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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%.
(1) One of the brothers receives 40% of the total amount, and the other two receive 30% each.
(2) The tax rate is 20%.
02 May 2025, 07:30
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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
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
