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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]

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13 Apr 2012, 14:56
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x percent of y percent of z is decreased by y percent. What is the result?

A. (100xyz - xy^2z) / 1,000,000
B. (xz - y) / 100
C. (xz - y) / 10,000
D. (xyz - 2y) / 100
E. (xyz - 2y) / 10,000

[Reveal] Spoiler:
A

I don't understand on these types of problems when to solve by direct algebra or "picking numbers" as the MGMAT book says. I calculated this probably like this:

( (x/100) * (y/100) * z ) - (y/100) = (xyz/10,000) - (y/100) = (xyz - 100y) / 10,000

MGMAT picks numbers out of thin air which I'm not the greatest at. Is there anyway to solve this with direct math?
[Reveal] Spoiler: OA
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Re: Percent of x percent of y... type question [#permalink]

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13 Apr 2012, 15:01
RyanP wrote:
X percent of Y percent of Z is decreased by Y percent. What is the result?

A) (100xyz - xy^2Z) / 1,000,000

B) (XZ-Y) / 100

C) (XZ-Y) / 10,000

D) (XYZ - 2Y) / 100

E) (XYZ - 2Y) / 10,000

[Reveal] Spoiler:
A

I don't understand on these types of problems when to solve by direct algebra or "picking numbers" as the MGMAT book says. I calculated this probably like this:

( (x/100) * (y/100) * z ) - (y/100) = (xyz/10,000) - (y/100) = (xyz - 100y) / 10,000

MGMAT picks numbers out of thin air which I'm not the greatest at. Is there anyway to solve this with direct math?

Algebraic approach as you asked:

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 $$100*(1-\frac{10}{100})=100*(1-0.1)=100*0.9=90$$).

Hope it's clear.
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Re: x percent of y percent of z is decreased by y percent. What [#permalink]

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13 Apr 2012, 15:05
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 [#permalink]

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13 Apr 2012, 15:08
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 [#permalink]

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19 Oct 2015, 05:55
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Re: x percent of y percent of z is decreased by y percent. What [#permalink]

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19 Oct 2015, 10:52
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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

[Reveal] Spoiler:
A

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Re: x percent of y percent of z is decreased by y percent. What   [#permalink] 19 Oct 2015, 10:52
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# x percent of y percent of z is decreased by y percent. What

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