A certain economics report defines a middle-income family as a family

To find the upper limit: (median income/2)*4 = 2 * median income = 74,304

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---73000

Let'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---- FALSE

For (ii) 73000>2*me
Do the same above calculations and we will arrive at the same result.

So, sufficient.

Answer: option D

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Let \(Me\) be the median family income. The original question:

Is \(\frac{Me}{2}\leq \$73{,}000\leq 2Me\) ?

1) We know that \(Me=\$37{,}152\). Clearly, we could get a definite to answer the original question. \(\implies\) Sufficient

2) We know that \(\frac{Me}{2}=\$18{,}576\). Clearly, we could get a definite to answer the original question. \(\implies\) Sufficient

Answer: D

A certain economics report defines a middle-class family as a family whose income is at least half, but no more than twice, the median family income. According to this report, is a family whose income is $73,000 considered a middle-class family?

(1) The median family income is $37,152
(2) The minimum income of a middle-class family is $18,576

The question is tricky because it is worded in a confusing way.

To be considered a middle class family: income needs to be at least half, but no more than double the median family income.

So if the median family income was $100, to be considered a middle-class family, your income needs to be between $50 and $200.

Statement 1 tells us the median family income directly. We don't need to calculate further -- this is sufficient to answer the question.

Statement 2 tells us the minimum income of a middle class family. We can deduce the range given the minimum (the minimum is half the median family income). Statement 2 is also sufficient.

Answer is D.

This question is a part of Are You Up For the Challenge: 700 Level Questions collection.

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