Manhattan CAT # 4 (Percentage Increase)

Question:

If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?

A) (10,000z + 100z(x – y) – xyz) /10,000

B) (10,000z + 100z(y – x) – xyz) /10,000

C) (100z(x – y) – xyz) /10,000

D)(100z(y – x) – xyz)/10,000

E) (10,000)/100yz + xy

Solution:

Start with z.

z dollars was marked up by x percent:

z * (100 + x)/100
e.g. marked up by 20% is the same as multiplying by (100 + 20)/100 = 120/100 = 1.2


Then it was discounted by y percent:

z * (100 + x)/100 * (100 - y)/100
e.g. discounted by 20% is the same as multiplying by (100 - 20)/100 = 80/100 = 0.8


Calculate the final price by multiplying through:
z * (100 + x)/100 * (100 - y)/100
-> z * [(100 + x)*(100 - y)]/10000
--> z * (10000 - 100y + 100x - xy)/10000
---> (10000z - 100yz + 100xz - xyz)/10000
----> (10000z + 100z(x-y) - xyz)/10000

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