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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.

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.

@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.
_________________

My dad once said to me: Son, nothing succeeds like success.

Re: What is the greatest integer in a set of five different [#permalink]

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05 Dec 2017, 04:55

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 1,3,4,5,7 so you can solve for the largest integer