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x percent of y percent of z is decreased by y percent. What

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x percent of y percent of z is decreased by y percent. What [#permalink] New post 23 Sep 2011, 00:05
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x percent of y percent of z is decreased by y percent. What is the result?
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[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jan 2012, 17:13, edited 2 times in total.
Added the OA and image
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Re: x percent of y percent of z is decreased by y percent . what [#permalink] New post 23 Sep 2011, 01:18
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Very easy question, you don't need options

Acc. to given statement,

y% of z= y/100*z

x%(y5 of z)=x/100*y/100*z

Now the entire thing is reduced by y%
When i say price of a product decreased by 5% we take the new price as (100-5)/100*old price

hence after y% decrease the expression simplifies to

(100-y)/100*(x/100*y/100*z)
=(100-y)*xyz/(10^6)
=(100xyz-100xy^2z)/10^6

You posted the incorrect oa

siddhans wrote:
Tried searching but couldnt find ....

x percent of y percent of z is decreased by y percent . what is the result?

[Reveal] Spoiler: OA
100XYZ - XY^2Z/1,000,000

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Re: x percent of y percent of z is decreased by y percent . what [#permalink] New post 23 Sep 2011, 03:15
I agree that you can get to answer directly, but many times the answers will be different ratio/multiple form of the answer, so you might need answer choices to work through. Also some times variables are too cluttery so some people with non-math background like me need numbers to work through.

x percent of y percent of z is decreased by y percent . what is the result?
let x = 10, y =20 and z =1000. (x percent of y percent of z = 10% 0f 20% of 1000 ; 10 % of (20% of 1000) ; 10% of 200 =20.

20 is decreased by y percent. that is 20 is decreased by 20%. so 20 - (20/100* 20) = 16 Now target answer is 16, plug in values .

A)100XYZ - XY^2Z/1,000,000

(100 *10*20*1000 - 10.(20^2)1000)/ 10^6

> (20,000,000 - 400,000,0) /10^6 = 16 (target). you may need to check other answers but in this case the numbers I have picked are so distinct that it wont give same answer. so answer is A.
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Re: x percent of y percent of z is decreased by y percent . what [#permalink] New post 23 Sep 2011, 04:26
siddhans wrote:
Tried searching but couldnt find ....

x percent of y percent of z is decreased by y percent . what is the result?



\frac{x}{100}*\frac{y}{100}*z(1-\frac{y}{100})
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Re: x percent of y percent of z is decreased by y percent . what [#permalink] New post 27 Jan 2012, 16:49
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Sorry. I'm stuck because for me the right translation is

x/100 * y/100 * z = (1- y/100) or not ??

I'd resolve this question by math because is pretty straighforward than the strategy of target.

anyone can help me ??

Thanks a lot
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Re: x percent of y percent of z is decreased by y percent . what [#permalink] New post 27 Jan 2012, 17:12
Expert's post
carcass wrote:
Sorry. I'm stuck because for me the right translation is

x/100 * y/100 * z = (1- y/100) or not ??

I'd resolve this question by math because is pretty straighforward than the strategy of target.

anyone can help me ??

Thanks a lot


It can be done by plug-in method though as you are doing with algebra I'll proceed with it.

x percent of y percent of z is decreased by y percent. What is the result?

Step by step:
1. y percent of z is \frac{y}{100}*z=\frac{yz}{100};
2. x percent of above value is \frac{x}{100}*\frac{yz}{100}=\frac{xyz}{10,000};
3. The above value is decreased by y percent: \frac{xyz}{10,000}*(1-\frac{y}{100})=\frac{xyz}{10,000}*(\frac{100-y}{100})=\frac{100xyz-xy^2z}{1,000,000} (for example 100 is decreased by 10 percent can be expressed as 100*(1-\frac{10}{100})=100*(1-0.1)=100*0.9=90).

Answer: A.

Hope it's clear.
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Re: x percent of y percent of z is decreased by y percent. What [#permalink] New post 28 Jan 2012, 02:40
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For the % decrease formula we have: Original (1 - %decrease/100)= new

So: xyz/100 * (1 - y/100)..............I do not know why my head told me equals % decrease....... :(

generally is pretty simple for me this kind of problem.

Thanks Bunel
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Re: x percent of y percent of z is decreased by y percent. What   [#permalink] 28 Jan 2012, 02:40
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