Source: Official Guide
When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
A. $1,600
B. $1,850
C. $2,250
D. $2,400
E. $2,750
The OA is C.
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When Leo imported a certain item, he paid a 7 percent import
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BTGmoderatorLU
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Brent@GMATPrepNow
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BTGmoderatorLU wrote:Source: Official Guide
When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
A. $1,600
B. $1,850
C. $2,250
D. $2,400
E. $2,750
The OA is C.
Here's a step-by-step algebraic solution.When Leo imported a certain item, he paid a 7% import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was $87.50 what was the total value of the item?
A $1600
B $1850
C $2250
D $2400
E $2750
Let T = the TOTAL value of the item.
Leo paid a 7% import tax on the portion of the total value of the item in EXCESS of $1000
So, Leo pays tax on the amount that's GREATER then $1000
So, Leo pays 7% tax on (T - 1000)
We can write: import tax = 7% of (T - 1000)
The amount of the import tax that Leo paid was $87.50
So, we write: $87.50 = 7% of (T - 1000)
Or: $87.50 = 0.07(T - 1000)
Expand to get: 87.50 = 0.07T - 70
Add 70 to both sides to get: 157.5 = 0.07T
NOTE: At this point, you might just plug in the answer choices to see which one makes the above equation true.
Or....
Divide both sides by 0.07 to get: 157.5/0.07 = T
Solve: 2250 = T
Answer: C
Cheers,
Brent
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fskilnik@GMATH
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\[{\text{?}}\,\,{\text{ = }}\,\,{\text{total}}\,\,{\text{value}}\,\, = \,\,\$ \,\,\left( {1000 + {\text{extra}}} \right)\]BTGmoderatorLU wrote:Source: Official Guide
When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
A. $1,600
B. $1,850
C. $2,250
D. $2,400
E. $2,750
\[{\text{87}}{\text{.5}}\,\,{\text{ = }}\,\,\frac{7}{{100}}\left( {{\text{extra}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{extra}}\,\,{\text{ = }}\,\,\frac{{{\text{100}}}}{7} \cdot \frac{1}{{10}}\left( {700 + 140 + 35} \right)\,\,\, = \,\,\,10 \cdot 125\]
\[? = \,1000 + 1250\,\,\,\left[ \$ \right]\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Scott@TargetTestPrep
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BTGmoderatorLU wrote:Source: Official Guide
When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
A. $1,600
B. $1,850
C. $2,250
D. $2,400
E. $2,750
The OA is C.
We know that when Leo imported the item, he paid a 7% import tax on the portion of the total value in excess of $1,000. "In excess of" is the key phrase here, and it means that Leo did not pay any tax on his items until he hit $1,000. The best way to complete this problem is to set up an equation.
First, let's say that T = total value of the item; therefore, (T - 1000) is the portion that is taxable.
Next, we can create an equation to determine T:
87.5 = 0.07(T - 1,000)
87.5 = 0.07T - 70
157.5 = 0.07T
157.5/0.07 = T
15,750/7 = T
T = 2,250
Alternate Solution:
Let's let x = the portion of the item's value on which he paid 7% tax. Thus, we have:
0.7x = 87.5
x = 1250
The taxable portion of the item was $1250, and the non-taxable portion was $1000. Therefore, the total value of the item is 1250 + 1000 = $2250.
Answer: C
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