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

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Senior Manager
Joined: 03 Mar 2010
Posts: 379
Schools: Simon '16 (M)
What is the greatest integer in a set of five different  [#permalink]

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12 May 2011, 01:23
1
1
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:21) correct 43% (02:08) wrong based on 81 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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Joined: 20 Dec 2010
Posts: 1829

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12 May 2011, 01:41
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.

Possible sets(considering all elements as different positive integers, sum=20, and the 3rd term=4)
{1,2,4,6,7}
{1,2,4,5,8}
{1,3,4,5,7}
Greatest integer can be 7 or 8.
Not Sufficient.

(2) The set contains only 1 even
number.

Clearly insufficient.
Possible sets(considering all elements different +ves, only one element even and the smallest integer=1):
{1,3,5,7,8}
{1,3,4,5,7}
Not Sufficient.

Combing both(all different positive integers, middle number 4(only even in the set), sum=20);
{1,3,4,5,7}
Greatest integer is definitely 7.
Sufficient.

Ans: "C"
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Senior Manager
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Posts: 379
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12 May 2011, 01:55
@fluke
Can you verify these two statements for me please?
1) Median and Mean of evenly spaced set of integers are equal --True.
2) if the median and mean are equal, set of integers can or cannot be evenly spaced -- True.

Thanks.
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12 May 2011, 07:52
using a and b

the set is 1,3,4,5,7. Hence C.
Director
Joined: 01 Feb 2011
Posts: 664

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12 May 2011, 18:57
1. Not sufficient

set could be any of the following

1 2 4 6 7

1 2 4 5 8

1 3 4 5 7

=> greatest number in the set could be 7 or 8.

2. Not sufficient

Together , Sufficient.

1 3 4 5 7

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Joined: 16 Nov 2010
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Location: United States (IN)
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17 May 2011, 07:33
(1)
Sum of integers = 20

So sum of remaining numbers = 19

S = {1,2,4,6,7}

S = {1,3,4,5,7}

Not Sufficient

(2)
S = {1,2,3,5,7}

S = {1,2,4,5,7}

Not Sufficient

(1) + (2)

S = {1,3,4,5,7}

Greatest integer = 7

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Manager
Joined: 06 Jul 2014
Posts: 99
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 640 Q48 V30
Re: What is the greatest integer in a set of five different  [#permalink]

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11 Aug 2017, 06:24
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.

Statement 1 alone is insufficient because many values are possible for the greatest integer such as 7 and 8.

Statement 2 alone is also insufficient because many values are possible for the greatest integer.

Combining 1 and 2, sufficient because the only possible value for the greatest integer is 7.
Intern
Joined: 18 Jan 2017
Posts: 33
Re: What is the greatest integer in a set of five different  [#permalink]

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05 Dec 2017, 04:55
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.

Info from prompt: set of five integers that includes 1 which is the smallest integer of the set. Looking for largest number in set.

1) The average (arithmetic mean) of all integers is 4 and the median of the set is also 4.
From this statement we know
average= 4 therefore the sum of the set = 20 --> average=sum/total --> 4=sum/5 --> sum=20
Also know that 4 is the median, therefore we could have the following 3 sets of numbers:
1,2,4,5,8
1,2,4,6,7
1,3,4,5,7

not sufficient because we have multiple answers- 7 or 8 could be the largest integer

2) The set contains only 1 even number.
not sufficient because it doesn't give you any information to figure out what the largest integer in the set is.

1 & 2 together
Only one of these sets has 1 even number
1,2,4,5,8
1,2,4,6,7
1,3,4,5,7
so you can solve for the largest integer
Re: What is the greatest integer in a set of five different &nbs [#permalink] 05 Dec 2017, 04:55
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