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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] New post   06 Oct 2023, 22:31
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Question Stats:

39% (03:20) correct 61% (03:35) wrong based on 174 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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Archit3110
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] New post   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] New post   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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varad98
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] New post   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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mohit12a
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Re: ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] New post   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] New post   25 Oct 2023, 10:13
Expert Reply
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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KK14
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ABC Office Supply offers a discount on orders over $500. It applies th [#permalink] New post   30 Dec 2023, 12:31
2
Kudos
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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ABC Office Supply offers a discount on orders over $500. It applies th [#permalink]
30 Dec 2023, 12:31
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