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# Consider seven integers whose median is 120 and range is 40. The media

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SVP
Joined: 23 Feb 2015
Posts: 1892
Consider seven integers whose median is 120 and range is 40. The media  [#permalink]

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08 Aug 2019, 08:53
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Difficulty:

35% (medium)

Question Stats:

76% (02:06) correct 24% (02:09) wrong based on 25 sessions

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Consider seven integers whose median is $$120$$ and range is $$40$$. The median for the three smallest integers is $$90$$. What is the possible range for the three largest integers?
I. $$35$$
II. $$12$$
III. $$0$$
A) I only
B)II only
C)I and III only
D)II and III only
E)III only
Senior Manager
Joined: 28 Jun 2019
Posts: 469
Re: Consider seven integers whose median is 120 and range is 40. The media  [#permalink]

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08 Aug 2019, 11:58
Imagine this series X,90,...,120,...,...,Y
Y-X=40
The largest possible amount for X is 89. So Y would be 129.
If the smallest number of three numbers is 120, the range would be 129-120=9
Just 0 can be the answer.
Option E

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Re: Consider seven integers whose median is 120 and range is 40. The media  [#permalink]

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08 Aug 2019, 19:29
Let the numbers be
a,90,c,120,e,f,g in ascending order

g - a = 40
if a = 90, g = 130. Now range of largest three can be 130 - 120 = 10, when e =120
Range of largest three cannot be greater than 10.

E is correct.
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Re: Consider seven integers whose median is 120 and range is 40. The media   [#permalink] 08 Aug 2019, 19:29