A house cost Ms. Jones C dollars in 1965. Three years

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

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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Source: Beat The GMAT — Problem Solving | Wed Jun 20, 2018 2:47 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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arosman: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Jun 20, 2018 9:11 am; Location: Chicago, IL; GMAT Score:770

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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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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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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Head of GMAT Instruction
[email protected]

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