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ABC Office Supply offers a discount on orders over $500. It applies th

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Sajjad1994
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ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   06 Oct 2023, 22:31
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40% (03:18) correct 60% (03:34) wrong based on 191 sessions
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Data Insights (DI) Butler 2023-24 [Question #20, Date: Oct-06-2023] [Click here for Details]


ABC Office Supply offers a discount on orders over $500. It applies the discount before calculating sales tax. Its most recent orders were for $1,086 and $693 in goods. After ABC applied the discount and added sales tax, the invoices for the two orders showed final charges of $1,106.50 and $706.08, respectively. Determine the discount rate (as a percentage of the order) and the tax rate (as a percentage of the discounted order).
Discount rate Tax rate
3%
5%
6.5%
7.25%
8%
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Official Answer
Discount rate: 5% Tax rate: 7.25%
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   10 Oct 2023, 19:13
we have
(1086-(1-(discount/100)) * ( 1+ tax/100) = 1106.50
and
(693-(1- discount/100)) * ( 1+ tax/100) = 706.80
plugin values
discount is 5% & tax is 7.25%
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   15 Oct 2023, 00:56
Archit3110 wrote:
we have
(1086-(1-(discount/100)) * ( 1+ tax/100) = 1106.50
and
(693-(1- discount/100)) * ( 1+ tax/100) = 706.80
plugin values
discount is 5% & tax is 7.25%


Archit3110
Could you please tell the time you allocated for this question?
& Do you have any shortcut to figure out the values that we need to plugin instead of finding it for each value?
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   18 Oct 2023, 02:40
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MHBS wrote:
Archit3110 wrote:
we have
(1086-(1-(discount/100)) * ( 1+ tax/100) = 1106.50
and
(693-(1- discount/100)) * ( 1+ tax/100) = 706.80
plugin values
discount is 5% & tax is 7.25%


Archit3110
Could you please tell the time you allocated for this question?
& Do you have any shortcut to figure out the values that we need to plugin instead of finding it for each value?



From question stem, you can conclude that there is net increase of 1% in price of product (1106/1086=1%). Now, instead of solving derived equation, imagine product of $100. Now plug in different values to identify what discount and tax value can increase product price to $101.

I took 3 minutes though to solve this, but can be reduced with practice.
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   24 Oct 2023, 22:19
a discount of 3% and tax rate of 5% also gives the same result. Could you please check it and let us know
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ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   25 Oct 2023, 10:13
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Official Explanation

Both invoices are about 1.9% higher than the price of the goods:

\(\frac{($1106.50-$1086)}{$1086}= \frac{($706.08-$693)}{$693} = 0.01887.\)

This suggests that the tax rate is higher than the discount rate and that the difference between the rates will be in the neighborhood of 2%. This estimate makes a systematic trial and error possible. Trying a 3% discount and 5% tax comes close but is a bit low. A discount of 5% and a tax rate of 7.25% fits the bill.
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ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   30 Dec 2023, 12:31
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MHBS wrote:
Archit3110 wrote:
we have
(1086-(1-(discount/100)) * ( 1+ tax/100) = 1106.50
and
(693-(1- discount/100)) * ( 1+ tax/100) = 706.80
plugin values
discount is 5% & tax is 7.25%


Archit3110
Could you please tell the time you allocated for this question?
& Do you have any shortcut to figure out the values that we need to plugin instead of finding it for each value?

MHBS
1106.5 /1086 = 1.01887; This is the net rate

Now with the options you can easily calculate -
for 3% discount and 5% tax rate
0.97*1.05 = 1.0185, quite close but let's see other options

for 5% discuount and 7.25% tax
0.95*1.0725 = 1.018875, which is the answer

It'll take approx 2 minutes with this approach
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   20 May 2024, 00:06
­1086 * (1 + discount) * (1 + tax) = 1106.5 
693 * discount * tax = 706.08

==> (1 + discount) * (1 + tax) = 1.0189

Try 0.97 * 1.05 = 1.0185 => need a bit higher

Try
0.97 * 1.065 = 1.03305 => too high
=> Raise discount rate to 5%
=> 0.95 * 1.065 = 1.01175 => too low
=> 0.95 * 1.0725 = 1.0189 

Discount rate = 5%
Tax rate = 7.25%


 
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] ABC Office Supply offers a discount on orders over $500. It applies th   30 May 2024, 01:39
This method can be helpful - We see that the overall change in both cases is close to 2%.
Now 2 operations are being performed to the initial principal amount - i) reduction by let's say d%, and then ii) increase by say s%

when 2 operations of this nature are performed the overall change will be = [(-d+s)-ds/100]
now we can plug in values to see which pair gives a net change closest to +2%. Upon putting d =5 and s=7.25 we have
=(-5+7.25)-5*7.25/100
= 2.25-29/80 which gives a result closest to 2, hence the answer.­
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink]
30 May 2024, 01:39
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