A total of $300,000 is inherited by three brothers. Each brother must

Question

A total of $300,000 is inherited by three brothers. Each brother must pay the same percentage of his share as tax. What is the average (arithmetic mean) amount each brother receives after paying tax?

(1) One of the brothers receives 40% of the total amount, and the other two receive 30% each.

(2) The tax rate is 20%.

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Bunuel · Accepted Answer

Official Solution:

A total of $300,000 is inherited by three brothers. Each brother must pay the same percentage of his share as tax. What is the average (arithmetic mean) amount each brother receives after paying tax? 
 
(1) One of the brothers receives 40% of the total amount, and the other two receive 30% each.
 
This gives the distribution of the $300,000. However, the tax rate is unknown, so we cannot determine the post-tax amount each brother receives. Not sufficient.
 
(2) The tax rate is 20%.
 
This implies that each brother pays 20% of his share in tax, which means that in total 20% is also paid on the full amount. Thus, regardless of how the $300,000 is divided, the total amount received after tax is 80% of $300,000 = $240,000, and the average amount each brother receives is $240,000/3 = $80,000. Sufficient.

Answer: B

SamplingCoast · Answer

In order to find the average amount received by each brother, all we need is the SUM received by all three.

To find this, the salient point is that we need to know how much is remaining after they paid the tax. Since each brother pays the same tax rate, the total amount of $300,000 will be taxed at the same tax rate paid by each.

So long as we find the tax rate we can find the average amount received by each brother.

(1) is insufficient since we cannot deduce the tax rate, and hence the remaining amount after paying the tax.

(2) Sufficient, since directly given. (1 - 0.2) * $300,000 is the remaining sum. Will be $240,000. Average is $240,000/3 = $80,000

Hence Answer is B

gmatophobia · Answer

Let's assume that

the pre-tax amount inherited by the three brothers is  x_1 ,  x_2  and  x_3  ⇒  x_1 + x_2 + x_3 = 300,000  
 the tax rate = r% 
 the amount inherited post tax =  \frac{100-r}{100}*x_1 ,  \frac{100-r}{100}*x_2  and  \frac{100-r}{100}*x_3

Average amount each brother received after paying tax =  \frac{\frac{100-r}{100}*x_1 + \frac{100-r}{100}*x_2 + \frac{100-r}{100}*x_3}{3}

=  \frac{(100-r)(x_1+x_2+x_3)}{300}

=  \frac{(100-r)(300,000)}{300}

=  (100-r)*1000

Hence, if any of the statements provide us the tax rate, the information will be sufficient to find the average amount each brother receives after paying tax.

Statement 1

(1) One of the brothers receives 40% of the total amount, and the other two receive 30% each.

The statement doesn't provide us the tax rate. Hence, the statement alone is not sufficient to answer the question.

Eliminate A, and D.

Statement 2

(2) The tax rate is 20%.

This statement provides us the tax rate. Hence, this statement is sufficient.

Option B

A total of $300,000 is inherited by three brothers. Each brother must

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