stne wrote:
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by
(A) \(0.25(1 + \frac{3z}{100})\)
(B) \(0.25(1 + \frac{z}{100})\)
(C) \(0.25(1 - \frac{3z}{100})\)
(D) \(0.75(1 - \frac{z}{100})\)
(E) \(0.75(1 + \frac{3z}{100})\)
Source: Gmat Hacks 1800
can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ?
Let initial amount be 100 after 25% discount we get 75 then z% discount will give \(\frac{(100-z)}{100}*75\) = \(\frac{100-z}{4}*3\)
So equivalent discount is
100 -\(\frac{300+3z}{4}\)
\(\frac{100+3z}{4}\)
Well as option A after simplification states \(\frac{100+3z}{400}\)
So why this difference ?
( Guaranteed Kudos for anyone who can help with this, thank you)
Responding to a pm:
You can easily figure this out by taking numbers instead of variables to understand the concept here:
Say there are 2 discounts - 25% and 20%
Question: What is the overall discount? (it will be in percentage terms only since no actual numbers are provided)
If you assume $100 and then arrive at $75 and then at 80/100 * $75 = $60
Then using the logic used by you above, you say this is $100 - $60 = $40
This 40 is your (100 + 3z)/4
But note that the answer cannot be 40. The overall discount will be in terms of percentage. We say that the discount is 40 per cent i.e. 40/100 i.e. 40%.
So it will be (100 + 3z)/400
Thank you , for clearing this up, Karishma. Without your guidance it would really have been difficult to understand this. Your awesomeness simply dazzles!