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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 13 Apr 2012, 14:56
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71% (01:47) correct 29% (01:04) wrong based on 14 sessions
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

Answer is
[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] New post 13 Apr 2012, 15:01
Expert's post
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

Answer is
[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).

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 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] New post 13 Apr 2012, 15:08
Expert's post
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".
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: x percent of y percent of z is decreased by y percent. What   [#permalink] 13 Apr 2012, 15:08
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