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What is the greatest integer in a set of five different [#permalink]
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12 May 2011, 02:23
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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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Re: Mean and Median [#permalink]
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12 May 2011, 02:41
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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Re: Mean and Median [#permalink]
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12 May 2011, 02:55
@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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Re: Mean and Median [#permalink]
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12 May 2011, 08:52
using a and b the set is 1,3,4,5,7. Hence C.
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Re: Mean and Median [#permalink]
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12 May 2011, 19:57
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
Answer is C.



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Re: Mean and Median [#permalink]
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17 May 2011, 08:33
(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 Answer  C
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Re: What is the greatest integer in a set of five different [#permalink]
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11 Aug 2017, 07:24
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.



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Re: What is the greatest integer in a set of five different [#permalink]
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05 Dec 2017, 05:55
jamifahad 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. 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 1,3,4,5,7so you can solve for the largest integer




Re: What is the greatest integer in a set of five different
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