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# If the set {3,10,5,7,x} has a median of 5, which of the following desc

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If the set {3,10,5,7,x} has a median of 5, which of the following desc  [#permalink]

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13 Apr 2018, 02:24
00:00

Difficulty:

15% (low)

Question Stats:

76% (00:42) correct 24% (00:34) wrong based on 58 sessions

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If the set {3,10,5,7,x} has a median of 5, which of the following describes all possible values for x?

A. x<5
B. x>5
C. x=5
D. x≤5
E. x≥5

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Re: If the set {3,10,5,7,x} has a median of 5, which of the following desc  [#permalink]

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13 Apr 2018, 03:42
If the set {3,10,5,7,x} has a median of 5,
X has to be less than or equal to 5.
as the number at 3rd place will be median.
If x is greater than 5, it will be placed in 3rd or higher place.

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Re: If the set {3,10,5,7,x} has a median of 5, which of the following desc  [#permalink]

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16 Apr 2018, 16:11
Bunuel wrote:
If the set {3,10,5,7,x} has a median of 5, which of the following describes all possible values for x?

A. x<5
B. x>5
C. x=5
D. x≤5
E. x≥5

A. x < 5

If x < 5, then in ascending order, the numbers would be:

x, 3, 5, 7, 10

or

3, x, 5, 7, 10

We see that in each case, we have median = 5.

At this point, we don’t have to check choices B, C and E since the correct answer must include the inequality x < 5. So we only have to check one more choice: D.

We see that x ≤ 5 includes x < 5 with one more case: x = 5. So we only have to check x = 5. (If x = 5 also works, then the answer would be D: x ≤ 5. If x = 5 doesn’t work, then the answer would be A: x < 5.)

If x = 5, then in ascending order, the numbers would be:

3, 5, 5, 7, 10

We see that we also have median = 5. Thus, for any values of x such that x ≤ 5, the median of the set will be 5.

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Re: If the set {3,10,5,7,x} has a median of 5, which of the following desc  [#permalink]

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28 Apr 2018, 18:06
Median is middle value when sequence is aRranged in ascending order

3,5,7,10
X need to be x<=5 for 5 to be median

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Re: If the set {3,10,5,7,x} has a median of 5, which of the following desc &nbs [#permalink] 28 Apr 2018, 18:06
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