So, criteria for being a middle class family:
\(\frac{Median}{2 }< MC < 2*Median\).............[1]
Is $73,000 considered a middle-class family income?
(1) The median family income is $37,152
So, we can use [1] inequality to know if 73,000 falls in the range. SUFFICIENT.
(2) The minimum income of a middle-class family is $18,576 Tricky one.
At a first glance, one may think this is not enough, but let's look.
Let's put the points on the number line.
me - median income; mc - middle class income
----me/2 ---min mc-------2*me ------
----me/2 ---18,576 -----2*me----
Now, where will 73000 lie? Two possibilities:
(i)----me/2 ---18,576 ---
73000---2*me----
(ii)---me/2 ---18,576 -----2*me---
73000Let's take extreme cases [we are getting there, hold on
]
For (i), 18,576 <73000< 2*me
Let's say 2me ~73000
=> me = 37500
me/2 = 18,750 > 18,576 ---So, the condition becomes false.
---18,576 ---
me/2----
73000---2*me----
FALSEFor (ii) 73000>2*me
Do the same above calculations and we will arrive at the same result.
So, sufficient.
Answer: option D
Let me know if you have further questions.
Please give kudos if it helped -> motivates