Problem Solving

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

I chose the correct answer by an educated guess. Their explanation is not making sense to me. Please help me.

Thanks.
~R

OKAY the way I posted question was confusing. Can any one try now. The OA is A

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

THANK YOU. I am getting at it now

~R

Picking numbers works great for this question (and any question with variables in the choices and complicated algebra).

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

Let's let z = 100 (the number we usually pick in percent questions with unspecified values), x = 25 and y = 40

So, we go from $100 to 1.25(100) = $125 to .6(125) = $75

Now we plug in our values for x, y and z into the choices until we find one that gets us $75.

a) (10000*100 + 100*100(25-40) - 100*25*40)/10000

dividing each part by 10000 to make life easy:

100 - 15 - 10 = 75! bingo!

It's possible that another choice will also work out for the specific numbers that we chose (the correct answer works for ANY set of numbers, other answers may work by fluke for a few specific sets of numbers), but the math is so time consuming that we're best off just picking (a) and taking the very small risk that it's not the right answer.

Also, a quick glance through (b)-(e) will show that there's no way that they'll work out to the same number as (a).

THANKS Stuart

I would reccomend that you take a look at the booklet that deals with VIC's in the manhattan gmat. It bascaly explains that pick imaginary smart numbers, make a variable chart (to keep your vairables neat) and then compute some type of target answer. Plug in those values and look for your target answer. It works like a charm.