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IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
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If the average (arithmetic mean) of four different positive integers i  [#permalink]

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3 00:00

Difficulty:   75% (hard)

Question Stats: 43% (02:35) correct 57% (02:33) wrong based on 36 sessions

### HideShow timer Statistics If the average (arithmetic mean) of four different positive integers is greater than 3 and less than 4, what is the range of the four numbers?

(1) One number is greater than 7

(2) The median of the four numbers is 2.5

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Re: If the average (arithmetic mean) of four different positive integers i  [#permalink]

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If the average (arithmetic mean) of four different positive integers is greater than 3 and less than 4, what is the range of the four numbers?

(1) One number is greater than 7

(2) The median of the four numbers is 2.5

Let the numbers be a, b, c, d in increasing order respectively: a < b < c < d. Given 3 < (a+b+c+d+)/4 < 4
which means 12 < a+b+c+d < 16. So their sum lies between 12 and 16 exclusive. their sum could be 13 or 14 or 15.

(1) So one of the numbers is at least 8. This can be 'd' only, because if two numbers are at least 8, then sum will be more than 16 which is not possible.
If d=8, then 4 < a+b+c < 8. Then a, b, c could be: 1, 2, 3 or 1, 2, 4. Here range of four numbers = 8-1 = 7.
If d=9, then 3 < a+b+c < 7. Then a, b, c could be: 1, 2, 3 only. Here range of four numbers = 9-1 = 8.
Since range is taking more than one values, this statement is Not Sufficient.

(2) Median will be the average of middle two values, b and c. It means (b+c)/2 = 2.5 or b+c = 5. on the basis of this condition, we can have:
a, b, c, d as 1, 2, 3, 8 respectively in which case range = 8-1 = 7
or a, b, c, d as 1, 2, 3, 7 respectively in which case range = 7-1 = 6
Since range is taking more than one values, this statement is Not Sufficient.

Combining the two statements, we can have a case: 1, 2, 3, 8 or we could also have a case: 1, 2, 3, 9. In both these cases, the conditions given in the question stem as well as that in two statements are being satisfied, but the range is coming different. So Not sufficient. Re: If the average (arithmetic mean) of four different positive integers i   [#permalink] 19 Jul 2018, 22:35
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# If the average (arithmetic mean) of four different positive integers i  