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If an item that originally sold for z dollars was marked up [#permalink]

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15 Nov 2006, 07:55

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A

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Difficulty:

55% (hard)

Question Stats:

74% (01:50) correct 26% (02:07) wrong based on 377 sessions

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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?

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?

Actually figured it out as I was typing it in by picking the following numbers:

z=$10, x=20%, y=50% 1.2z*.5= 6

Final price should be $6.

Any other ways?

Matt, that is the easier way. Other way is to directly multiply and take the common factors out..but that seems to be time taking in this problem. As you know, whenever its possible, solving by substituting the numbers is the best way to solve problems when we are under time pressure
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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?

To me, for some questions, picking nos. and applying those in each ans choice and finding the right choice seems tedious. I guess it depends on the method of practice and the strength of the individual, as I see in many threads, and of course, the time pressure.

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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)/10000

D. (100z(y – x) – xyz)/10000

E. 10000 /(x – y)

We are given that an item that originally sold for z dollars was marked up by x percent and then discounted by y percent; thus, the final price of the item is:

z(1 + x/100)(1 - y/100)

z[(100 + x)/100][(100 - y)/100]

z[(10,000 + 100x - 100y - xy)/10,000

[(10,000z + 100xz - 100yz - xyz)/10,000

[(10,000z + 100z(x - y) - xyz)/10,000

Answer: A
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Re: If an item that originally sold for z dollars was marked up [#permalink]

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07 Nov 2017, 00:30

Ans is A

x% rise and y percent fall net change formula is (a + b + ab/100 )% if rise +ve and if fall -ve so x is + and y is - net change will be x-y - xy/100 and this is % of z so net change ie rise => z( x-y-xy/100)1/100 and last price was z so new one is z+ z( x-y - xy/100)1/100 so becomes A
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