It is currently 23 Oct 2017, 14:18

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 29 Jan 2011
Posts: 343

Kudos [?]: 244 [1], given: 87

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

### Show Tags

23 Sep 2011, 01:05
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:13) correct 24% (01:42) wrong based on 145 sessions

### HideShow timer Statistics

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

problem.png [ 18.37 KiB | Viewed 4134 times ]
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jan 2012, 18:13, edited 2 times in total.

Kudos [?]: 244 [1], given: 87

Manager
Joined: 20 Aug 2011
Posts: 144

Kudos [?]: 106 [1], given: 0

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

### Show Tags

23 Sep 2011, 02:18
1
KUDOS
1
This post was
BOOKMARKED
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?

[Reveal] 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.

Kudos [?]: 106 [1], given: 0

Manager
Joined: 14 Mar 2011
Posts: 198

Kudos [?]: 132 [0], given: 21

Re: x percent of y percent of z is decreased by y percent . what [#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.

Kudos [?]: 132 [0], given: 21

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2055 [0], given: 376

Re: x percent of y percent of z is decreased by y percent . what [#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?

$$\frac{x}{100}*\frac{y}{100}*z(1-\frac{y}{100})$$
_________________

Kudos [?]: 2055 [0], given: 376

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9096 [0], given: 1155

Re: x percent of y percent of z is decreased by y percent . what [#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
_________________

Kudos [?]: 9096 [0], given: 1155

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129505 [0], given: 12201

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

### Show Tags

27 Jan 2012, 18:12
Expert's post
2
This post was
BOOKMARKED
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.
_________________

Kudos [?]: 129505 [0], given: 12201

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9096 [0], given: 1155

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

### Show Tags

28 Jan 2012, 03:40
1
This post was
BOOKMARKED
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
_________________

Kudos [?]: 9096 [0], given: 1155

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16535

Kudos [?]: 274 [0], given: 0

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

### Show Tags

10 Oct 2014, 20:03
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.
_________________

Kudos [?]: 274 [0], given: 0

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2633 [0], given: 193

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 [#permalink]

### Show Tags

15 Oct 2014, 21:05
2
This post was
BOOKMARKED
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

Kudos [?]: 2633 [0], given: 193

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2633 [0], given: 193

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 [#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

Kudos [?]: 2633 [0], given: 193

Intern
Joined: 10 Oct 2014
Posts: 6

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

Location: United States
Re: x percent of y percent of z is decreased by y percent. What [#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?

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

really a tough one. m stuck in it what is the result?? can you show it?

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16535

Kudos [?]: 274 [0], given: 0

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

### Show Tags

15 Jun 2016, 17:20
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.
_________________

Kudos [?]: 274 [0], given: 0

Re: x percent of y percent of z is decreased by y percent. What   [#permalink] 15 Jun 2016, 17:20
Display posts from previous: Sort by