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# In a game five students A,B,C,D and E got 3,1,c,d and e scores respect

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Director
Joined: 18 Feb 2019
Posts: 582
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
In a game five students A,B,C,D and E got 3,1,c,d and e scores respect  [#permalink]

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07 Mar 2019, 01:07
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45% (medium)

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68% (02:19) correct 32% (02:25) wrong based on 22 sessions

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In a game five students A,B,C,D and E got 3,1,c,d and e scores respectively. If the median score is c and each student get a distinct integer score greater than or equal to 1, which of the following must be true?

I. The average score of the five students is greater than 3.
II. D scored more than 4.
III. Exactly one of D or E scored 2.

A. I only
B. I & II only
C. II & III only
D. I & III only
E. I,II & III
Math Expert
Joined: 02 Aug 2009
Posts: 8023
In a game five students A,B,C,D and E got 3,1,c,d and e scores respect  [#permalink]

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07 Mar 2019, 06:36
In a game five students A,B,C,D and E got 3,1,c,d and e scores respectively. If the median score is c and each student get a distinct integer score greater than or equal to 1, which of the following must be true?

Before we move to options, let us see what does the given information tell us..
c as the median means it is the 3rd value in ascending order....
But if any of c, d, or e is 2, the ascending order will be 1, 2, 3, _, _, so 3 and NOT c will be the median.
This tells us that there is no 2 in the set
This further tells us that c>3 and D and E are more than c or more than 4

I. The average score of the five students is greater than 3.
Let us take the least possible value ----- 1, 3, 4, 5, 6 so average = 19/6 >3..TRUE

II. D scored more than 4.
c is at least 4, and D is greater than c or >4....TRUE

III. Exactly one of D or E scored 2.
No one has scored 2, so FALSE

A. I only
B. I & II only
C. II & III only
D. I & III only
E. I,II & III

Option I and II are true, hence B
_________________
In a game five students A,B,C,D and E got 3,1,c,d and e scores respect   [#permalink] 07 Mar 2019, 06:36
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# In a game five students A,B,C,D and E got 3,1,c,d and e scores respect

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