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OG PS 11

This topic has 5 expert replies and 1 member reply
paml Junior | Next Rank: 30 Posts Default Avatar
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OG PS 11

Post Sat Feb 07, 2015 12:43 pm
OG 13th ed/2015
p. 153
Problem Solving Practice Question #11.

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

I don't quite understand this part of the question and how to set it up properly: "7% import tax on the portion of the total value of the item in excess of $1000". I'm not clear on what the italicized portion means.

Is it saying he paid a 7% import tax on the $1000 portion of the item? The answer explanation sets it up as .07(t - 1000)

The way I set it up was .07x = 87.5
x=1250
Then I just added 1000 and got the answer C: 2250
Is this a wrong/bad way of setting it up?

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paml Junior | Next Rank: 30 Posts Default Avatar
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Post Sat Feb 07, 2015 2:26 pm
Thank you Brent & Mitch!

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Post Sun Feb 08, 2015 10:18 pm
Another approach here!

Suppose the item cost Leo $x. We know that the first $1000 is tax free, so Leo only pays 7% tax on the rest of the price, or $(x - 1000). We know that tax amounted to $87.50, so we have

87.50 = 7% of (x - 1000), or
87.5 = .07(x - 1000), or
87.5 = .07x - 70, or
157.5 = .07x, or
15750 = 7x, or
2250 = x

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paml Junior | Next Rank: 30 Posts Default Avatar
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Post Sat Feb 07, 2015 2:26 pm
Thank you Brent & Mitch!

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Matt@VeritasPrep GMAT Instructor
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Post Sun Feb 08, 2015 10:18 pm
Another approach here!

Suppose the item cost Leo $x. We know that the first $1000 is tax free, so Leo only pays 7% tax on the rest of the price, or $(x - 1000). We know that tax amounted to $87.50, so we have

87.50 = 7% of (x - 1000), or
87.5 = .07(x - 1000), or
87.5 = .07x - 70, or
157.5 = .07x, or
15750 = 7x, or
2250 = x

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Post Sat Feb 07, 2015 1:14 pm
paml wrote:
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

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Post Sat Feb 07, 2015 1:02 pm
paml wrote:
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

I don't quite understand this part of the question and how to set it up properly: "7% import tax on the portion of the total value of the item in excess of $1000". I'm not clear on what the italicized portion means.

Is it saying he paid a 7% import tax on the $1000 portion of the item? The answer explanation sets it up as .07(t - 1000)

The way I set it up was .07x = 87.5
x=1250
Then I just added 1000 and got the answer C: 2250
Is this a wrong/bad way of setting it up
?
Your solution is fine. It's pretty much the same as the official solution, except you're not showing all of the steps (i.e., you're making a few moves in your head)

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
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