Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Apr 2016, 03:07
GMAT Club Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 20 Feb 2012
Posts: 11
Followers: 0

Kudos [?]: 5 [1] , given: 0

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

Show Tags

New post 13 Apr 2012, 15:56
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (02:25) correct 21% (01:02) wrong based on 38 sessions

HideShow timer Statictics

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
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32539
Followers: 5627

Kudos [?]: 68255 [0], given: 9797

Re: Percent of x percent of y... type question [#permalink]

Show Tags

New post 13 Apr 2012, 16:01
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.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 20 Feb 2012
Posts: 11
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: x percent of y percent of z is decreased by y percent. What [#permalink]

Show Tags

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?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32539
Followers: 5627

Kudos [?]: 68255 [0], given: 9797

Re: x percent of y percent of z is decreased by y percent. What [#permalink]

Show Tags

New post 13 Apr 2012, 16:08
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 the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9231
Followers: 454

Kudos [?]: 114 [0], given: 0

Premium Member
Re: x percent of y percent of z is decreased by y percent. What [#permalink]

Show Tags

New post 19 Oct 2015, 06:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 6204
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 261

Kudos [?]: 1834 [1] , given: 160

Re: x percent of y percent of z is decreased by y percent. What [#permalink]

Show Tags

New post 19 Oct 2015, 11:52
1
This post received
KUDOS
Expert's post
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:
[Reveal] Spoiler:
A


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: x percent of y percent of z is decreased by y percent. What   [#permalink] 19 Oct 2015, 11:52
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic If 45% of z is 120% of y and y is 75% of x, what percent of x is z? shyind 1 04 Aug 2015, 23:44
2 Experts publish their posts in the topic X is what percent greater than Y percent of Z? sugu86 4 26 Apr 2012, 00:42
10 Experts publish their posts in the topic x percent of y percent of z is decreased by y percent. What siddhans 10 23 Sep 2011, 01:05
Experts publish their posts in the topic x is what percent of y percent of z, in terms of x, y and z? afyl128 5 28 Oct 2010, 13:51
x is what percent cheaper than y ksharma12 2 04 Jul 2010, 01:13
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.