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

Question

If the value of a piece of property decreases by 10 percent while the new tax rate on the property represents 110% of the original tax rate, 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.

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Dereno · Answer

Let the value of the product = 100

We are given that the value decreases by 10% = NEW value = 90

More over, it’s given that the Old tax rate x = 110% of New tax rate y

y = 110% x

y : x = 11:10

Lets look into the taxes,

Old value = 100, tax rate x = 10% , then the old tax collected = 10

New value = 90, tax rate = 11%, then the new tax collected = 9.9

Percent change = (10-9.9)/10

= (0.1/10)*100

= 1%

Decrease by 1% from the original tax amount.

Option D

AbhishekP220108 · Answer

Step 1: Pick Some Easy Numbers
Let's just invent some simple values for the property and the tax rate 
 * Let's say the property is worth $1,000.
 * And let's pretend the original tax rate is 10%.
Based on these numbers, the original tax bill would be 10% of $1,000, which is $100.

Step 2: Apply the Changes
Now, let's adjust those numbers based on what the question says.
 * New Property Value: The value decreases by 10%. A 10% drop from $1,000 is $100. So, the new value is $900.
 * New Tax Rate: The rate represents 110% of the original. This means it increases by 10%. So, the new rate is 110% of our original 10%, which is 11%.

Step 3: Calculate the New Tax Bill
Now we just calculate the tax using our new numbers:
New Tax = 11% of $900
New Tax = 0.11 × 900 = $99

Step 4: Compare the Old and New
So, what's the final effect?
 * The original tax was $100.
 * The new tax is $99.
The tax bill went down by $1. Since our original tax was a convenient $100, a $1 drop is exactly a 1 percent decrease.
This shows the correct answer is (D) Taxes decrease by 1 percent.

CareerLauncherIE · Answer

Let's understand the question better,

Let the property value be V and the tax rate be T.

Original taxes = V×T.

The property value decreases by 10%, so new value = 0.9V

The new tax rate is 110% of the original, so new rate = 1.1T

New taxes = 0.9V×1.1T=0.99VT

Compare with original taxes: 0.99VT/VT=0.99 → taxes decreased by 1%.

Final Answer: Option(D)

Free GMAT Diagnostic test for reference :-  https://2ly.link/29mFF

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