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# What is the greatest integer in a set of five different positive integ

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Joined: 02 Sep 2009
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What is the greatest integer in a set of five different positive integ  [#permalink]

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30 Oct 2019, 02:09
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65% (hard)

Question Stats:

53% (02:29) correct 48% (01:43) wrong based on 40 sessions

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What is the greatest integer in a set of five different positive integers if 1 is the smallest integer in the set?

(1) The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
(2) The set contains only 1 even number.

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What is the greatest integer in a set of five different positive integ  [#permalink]

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Updated on: 30 Oct 2019, 23:03
Bunuel wrote:
What is the greatest integer in a set of five different positive integers if 1 is the smallest integer in the set?

(1) The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
(2) The set contains only 1 even number.

set S= (1,a,b,c,d)
#1
The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
S= (1,a,4,c,d) ; sum = 20
a+c+d= 15
now we can have many possibilities of having greatest integers
(3,5,7) , (2,6,7), (2,5,8)
insufficient
#2
The set contains only 1 even number
other info not know insufficient
from 1 &2
only possibility is
(1,3,4,5,7) greatest = 7
IMO C

Originally posted by Archit3110 on 30 Oct 2019, 08:52.
Last edited by Archit3110 on 30 Oct 2019, 23:03, edited 3 times in total.
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Re: What is the greatest integer in a set of five different positive integ  [#permalink]

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30 Oct 2019, 16:17
Hello there!
(10,3,2) pair is not valid as median will change to 3. Rest of the explanation is perfect.

Archit3110 wrote:
Bunuel wrote:
What is the greatest integer in a set of five different positive integers if 1 is the smallest integer in the set?

(1) The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
(2) The set contains only 1 even number.

set S= (1,a,b,c,d)
#1
The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
S= (1,a,4,c,d) ; sum = 20
a+c+d= 15
now we can have many possiblities of having greatest integers
(10,3,2) or (9,2,4) or (7,5,3)
insufficient
#2
The set contains only 1 even number
other info not know insufficient
from 1 &2
only possibility is
(1,3,4,5,7) greatest = 7
IMO C
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Posts: 5428
Location: India
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Re: What is the greatest integer in a set of five different positive integ  [#permalink]

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30 Oct 2019, 21:07
gvij2017

Edited thanks

gvij2017 wrote:
Hello there!
(10,3,2) pair is not valid as median will change to 3. Rest of the explanation is perfect.

Archit3110 wrote:
Bunuel wrote:
What is the greatest integer in a set of five different positive integers if 1 is the smallest integer in the set?

(1) The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
(2) The set contains only 1 even number.

set S= (1,a,b,c,d)
#1
The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
S= (1,a,4,c,d) ; sum = 20
a+c+d= 15
now we can have many possiblities of having greatest integers
(10,3,2) or (9,2,4) or (7,5,3)
insufficient
#2
The set contains only 1 even number
other info not know insufficient
from 1 &2
only possibility is
(1,3,4,5,7) greatest = 7
IMO C

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Joined: 17 Jul 2017
Posts: 212
What is the greatest integer in a set of five different positive integ  [#permalink]

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30 Oct 2019, 21:36
Archit3110 wrote:
Bunuel wrote:
What is the greatest integer in a set of five different positive integers if 1 is the smallest integer in the set?

(1) The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
(2) The set contains only 1 even number.

set S= (1,a,b,c,d)
#1
The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
S= (1,a,4,c,d) ; sum = 20
a+c+d= 15
now we can have many possiblities of having greatest integers
(9,2,4) or (7,5,3)
insufficient
#2
The set contains only 1 even number
other info not know insufficient
from 1 &2
only possibility is
(1,3,4,5,7) greatest = 7
IMO C

Hi

In (9,2,4) isnot 4 repeated , but we are told they are unique integers so how is this possible?
if median is 4 then others be less than 4 or greather than 4 if numbers are unique.Plz clear

Bunuel can u plz clear this
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Re: What is the greatest integer in a set of five different  [#permalink]

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25 Nov 2019, 02:26
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Re: What is the greatest integer in a set of five different   [#permalink] 25 Nov 2019, 02:26
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