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OG PS 11

by paml » Sat Feb 07, 2015 12:43 pm

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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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by GMATGuruNY » Sat Feb 07, 2015 12:53 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
We can PLUG IN THE ANSWERS, which represent the total value of the item.
When the correct answer choice is plugged in, the tax will be $87.50.

Answer choice D: 2400
Portion in excess of 1000 = 2400-1000 = 1400.
7% tax on this portion = (7/100)(1400) = 98.
Since the tax is too great, the correct answer choice must be smaller.
Eliminate D and E.

Answer choice B: 1850
Portion in excess of 1000 = 1850-1000 = 850.
7% tax on this portion = (7/100)(850) ≈ 60.
Since the tax is too small, the correct answer choice must be greater.
Eliminate A and B.

The correct answer is C.
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by Brent@GMATPrepNow » Sat Feb 07, 2015 12:59 pm
paml wrote:
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.
In other words, the first $1000 is "free" (there's no tax).
So, for example, if the TOTAL value is $800, then there's no tax charged.
Likewise, if the TOTAL value is $1000, then there's no tax charged.

However, if the TOTAL value were $1100, then Leo would pay 7% on $100 (since $1100 EXCEEDS $1000 by $100)
If the TOTAL value were $1600, then Leo would pay 7% on $600 (since $1600 EXCEEDS $1000 by $600)

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by Brent@GMATPrepNow » 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)

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by Brent@GMATPrepNow » 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

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by paml » Sat Feb 07, 2015 2:26 pm
Thank you Brent & Mitch!
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by Matt@VeritasPrep » 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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by [email protected] » Thu Feb 22, 2018 11:50 am
Hi All,

We're told that 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 and the amount of the import tax that Leo paid was $87.50. We're asked for the total value of the item. This question has a great 'round number shortcut' that you can take advantage of to avoid any heavy calculations.

With a 7% import tax, every $1000 increase in price ABOVE the initial value of the item will lead to a $70 increase in tax (since 7% of $1,000 = $70. Thus....

A $1,000 item = $0 in tax
A $2,000 item = $70 in tax
A $3,000 item = $140 in tax
Etc.

The total tax on the item is $87.50 - which is just a bit higher than $70, so the total price of the item will be a bit higher than $2,000. There's really only one answer that 'fits' here, but if you narrowed it down to Answers C and D and felt that you need to do a bit more work, then you can go in $500 increments (since 7% of $500 = HALF of $70 ---> $35)....

A $1,500 item = $35 in tax
A $2,000 item = $70 in tax
A $2,500 item = $105 in tax

$87.50 is closer to $70 than it is to $105, so the total price of the item would have to be closer the $2,000 than $2,500.

Final Answer: C

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by Scott@TargetTestPrep » Thu Mar 15, 2018 9:27 am
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

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

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