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# A set of data contains the terms 1, 2, 3, 4, x. If the median of the s

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Math Expert
Joined: 02 Sep 2009
Posts: 52431
A set of data contains the terms 1, 2, 3, 4, x. If the median of the s  [#permalink]

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09 Apr 2018, 01:13
00:00

Difficulty:

25% (medium)

Question Stats:

75% (00:40) correct 25% (00:52) wrong based on 39 sessions

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A set of data contains the terms 1, 2, 3, 4, x. If the median of the set is 3, which of the following represents the complete solution set for x?

A. x > 2
B. x > 3
C. x > 4
D. x ≥ 3
E. x ≥ 4

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Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 678
Re: A set of data contains the terms 1, 2, 3, 4, x. If the median of the s  [#permalink]

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09 Apr 2018, 01:19
Bunuel wrote:
A set of data contains the terms 1, 2, 3, 4, x. If the median of the set is 3, which of the following represents the complete solution set for x?

A. x > 2
B. x > 3
C. x > 4
D. x ≥ 3
E. x ≥ 4

Since we know the middle number is the median of a set of odd # of elements (such as given set), x has to be to the right of 3

Now we are left with two options that resemble this thought. B. x > 3 and D. x ≥ 3

What will the median be if x = 3? {1, 2, 3, 3, 4} it is still 3 , so it works!

Hence x ≥ 3.

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“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

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Joined: 22 May 2016
Posts: 2375
A set of data contains the terms 1, 2, 3, 4, x. If the median of the s  [#permalink]

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09 Apr 2018, 05:21
Bunuel wrote:
A set of data contains the terms 1, 2, 3, 4, x. If the median of the set is 3, which of the following represents the complete solution set for x?

A. x > 2
B. x > 3
C. x > 4
D. x ≥ 3
E. x ≥ 4

In a list of odd terms the median is the center term. Half of the values will be to the left of the median, and half will be to the right.

Five terms? term, term, 3, term, term
Median, 3, is the third term

Placement of x:
1, 2, x, 3, 4
x can = 3

1, 2, 3, x, 4
1, 2, 3, 4, x
x can be 3, 4, OR > 4

x ≥ 3

List: If not sure, try possible values for $$x$$.It takes ~30 seconds to list them

Median must be 3

x < 1 (pick any integer)
-7, 1, 2, 3, 4? NO. 2 is the median

x = 1
1, 1, 2, 3, 4? NO. 2 is the median

x = 2
1, 2, 2, 3, 4? NO. 2 is the median

x = 3
1, 2, 3, 3, 4? Yes. 3 is the median

x > 3, = 4
1, 2, 3, 4, 4? Yes. 3 is the median

x > 3 (pick any integer)
1, 2, 3, 4, 8? Yes. 3 is the median

x can = 3; x can be > 3
x ≥ 3

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A set of data contains the terms 1, 2, 3, 4, x. If the median of the s &nbs [#permalink] 09 Apr 2018, 05:21
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