A house cost Ms. Jones C dollars in 1965. Three years later she sold the house for 25% more than she paid for it. She has to pay a tax of 50% of the gain. (The gain is the selling price minus the cost.) How much tax must Ms. Jones pay?
(A) C/24
(B) C/8
(C) C/4
(D) C/2
(E) 0.6C
The OA is the option B.
Is there a strategic approach for solving this PS question? Could anyone show it to me?
A house cost Ms. Jones C dollars in 1965. Three years
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A house cost Ms. Jones C dollars in 1965. Three years later she sold the house for 25% more than she paid for it.VJesus12 wrote:A house cost Ms. Jones C dollars in 1965. Three years later she sold the house for 25% more than she paid for it. She has to pay a tax of 50% of the gain. (The gain is the selling price minus the cost.) How much tax must Ms. Jones pay?
(A) C/24
(B) C/8
(C) C/4
(D) C/2
(E) 0.6C
So, 3 years later, the house sold for 1.25C dollars
She has to pay a tax of 50% of the gain. (The gain is the selling price minus the cost.) How much tax must Ms. Jones pay?
Gain = selling price - cost
= 1.25C - C
= 0.25C
Tax = 50% of the gain
= 50% of 0.25C
= (1/2)(0.25C)
= (1/2)(1/4)(C)
= (1/8)(C)
= C/8
Answer: B
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Hello Vjesus12.
This is how I'd do the PS question.
We know that the house cost Ms. Jones C dollars in 1965 and she sold it, 3 years later, for 25% more than she paid for it. Then she earned: 25%*C dollars (the gain)
Now, since she has to pay a tax of 50% of the gain, then she has to pay $$50\%\cdot25\%\cdot C=\frac{50}{100}\cdot\frac{25}{100}\cdot C=\frac{1}{2}\cdot\frac{1}{4}\cdot C=\frac{1}{8}C.$$ Therefore, the correct answer is the option B.
I hope it helps you. <i class="em em-smiley"></i>
This is how I'd do the PS question.
We know that the house cost Ms. Jones C dollars in 1965 and she sold it, 3 years later, for 25% more than she paid for it. Then she earned: 25%*C dollars (the gain)
Now, since she has to pay a tax of 50% of the gain, then she has to pay $$50\%\cdot25\%\cdot C=\frac{50}{100}\cdot\frac{25}{100}\cdot C=\frac{1}{2}\cdot\frac{1}{4}\cdot C=\frac{1}{8}C.$$ Therefore, the correct answer is the option B.
I hope it helps you. <i class="em em-smiley"></i>
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Since 25% = 1/4 and 50% = 1/2, let C = the LCM of the two denominators = 4*2 = 8.VJesus12 wrote:A house cost Ms. Jones C dollars in 1965. Three years later she sold the house for 25% more than she paid for it. She has to pay a tax of 50% of the gain. (The gain is the selling price minus the cost.) How much tax must Ms. Jones pay?
(A) C/24
(B) C/8
(C) C/4
(D) C/2
(E) 0.6C
Since Ms. Jones sells the house for 25% above cost, her profit is equal to 1/4 of the cost:
(1/4)(8) = 2.
Since she must pay a tax equal to 50% of her profit, the tax = (1/2)(2) = 1.
Now plug C=8 into the answers to see which yields a tax of $1.
Only B works:
C/8 = 8/8 = 1.
The correct answer is B.
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Original Cost: C
Sale Price: 1.25C
Gains before taxes: 1.25C - C = .25C
Taxes: .25C * .5 = (1/4) * C * (1/2) ------> C/8
Answer: B
Sale Price: 1.25C
Gains before taxes: 1.25C - C = .25C
Taxes: .25C * .5 = (1/4) * C * (1/2) ------> C/8
Answer: B
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Ms. Jones's profit on the house is 1.25C - C = 0.25C dollars and thus she must have paid:VJesus12 wrote:A house cost Ms. Jones C dollars in 1965. Three years later she sold the house for 25% more than she paid for it. She has to pay a tax of 50% of the gain. (The gain is the selling price minus the cost.) How much tax must Ms. Jones pay?
(A) C/24
(B) C/8
(C) C/4
(D) C/2
(E) 0.6C
0.25C x 0.5 = C/4 x 1/2 = C/8 dollars in taxes.
Answer: B
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