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

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x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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


A. \(\frac{100xyz - xy^2z}{1,000,000}\)

B. \(\frac{xz - y}{100}\)

C. \(\frac{xz - y}{10,000}\)

D. \(\frac{xyz - 2y}{100}\)

E. \(\frac{xyz - 2y}{10,000}\)

Attachment:
problem.png
problem.png [ 18.37 KiB | Viewed 4591 times ]

Originally posted by siddhans on 23 Sep 2011, 01:05.
Last edited by Bunuel on 01 Apr 2018, 11:10, edited 3 times in total.
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Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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New post 23 Sep 2011, 02:18
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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?

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 is the res  [#permalink]

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New post 23 Sep 2011, 04:15
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 is the res  [#permalink]

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New post 23 Sep 2011, 05:26
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 is the res  [#permalink]

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New post 27 Jan 2012, 17:49
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 is the res  [#permalink]

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New post 27 Jan 2012, 18:12
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 is the res  [#permalink]

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New post 28 Jan 2012, 03:40
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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 is the res  [#permalink]

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New post 13 Apr 2012, 16:05
I see the process you went through but I'm still not sure I understand it. How do you know to multiply (1-y/100) instead of subtracting it? The word decrease makes me automatically think it has to be subtracted.

In this types of problems, are you only going to add/subtract if it says greater than or less than?
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Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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New post 13 Apr 2012, 16:08
RyanP wrote:
I see the process you went through but I'm still not sure I understand it. How do you know to multiply (1-y/100) instead of subtracting it? The word decrease makes me automatically think it has to be subtracted.

In this types of problems, are you only going to add/subtract if it says greater than or less than?


The question does not say "decreased by y", it says "decreased y PERCENT".
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Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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New post 15 Oct 2014, 21:05
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x percent of y percent of z is decreased by y percent

Making the statement more mathematical friendly

x% of y% of z is decreased by y%

x% of (y% of z) is decreased by y%

\((x% of \frac{yz}{100})\) is decreased by y%

\(\frac{xyz}{100 * 100}\) is decreased by y%

\(\frac{xyz}{100*100} - \frac{xy^2z}{100*100*100}\)

\(\frac{100xyz - xy^2z}{100*100*100}\)

Answer = A


Small Tip:

Number of times you see the % sign (2 zero's), those number of zero's in the denominator

\(a%b = \frac{ab}{10^2}\)

\(a%b%c = \frac{abc}{10000}\)

\(a%b%c%d = \frac{abcd}{10^6}\)

\(a%b%c%d......... n = \frac{abcd......n}{10^{(n-1)}}\)
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Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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New post 15 Oct 2014, 21:09
siddhans wrote:
x percent of y percent of z is decreased by y percent. What is the result?
Attachment:
problem.png


The OA of this question is very distinct. All the options are levelled with the denominator, so no further simplification required on the OA.

Once you know the trick as stated in earlier post, its quite obvious that answer = A (it has 10^6 in the denominator)

No calculation required!!
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Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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New post 16 Oct 2014, 05:53
blink005 wrote:
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?

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


really a tough one. m stuck in it what is the result?? can you show it?
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Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

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New post 19 Oct 2015, 11:52
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Hi All,

This question can certainly be solved by TESTing VALUES. The 'shortcuts' involve selecting nice 'round' numbers for the 3 variables AND recognizing that the 5 answer choices have 'pieces' in common (so you can avoid redoing some of the calculations).

We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.

IF....
X = 10
Y = 50
Z = 100

First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5

So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.

Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a MATCH
Answer B. (xz - y) / 100 = (1,000 - 50)/100 = 950/100 = 9.5 NOT a match
Answer C. (xz - y) / 10,000 = 950/10,000 = .095 NOT a match
Answer D. (xyz - 2y) / 100 = (50,000 - 100)/100 = 49,900/100 = 499 NOT a match
Answer E. (xyz - 2y) / 10,000 = 49,900/10,000 = 4.99 NOT a match

Final Answer:

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