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If the median of the 5 integers is 10, is the range of the integers gr

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If the median of the 5 integers is 10, is the range of the integers gr  [#permalink]

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New post 27 Mar 2017, 18:03
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If the median of the 5 integers is 10, is the range of the integers greater than 4?

1) The average (arithmetic mean) of the 5 integers is 12.
2) The smallest of the 5 integers is 10.

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If the median of the 5 integers is 10, is the range of the integers gr  [#permalink]

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New post 27 Mar 2017, 19:10
ziyuen wrote:
If the median of the 5 integers is 10, is the range of the integers greater than 4?

1) The average (arithmetic mean) of the 5 integers is 12.
2) The smallest of the 5 integers is 10.



1) set with minimum values(range) be= 10,10,10,15,15
thus range = 15-10=5>4
suff

2) set could be anything 10,10,10,10,11...NO
or 10,11,12,13,14,15...YES
insuff

Ans A
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If the median of the 5 integers is 10, is the range of the integers gr  [#permalink]

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New post 27 Mar 2017, 20:54
ziyuen wrote:
If the median of the 5 integers is 10, is the range of the integers greater than 4?

1) The average (arithmetic mean) of the 5 integers is 12.
2) The smallest of the 5 integers is 10.


Statement 1: their sum is 60.

Since median i.e. 3rd number is 10, the set is {X, X, 10, X, X}

First two values can be less than or equal to 10. If they are less than 10, to get average as 12 or sum as 60, values after 10 will be considerably greater than 10.
We can get optimum values of numbers after 10, when numbers before 10 are equal to 10.

The set becomes - {10, 10, 10, X, X}
Even in this set, two values after 10 should add up to 30, to get average as 12 or sum as 60. So the optimum values they can have is 15,15 to get minimum possible range.
And in this scenario we get range of the set as 5 ........... Sufficient.

Statement 2: Smallest integer is 10.

Means the set is {10, 10, 10, X, X}. We are not given any information about the later two values of this set.
They can be {10, 10} range -0 or
They can be{15,15} range 5 ...................... Insufficient.

IMO A.
If the median of the 5 integers is 10, is the range of the integers gr &nbs [#permalink] 27 Mar 2017, 20:54
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