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Tracey sold her house for 40 percent more than the amount that she bou

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Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 29 Dec 2014, 09:01
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Tough and Tricky questions: Percents.



Tracey sold her house for 40 percent more than the amount that she bought it for. If she has to pay a brokerage fee of 5 percent of the selling price of the home, and then has to pay 40 percent of the leftover profit in taxes, what is the net after-tax percent profit Tracey makes on the sale?

A. 12%
B. 14.4%
C. 16%
D. 19.8%
E. 21%

Kudos for a correct solution.

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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 29 Dec 2014, 10:09
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Lets assume Cost price is 100. Then the selling price will be 1.4*100= 140.
5% brokerage fee= 5% of 140 = 7
After brokerage amount left is 140-7=133.
Next, taxes are 40% of left over profit which is 40% of (133-100)=40% of 33 which is 19.8.
Hence answer is D.

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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 29 Dec 2014, 10:14
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The tricky part in this question is to see which numbers the percentage are referring to. Since we are asked about the percent profit, we don't need to use any absolute values in our calculation.

We start with the 40% That Tracey makes on the sales of the house. The 40% profit refers to the original house price, but the agent fee refers to the final sales price. As the sales price is 40% higher than the original purchase price, we need to convert the 5% fee into percent of the original price. For that, we can pick numbers. We assume that the original price was 100. The sales price them was 140, as it is 40% higher. The 5% agent fee of a final sales price of 140 is 7. After paying the agent, Tracey is therefore left with 133, or 33% of the original price.

Of that 33%, she then needs to pay 40% tax. We can directly calculate what is left for Tracey after the tax, 60% of her 33% pre-tax profit.

\(\frac{33}{100}*\frac{6}{10}=\frac{198}{1000}=19.8%\)

Answer D.
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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 30 Dec 2014, 11:03
Bunuel wrote:

Tough and Tricky questions: Percents.



Tracey sold her house for 40 percent more than the amount that she bought it for. If she has to pay a brokerage fee of 5 percent of the selling price of the home, and then has to pay 40 percent of the leftover profit in taxes, what is the net after-tax percent profit Tracey makes on the sale?

A. 12%
B. 14.4%
C. 16%
D. 19.8%
E. 21%

Kudos for a correct solution.


Sale price =140% of the original price
Brokerage = 5% of the sale price = 140*.05 = 7% of sale price

Remaining amount in hand = 133% of original price

Profit before tax = 33%

tax = Profit before tax * 40/100
= 33*.4 = 13.2%

Profit after tax = 33-13.2 = 19.8%

Ans D
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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 30 Dec 2014, 20:00
Answer = D. 19.8%

Initial cost = 100

Selling price = 140

Brokerage \(= \frac{140*5}{100} = 7\)

Selling price less brokerage = 140-7 = 133

40% tax on profit \(= \frac{33*40}{100} = 13.2\)

Net profit = 33 - 13.2 = 19.8
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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 08 Jan 2015, 08:12
Bunuel wrote:

Tough and Tricky questions: Percents.



Tracey sold her house for 40 percent more than the amount that she bought it for. If she has to pay a brokerage fee of 5 percent of the selling price of the home, and then has to pay 40 percent of the leftover profit in taxes, what is the net after-tax percent profit Tracey makes on the sale?

A. 12%
B. 14.4%
C. 16%
D. 19.8%
E. 21%

Kudos for a correct solution.


OFFICIAL SOLUTION:

(D) If Tracey sells her house for 40% more than what she bought it for, and then pays 5% of the selling price in brokerage fees, she will have paid 5% of 140% of what they bought the house for.

So her brokerage fees are 0.05 × 1.4 = .07, or 7% of what she paid for the house. She will have a before tax profit of 33%.

Tracey now has to pay 40% of the 33% profit in taxes, which means she gets to keep 60% of the 33%:0.6(.33) = 0.198.

Tracey made a profit of 19.8% on the house.

The correct answer is choice (D).
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 26 Mar 2016, 08:47
Bunuel wrote:

Tough and Tricky questions: Percents.



Tracey sold her house for 40 percent more than the amount that she bought it for. If she has to pay a brokerage fee of 5 percent of the selling price of the home, and then has to pay 40 percent of the leftover profit in taxes, what is the net after-tax percent profit Tracey makes on the sale?

A. 12%
B. 14.4%
C. 16%
D. 19.8%
E. 21%

Kudos for a correct solution.


Assume that the house was bought for $ 100. Further calculations will lead you to answer D.
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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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New post 22 Jun 2016, 23:53
buying price=100
profit=40
selling price=140
profit after paying brokerage fee=40-5%of 140=33
profit after paying tax=33*3/5=19.8 (60%=3/5)

ans:D
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Re: Tracey sold her house for 40 percent more than the amount that she bou  [#permalink]

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