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# One-fifth of the light switches produced by a certain factory are defe

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Manager
Joined: 16 Apr 2009
Posts: 147
Schools: Ross
One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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Updated on: 19 Dec 2018, 08:43
3
32
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:31) correct 29% (02:42) wrong based on 612 sessions

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One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Project PS Butler : Question #87

Originally posted by vannu on 14 Aug 2009, 06:52.
Last edited by HKD1710 on 19 Dec 2018, 08:43, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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Joined: 25 Jul 2009
Posts: 79
Schools: NYU, NUS, ISB, DUKE, ROSS, DARDEN
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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14 Aug 2009, 09:03
5
3
vannu wrote:
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and 1/20 th of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Assume x as the number of switches and that x =100
Defective Switches = 1/5 * 100 = 20
Defective Switches that are rejected = 4/5 * 20 = 16
Defective Switches that are sold = 20 - 16 = 4

Non-defective Switches = 100 - 20 = 80
Non-defective Switches mistakenly rejected = 80*1/20 = 4
Non-defective Switches that are sold = 80 - 4 = 76

Total sold in the market = 76 + 4 = 80
% of defective = (4/80)*100 = 5%

ANS: B
##### General Discussion
Senior Manager
Joined: 18 Jun 2009
Posts: 309
Location: San Francisco
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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14 Aug 2009, 07:55
vannu wrote:
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

I guess there is somethings missing here "Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake"
Manager
Joined: 25 Jul 2009
Posts: 79
Schools: NYU, NUS, ISB, DUKE, ROSS, DARDEN
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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14 Aug 2009, 07:59
vannu wrote:
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

There seems to be some missing data in the highlighted part.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1317
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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14 Aug 2009, 08:58
1
1
vannu wrote:
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and 1/20 th of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

assume 1000 produced

200 defective , 160 defective and rejected, 40 nondefective rejected by mistake

40 defective and not rejected , 760 non defective and not rejected, total non rejected and sold = 800

percent of the switches sold by the factory are defective = 40/800*100 = 5%
Manager
Joined: 15 Feb 2011
Posts: 162
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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10 Jul 2011, 10:40
This may be a very stupid question but please help me understand how did we derive at(4/80)*100 ??

Is there a formula for this??
Retired Moderator
Joined: 20 Dec 2010
Posts: 1462
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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10 Jul 2011, 11:04
4
vannu wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 th of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

 Rejected Not Rejected Defective a b c Not Defective d e f g h i

Fill in this order:
i=100
1/5 of total= Defective i.e. 1/5*100=20 Defective. c=20
Not Defective=100-20=80, f=80

4/5 of Defective=Rejected= 4/5*20=16. a=16
b=c-a i.e. b=20-16=4

1/20 th of the nondefective switches are rejected
1/20*80=4. d=4
g=a+d=16+4=20

h=i-g=100-20=80

Defective+Not Rejected=b=4
Total Not Rejected=h=80

%=4/80*100=5

 Rejected Not Rejected Defective 16 4 20 Not Defective 4 e 80 20 80 100

Ans: "B"
Manager
Status: GMAT Date: 10/08/15
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Location: United States (MA)
Concentration: Human Resources, Strategy
GMAT 1: 640 Q48 V35
GPA: 3.5
WE: Human Resources (Consumer Products)
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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25 Apr 2015, 04:49
Option B --> 5 %

Just took 100 as the total number of switches and filled in numbers from there on.

