When Leo imported a certain item, he paid a 7 percent import

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

When Leo imported a certain item, he paid a 7 percent import

by BTGmoderatorLU » Sun Sep 16, 2018 7:56 am

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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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Source: Beat The GMAT — Problem Solving | Sun Sep 16, 2018 7:56 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 » Sun Sep 16, 2018 8:02 am

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.

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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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Sun Sep 16, 2018 10:34 am

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

\[{\text{?}}\,\,{\text{ = }}\,\,{\text{total}}\,\,{\text{value}}\,\, = \,\,\$ \,\,\left( {1000 + {\text{extra}}} \right)\]
\[{\text{87}}{\text{.5}}\,\,{\text{ = }}\,\,\frac{7}{{100}}\left( {{\text{extra}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{extra}}\,\,{\text{ = }}\,\,\frac{{{\text{100}}}}{7} \cdot \frac{1}{{10}}\left( {700 + 140 + 35} \right)\,\,\, = \,\,\,10 \cdot 125\]
\[? = \,1000 + 1250\,\,\,\left[ \$ \right]\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Apr 18, 2019 5:42 pm

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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