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13 Apr 2018, 03:24
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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
A. x<5
B. x>5
C. x=5
D. x≤5
E. x≥5
13 Apr 2018, 04:42
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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.
Answer D
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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.
Answer D
Posted from my mobile device
16 Apr 2018, 17:11
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Bunuel
Let’s analyze each answer choice.
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.
Answer: D
