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# If the value of a piece of property decreases by 10 percent

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Intern
Joined: 24 Jul 2007
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If the value of a piece of property decreases by 10 percent [#permalink]

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08 Aug 2007, 07:22
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Difficulty:

25% (medium)

Question Stats:

68% (01:05) correct 32% (01:18) wrong based on 100 sessions

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If the value of a piece of property decreases by 10 percent while the tax rate on the property increases by 10 percent, what is the effect on the taxes?

A. Taxes increase by 10 percent
B. Taxes increase by 1 percent
C. There is no change in taxes
D. Taxes decrease by 1 percent
E. Taxes decrease by 10 percent
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Jan 2013, 03:55, edited 1 time in total.
Renamed the topic, edited the question and added OA.

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Director
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08 Aug 2007, 07:42
it's hard to explain, but the 10% increase isn't referring to an additional 10% of tax on the houses but an increase of 10% of the 10%.

.1 x 1.1 = .11
10% x 1.1 = 11%

then I just plugged in numbers

100,000 x .1 = 10,000
90,000 x .11 = 9,900

decrease of 1%

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08 Aug 2007, 08:25
I was thinking additional 10% on the house, it's clear now. Thanks!

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10 Jan 2013, 22:05
eschn3am wrote:
it's hard to explain, but the 10% increase isn't referring to an additional 10% of tax on the houses but an increase of 10% of the 10%.

.1 x 1.1 = .11
10% x 1.1 = 11%

then I just plugged in numbers

100,000 x .1 = 10,000
90,000 x .11 = 9,900

decrease of 1%

Still don't understand the wording too well; can someone elaborate on this?
Thanks!

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Concentration: Strategy, Finance
Re: If the value of a piece of property decreases by 10 percent [#permalink]

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10 Jan 2013, 22:26
Consider value of the property = 100
Tax rate on the property = 40%
Thus, original tax amount = 40% of 100 = 40

Property value after 10% decrease = 90
Tax rate value after 10% Increase = 44%

New total tax amount = 44% of 90 = 39.6 (reduced below the original tax amount 40)

Net decrease in tax amount = 0.4 (i.e. 1% decrease)

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12 May 2013, 09:18
essarr wrote:
eschn3am wrote:
it's hard to explain, but the 10% increase isn't referring to an additional 10% of tax on the houses but an increase of 10% of the 10%.

.1 x 1.1 = .11
10% x 1.1 = 11%

then I just plugged in numbers

100,000 x .1 = 10,000
90,000 x .11 = 9,900

decrease of 1%

Still don't understand the wording too well; can someone elaborate on this?
Thanks!

Lets say value of the property is \$V and tax on that \$V is T% . Hence the tax amount on the \$V is = \$VT
now value is decreased by 10 % ( 0.9V) and tax increased by 10% ( 1.1 T) , the new tax amount is 0.9V*1.1T = 0.99VT

Hence new tax amount decreases by 0.01VT ( i.e 1% the original)
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Re: If the value of a piece of property decreases by 10 percent [#permalink]

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12 May 2013, 22:13
johngrg wrote:
If the value of a piece of property decreases by 10 percent while the tax rate on the property increases by 10 percent, what is the effect on the taxes?

A. Taxes increase by 10 percent
B. Taxes increase by 1 percent
C. There is no change in taxes
D. Taxes decrease by 1 percent
E. Taxes decrease by 10 percent

Initial value =100 ,tax rate = 100%. Thus, the tax to be paid = 100. After the required change,
the new value = 90 and the new tax rate = 110%. The new tax amount to be paid = 99. Change in tax paid = 1% decrease.
D.
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Re: If the value of a piece of property decreases by 10 percent   [#permalink] 12 May 2013, 22:13
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