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Behavioral experiment

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Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
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Behavioral experiment [#permalink]  20 Nov 2011, 04:45
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During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer?
(A) 0%
(B) 10%
(C) 20%
(D) 30%
(E) 40%

Any idea how to solve this question guys?
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E.

MGMAT 1 --> 530
MGMAT 2--> 640
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GMAT ==> 730

Manager
Status: Meh, I can't take the GMAT before 2017.
Joined: 20 Aug 2011
Posts: 145
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Kudos [?]: 81 [3] , given: 0

Re: Behavioral experiment [#permalink]  20 Nov 2011, 06:32
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KUDOS
As any power of 7 is odd, the product of 7^any integer and 3 will always be odd.
Sum of this odd number & double the age of a student will always be odd.
Therefore, all lucky numbers in the class will be odd.

The results of the experiment will yield a set of 28 odd integers
Arrange the numbers in ascending order.
Median of the set will be average of the 14th & 15th elements in the set.
Both these integers are odd; hence, their sum will always be even and their average will always be an integer.
Therefore, the probability that the median lucky number in the class will be a non-integer is 0%.
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Manager
Joined: 29 Oct 2011
Posts: 184
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
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Re: Behavioral experiment [#permalink]  20 Nov 2011, 10:46
The only way to have a non-integer median is if the two middle numbers are odd and even. That is not possible in this case since all lucky numbers will be odd (7^x is odd, time 3 is odd, plus even number is odd).
Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 49

Kudos [?]: 1860 [0], given: 217

Re: Behavioral experiment [#permalink]  20 Nov 2011, 21:27
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Re: Behavioral experiment   [#permalink] 20 Nov 2011, 21:27
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