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

Question

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

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

Archit3110 · Answer

#1
(1) The median family income is $37,152
so min salary is $18,576 and <twice median
sufficient 
#2The minimum income of a middle-class family is $18,576
same as #1
sufficient
Option D

Akp880 · Answer

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

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

Explanation:

Median family income/2<= middle class family income<=2*Median family income

S1: given median family income=37152

So 37152/2<=middle class family income<=74304

Given family income= 73000
Thus this family can be called middle class family.

S1 sufficient.

S2: given min middle class family income= 18576
So max permissible middle class family income= 18576*4(i.e (median income/2)*4)
=74304

This family also is middle income family

Hence S2 also sufficient

Thus D is the correct answer.

Regards,
Atul pandey

Posted from my mobile device

scruzsalas · Answer

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

Target4bschool · Answer

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

Let me know if you have further questions.
Please give kudos if it helped -> motivates

ZoltanBP · Answer

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

Basshead · Answer

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

(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.

Bunuel · Answer

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

pierjoejoe · Answer

i don't really understand how can i get to the conclusion that "minimum" in the second statement refers to the half the median (as the lower bound in the relationship established in the text of the problem for the definition of medium class). and not just the minimum income inside a family.

in the second case ("minimum" referring to the minimum income inside the family) how can i solve the problem.

Bunuel

in the second case ("minimum" referring to the minimum income inside the family) how can i solve the problem.

Bunuel

gchandana · Answer

So middle-class family incomes are all incomes between half of the median and twice the median, inclusive.
When the statment said minimum is 18,576, it is referring to the half of median, because that is lowest possible income of middle class families.

Or, for example, if the statement said the maximum is 146,000, then it would be referring to twice the median, as it is the maximum possible income.

Hope it helps.

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

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

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