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

Question

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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).

KK14 · Accepted Answer

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

Archit3110 · Answer

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%

MHBS · Answer

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?

varad98 · Answer

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.

mohit12a · Answer

a discount of 3% and tax rate of 5% also gives the same result. Could you please check it and let us know

Sajjad1994 · Answer

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.

Gemmie · Answer

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%

bhattarbharat · Answer

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 =  
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.

sayan640 · Answer

I also used the similar approach but still it took me a while.  KarishmaB   chetan2u   GMATinsight  Is there any systematic way by which we can go about using the 'trial and error' method in order to solve this question ?

KarishmaB · Answer

The discount rate and the tax rate applied for both are same so we can work with any one transaction. 706.08 - 693 = 13.08 13.08/693 = 1.887% (Use the calculator) We need two successive percentage changes to add up to 1.887%. The discount would be lower and tax rate higher since overall cost is higher than before. For an effective percentage change of 1.887%, the two percentages should have a difference of a bit more than 1.887%. -3% and +5% will give an overall percentage change of 2 - 15/100 = 1.85% (not enough) -5% and +7.25% will give an overall percentage change of 2.25 - 5*7.25/100 = 1.887% (Use the calculator again here) ANSWER: Discount = 5% and Tax = 7.25% Successive percentage changes are discussed here: https://anaprep.com/arithmetic-successi ... e-changes/

chetan2u · Answer

I don't think there would be any shortcuts here except for using a bit of logic to eliminate certain options.

You can use calculator to find the final change => (1106.50-1086)/1086 *100 = 1.88%

So, the final answer is 1.88% above the initial price, which means there should be more than 1.88% difference in tax rate and discount. Tax rate is surely more than discount and it really does not matter which is applied first.

The above would limit the lower value to 8-1.88 or 6.12, meaning only possibilities are 3 and 5.

You have no option but to try for combination of 3 and 5, which will give you 1.85
The next combination 3 and 6.5 takes it above 2%. Thus no need to check any further as increasing tax rate while keeping discount at 3% would only increase the final percentage increase beyond 2%.

The next possible combination would be 5 and 6.5, but here the difference is less than 1.88.

5 and 7.25 gets you the answer.

So the trials would be for (3,5) (3,6.5) and (5,7.25).

However, I really doubt that an actual question will get two options so close 1.85 from (3,5) and 1.88 from (5,7.25).

bumpbot · Answer

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