adkikani wrote:

niks18I think there was a gap in putting my query as well as steps.

Here is my re framed query:

**Quote:**

A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

**Quote:**

A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price

Let us say original price is $100 since i am dealing with %tages and discounts.

I can have all sort of combinations from :

100 * 0.8 * 1.05 .. . . (1) when p =20

to

100*0.7*1.05 .. . . (2) when p =30

Note that both values of p are permissible since all I am given in question stem is: p> 10

As you can see, both (1) and (2) are permissible and yet shall yield a different final answer,

the one that is not permissible in PS. We need to get an unique ans to a Q in PS

Hi

adkikaniNote, here you are "assuming" values for "p" and each of your assumption will give a different value. hence value of the equation at p=20 and p=30 will be different. However important point to note is that whatever value you assume, you must stick to that value and then check the options by substituting only that particular value of p.

so for this question you are assuming p=20, then you will get the final price as 100*0.8*1.05=84. Note this is the final price under the assumed condition and not the "Actual" final price because we don't know the actual value of "p"

now when testing the options you will have to use p=20 only.

In quant question we need to know the unique value, but since you are solving this question through substitution method, you can assume any value permissible under the given condition and test the equation accordingly. There will be however only ONE option that will give you the correct value for the assumed parameter, in this case only Option C will give you the correct value for any assumed value of p, hence you are getting a unique solution.