Defective - 20 Non- Defective - 80
Rejected - 16 Rejected by mistake (1/20) - 4
Not rejected - 4 Net non-defective -- 80-4 = 76

# Sold but defective - 4
# sold - 76

--> 4/76 = ~5%

Thanks,
aimtoteach

Please give kudos if this helped!!

vannu wrote:
One-fifth of the light switches produced by a cer¬tain factory are defective. Four-fifths of the defective switches are rejected and 1/20 th of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%
Math Expert
Joined: 02 Sep 2009
Posts: 65764
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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25 Apr 2015, 04:59
vannu wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Similar question to practice: one-fifth-of-the-batteries-produced-by-an-upstart-factory-are-defectiv-189100.html
_________________
Manager
Status: GMAT Date: 10/08/15
Joined: 17 Jul 2014
Posts: 83
Location: United States (MA)
Concentration: Human Resources, Strategy
GMAT 1: 640 Q48 V35
GPA: 3.5
WE: Human Resources (Consumer Products)
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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25 Apr 2015, 05:08
Bunuel wrote:
vannu wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Similar question to practice: one-fifth-of-the-batteries-produced-by-an-upstart-factory-are-defectiv-189100.html

Thank you Bunuel - it was a good one indeed!!

Thanks,
aimtoteach
Intern
Joined: 21 Apr 2016
Posts: 27
Location: United States
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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01 Sep 2016, 07:35
fluke wrote:
vannu wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 th of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

 Rejected Not Rejected Defective a b c Not Defective d e f g h i

Fill in this order:
i=100
1/5 of total= Defective i.e. 1/5*100=20 Defective. c=20
Not Defective=100-20=80, f=80

4/5 of Defective=Rejected= 4/5*20=16. a=16
b=c-a i.e. b=20-16=4

1/20 th of the nondefective switches are rejected
1/20*80=4. d=4
g=a+d=16+4=20

h=i-g=100-20=80

Defective+Not Rejected=b=4
Total Not Rejected=h=80

%=4/80*100=5

 Rejected Not Rejected Defective 16 4 20 Not Defective 4 e 80 20 80 100

Ans: "B"

Hello!
Somehow, I am completely missing the caveat for this problem!

I am getting an answer of 25% which is clearly wrong!
What am I doing wrong? I have attached the chart I am working off of attached here.
Is it something to do with the 'mistakenly labeled rejected' bit?

So confused!
Attachments

Screen Shot 2016-09-01 at 11.33.23 AM.png [ 29.23 KiB | Viewed 12253 times ]

VP
Joined: 07 Dec 2014
Posts: 1260
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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01 Sep 2016, 13:48
1
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

This made it easier for me.
.04/.8=.05=5%
Attachments

switches.png [ 24.47 KiB | Viewed 12028 times ]

Intern
Joined: 12 Jun 2018
Posts: 1
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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12 Jun 2018, 19:42
DeeptiM wrote:
This may be a very stupid question but please help me understand how did we derive at(4/80)*100 ??

Is there a formula for this??

When ever we find percent of something from something we usually do

The number/total number * 100

In the que we need to find % of no of defective swithches

No of defective switches sold from total switches is 4
And the total no of switches sold is 80

So we take 4/80 *100

Posted from my mobile device
Director
Joined: 09 Mar 2018
Posts: 978
Location: India
Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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12 Feb 2019, 07:26
vannu wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Total number of bulbs = 500

We need to find
D -> defective ND -> Not defective
R-> rejected NR -> not rejected

----------D---------ND----------
R--------80---------20---------100
NR------20---------380--------400
---------100-------400---------500

To find 20/400 * 100

5%
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Quote which i can relate to.
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Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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13 Feb 2019, 18:42
vannu wrote:
One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

We can let the total number of switches = n

So n/5 are defective and 4n/5 are not.

4/5 x n/5 = 4n/25 defective switches are rejected. Thus 1/5 x n/5 = n/25 defective switches are not rejected and are sold.

1/20 x 4n/5 = 4n/100 = n/25 non-defective switches are rejected by mistake.

Thus, a total of 5n/25 = n/5 switches are rejected. So a total of 4n/5 switches are not rejected and are sold.

So the percent of the switches sold that are defective is:

(n/25)/(4n/5) = 5n/(100n) = 1/20 = 5%

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Re: One-fifth of the light switches produced by a certain factory are defe  [#permalink]

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23 Feb 2020, 07:13
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Re: One-fifth of the light switches produced by a certain factory are defe   [#permalink] 23 Feb 2020, 07:13