Given that Set X has Median = 60 and Number of observations = 5
Given that Set Y has Median = 70 and Number of observations = 5

And All observations in sets X and Y are between 55 and 75.

Quantity A: The median of the 10 observations if we mix sets X and Y

Now, Set X has 5 observations and median = 60
=> Middle term = 60
And two terms will be greater than 55 and less than or equal to 60
And two terms will be greater than or equal to 60 and less than 75

Set Y has 5 observations and median = 70
=> Middle term = 70
And two terms will be greater than 55 and less than or equal to 70
And two terms will be greater than or equal to 70 and less than 75

Minimum value of median of the set of 10 observations will be when the middle term is minimum
=> Set X can be taken as 56, 56, 60, 60, 60
Set Y can be taken as 56, 56, 70, 70, 70
=> Total set becomes 56, 56, 56, 56, 60, 60, 60, 70, 70, 70
Median = mean of middle two terms = \(\frac{60 + 60}{2}\) = 60

Maximum value of median of the set of 10 observations will be when the middle term is maximum
=> Set X can be taken as 60, 60, 60, 60, 74
Set Y can be taken as 70, 70, 70, 74, 74
=> Total set becomes 60, 60, 60, 60, 70, 70, 70, 74, 74, 74
Median = mean of middle two terms = \(\frac{70 + 70}{2}\) = 70

Clearly, Quantity A can be greater than equal to or even less than Quantity B(65)

So, Answer will be D
Hope it helps!

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