When Leo imported a certain item, he paid a 7

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

Here's a step-by-step algebraic solution.

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

Hi VJesus12,

You can approach this question by TESTing THE ANSWERS. Instead of setting this up algebraically, you can use the 'spread' of the answer choices to your advantage.

Here, if the total value of the item were $2,000, then the tax would only apply to the amount over $1,000....
$1,000 x .07 = $70.
Since the tax is supposed to be $87.50, we know that the answer has to be GREATER than $2,000.

Let's TEST ANSWER D: $2,400.
$1,400 x .07 = $98
This is TOO MUCH, so Answer D is too big. There's only one answer that makes sense...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich