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

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

OA C

Source: Official Guide

GMAT/MBA Expert

User avatar
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 » Tue Nov 13, 2018 5:17 am
BTGmoderatorDC 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
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
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Tue Nov 13, 2018 10:20 am
Hi All,

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.
Eliminate Answers A and B.

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]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Sun Jan 27, 2019 6:37 pm
BTGmoderatorDC 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

OA C

Source: Official Guide
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage