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If the sum of the 7 positive integers is smaller than 12, what is the

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If the sum of the 7 positive integers is smaller than 12, what is the  [#permalink]

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New post 02 Apr 2017, 14:58
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If the sum of the 7 positive integers is smaller than 12, what is the range of the 7 integers?

1) The sum of the 7 integers is 11
2) The median of the 7 integers is 2

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Re: If the sum of the 7 positive integers is smaller than 12, what is the  [#permalink]

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New post 02 Apr 2017, 16:25
ziyuen wrote:
If the sum of the 7 positive integers is smaller than 12, what is the range of the 7 integers?

1) The sum of the 7 integers is 11
2) The median of the 7 integers is 2



1) if (1,1,1,1,1,1,5)
range =4

if (1,1,1,1,1,2,4)
range=3
not suff

2) only posible value = (1,1,1,2,2,2,2)
range =3
suff

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Re: If the sum of the 7 positive integers is smaller than 12, what is the  [#permalink]

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New post 21 Dec 2017, 11:22
Hi All,

We're told that the sum of 7 POSITIVE INTEGERS is LESS than 12. Since that sum has to be so small, there are a limited number of possibilities for the 7 integers. For example....

We could have....
Seven 1s - and the sum would be 7
Five 1s and two 2s - and the sum would be 9
Six 1s and one 4 - and the sum would be 10
Four 1s, two 2s and one 3 - and the sum would be 11
Etc.

We're asked for the RANGE of the 7 integers.

1) The sum of the 7 integers is 11

With a sum of 11, we could have....
Four 1s, two 2s and one 3 - and the RANGE = 2
Six 1s and one 5 - and the RANGE = 4
Fact 1 is INSUFFICIENT

2) The median of the 7 integers is 2

With a MEDIAN of 2, we must have three numbers less than/equal to 2 and three other numbers greater than/equal to 2...

_ _ _ 2 _ _ _

Since we're dealing with POSITIVE INTEGERS, there's only one way for this to occur...

1 1 1 2 2 2 2

Thus, the range MUST equal 1.
Fact 2 is SUFFICIENT

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Re: If the sum of the 7 positive integers is smaller than 12, what is the   [#permalink] 21 Dec 2017, 11:22
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