case

To maximize the lowest value we can start going backward from median value keeping every previous value highest
Highest value of the 6th term which must be less than 13 is = 12
Highest value of the 5th term which must be less than 12 is = 11
Highest value of the 4th term which must be less than 11 is = 10
Highest value of the 3rd term which must be less than 10 is = 9
Highest value of the 2nd term which must be less than 9 is = 8
Highest value of the 1st term which must be less than 8 is = 7

Lowest value is 7 i.e. highest value = 20+7 = 27

How does the 7th Term become 13?

Im sorry but im having a really hard time understanding answers posted by you on other questions as well. I would like to request to give a detailed analysis. Thanks in advance.

Median = 7th term because median term = (n+1)/2 th term = (13+1)/2 th term = 7th term

Now, I am going towards lowest value by decreasing the value from median and the decrease must be lowest because the lowest value should be as big as possible for the highest value to be as big as possible

Let me know if there is still something that bothers you in explanation.
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GMATinsight
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e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Re: A set of 13 different integers has a median of 20 and a range of 20.   [#permalink] 04 Oct 2018, 06:11
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