GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jul 2018, 21:00

### 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

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

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 29 Jan 2011
Posts: 314
x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

Updated on: 01 Apr 2018, 11:10
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:13) correct 23% (01:48) wrong based on 146 sessions

### HideShow timer Statistics

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 [ 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.
Manager
Joined: 20 Aug 2011
Posts: 134
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

23 Sep 2011, 02:18
1
1
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

_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Manager
Joined: 14 Mar 2011
Posts: 195
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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.
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1899
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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?

$$\frac{x}{100}*\frac{y}{100}*z(1-\frac{y}{100})$$
_________________
Board of Directors
Joined: 01 Sep 2010
Posts: 3439
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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

Hope it's clear.
_________________
Board of Directors
Joined: 01 Sep 2010
Posts: 3439
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

28 Jan 2012, 03:40
1
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
_________________
Intern
Joined: 20 Feb 2012
Posts: 11
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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".
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

15 Oct 2014, 21:05
2
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%

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

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

Small Tip:

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

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

$$a%b%c = \frac{abc}{10000}$$

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

$$a%b%c%d......... n = \frac{abcd......n}{10^{(n-1)}}$$
_________________

Kindly press "+1 Kudos" to appreciate

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

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!!
_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 10 Oct 2014
Posts: 6
Location: United States
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

16 Oct 2014, 05:53
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?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12004
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

19 Oct 2015, 11:52
1
1
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

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

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

Non-Human User
Joined: 09 Sep 2013
Posts: 7312
Re: x percent of y percent of z is decreased by y percent. What is the res  [#permalink]

### Show Tags

11 Oct 2017, 06:49
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.
_________________
Re: x percent of y percent of z is decreased by y percent. What is the res &nbs [#permalink] 11 Oct 2017, 06:49
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.