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# If 6 positive integers have a sum less than 8, what is the value of th

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Math Expert
Joined: 02 Sep 2009
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If 6 positive integers have a sum less than 8, what is the value of th  [#permalink]

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22 Jan 2018, 01:35
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55% (hard)

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62% (01:39) correct 38% (02:09) wrong based on 46 sessions

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If 6 positive integers have a sum less than 8, what is the value of the greatest of the integers?

(1) The average (arithmetic mean) of the 6 integers is 7/6.
(2) The median of the integers is 1.

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Re: If 6 positive integers have a sum less than 8, what is the value of th  [#permalink]

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22 Jan 2018, 05:39
Statement 1 says average is 7/6 so sum of 6 positive integers is 7. So there should be five 1s and a 2. So sufficient. Statement 2 says median is 1. So first 3 nbr is 1 and sinse sum is less than 8. It should have five 1s and a 2 so sufficient. Answer is D.

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Re: If 6 positive integers have a sum less than 8, what is the value of th  [#permalink]

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22 Jan 2018, 05:41
In another thought statement 2 can have 6 as well 7 as sum so not sufficient. So changing my answer to A

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Re: If 6 positive integers have a sum less than 8, what is the value of th  [#permalink]

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22 Jan 2018, 10:36
A.
Let the numbers be a1,a2,a3,a4,a5,a6
Sum of numbers = 7/6*6
=7 sufficient
The only way for 6 positive numbers to sum them 7 is if 5 of these are 1 and one number is 2.
Stmt 2 gives two options sum to be 6 or 7. Hence not sufficient.
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Re: If 6 positive integers have a sum less than 8, what is the value of th  [#permalink]

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22 Jan 2018, 10:54
St:1 Mean =Sum/n
It is given therefore sum should be 7 .The greatest integer in that case will be 2.First five all 1 and last one 2.

St :2 Insufficent as we can have sum 6 and 7 both.

Therefore A

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Re: If 6 positive integers have a sum less than 8, what is the value of th  [#permalink]

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22 Jan 2018, 10:55
Let S = sum of 6 positive integers. => S >= 6. From the question, we know that S <= 7
From ST1, S = 7 => only 1 number must be equal to 2 => the greatest number is 2
From st2, we are not sure whether the greatest number is 1 or 2.
Re: If 6 positive integers have a sum less than 8, what is the value of th   [#permalink] 22 Jan 2018, 10:55
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