When Leo imported a certain item, he paid a 7

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

When Leo imported a certain item, he paid a 7

by VJesus12 » Sat Oct 14, 2017 6:53 am

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 Official Answer is C.

I got confused because of the 7 percent. I'd appreciate some help here please.

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Source: Beat The GMAT — Problem Solving | Sat Oct 14, 2017 6:53 am

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

by Brent@GMATPrepNow » Sat Oct 14, 2017 7:01 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

Answer

by EconomistGMATTutor » Sat Oct 14, 2017 7:44 am

Hi Vjesus12.

You have to be careful here. The statement says that Leo paid a 7% import tax on the portion of the total value of the item in excess of $1000.

Let's suppose that X is the total value of the item. According to the statement above,$$X>1000$$ and we have to calculate 7% of the excess, i.e., 7%*(X-1000).

Now, the amount that Leo paid was $87.50. So, we can set the equation $$7\%\cdot\left(X-1000\right)=87.50,$$ which is equivalent to $$X-1000=1250.$$ Now, we can conclude that $$X=2250.$$

So, the answer is option C.

I hope this answer can help you.

Feel free to follow me.

GMAT Prep From The Economist
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by [email protected] » Sat Oct 14, 2017 10:58 am

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

Contact Rich at [email protected]

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

by Jeff@TargetTestPrep » Fri Jan 05, 2018 7:38 am

VJesus12 wrote: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

We know that when Leo imports a certain item, he pays 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 does not pay any tax on his items until he hits $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

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]