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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

by VJesus12 » Wed Jun 20, 2018 2:47 am

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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. 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?
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by Brent@GMATPrepNow » Wed Jun 20, 2018 5:09 am
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
A house cost Ms. Jones C dollars in 1965. Three years later she sold the house for 25% more than she paid for it.
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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by Vincen » Wed Jun 20, 2018 6:28 am
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>
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by GMATGuruNY » Wed Jun 20, 2018 7:05 am
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 25% = 1/4 and 50% = 1/2, let C = the LCM of the two denominators = 4*2 = 8.
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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Question

by arosman » Wed Jun 20, 2018 9:40 am
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
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by Jeff@TargetTestPrep » Thu Jun 21, 2018 4:09 pm
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
Ms. Jones's profit on the house is 1.25C - C = 0.25C dollars and thus she must have paid:

0.25C x 0.5 = C/4 x 1/2 = C/8 dollars in taxes.

Answer: B

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