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

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