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

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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%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Apr 2015, 04:58, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: One-fifth of the light switches produced by a certain factory are defe [#permalink]

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New post 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%
[Reveal] Spoiler:
B



I guess there is somethings missing here "Four-fifths of the defective switches are rejected and of the nondefective switches are rejected by mistake"
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New post 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%
[Reveal] Spoiler:
B



There seems to be some missing data in the highlighted part.
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Re: One-fifth of the light switches produced by a certain factory are defe [#permalink]

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New post 14 Aug 2009, 08:46
i too got confused by the highlighted sentence.. is the prblm statemnt clear..
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New post 14 Aug 2009, 08:47
I edited the question. Sorry for the inconvenience.
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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%
[Reveal] Spoiler:
B


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%
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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%
[Reveal] Spoiler:
B


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
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New post 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??
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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%
[Reveal] Spoiler:
B





RejectedNot Rejected
Defectiveabc
Not Defectivedef
ghi


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




RejectedNot Rejected
Defective16420
Not Defective4e80
2080100


Ans: "B"
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New post 10 Jul 2011, 11:15
thanks fluke, dis approach did help me understand the question better...

this was my first post..i have couple of more questions wherein i need your advice..pls suggest if i need to open up a new topic for every question or can i post my queries alongside the existing post..like what i did in this one..

thanks again!!
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New post 10 Jul 2011, 11:51
DeeptiM wrote:
thanks fluke, dis approach did help me understand the question better...

this was my first post..i have couple of more questions wherein i need your advice..pls suggest if i need to open up a new topic for every question or can i post my queries alongside the existing post..like what i did in this one..

thanks again!!


Please reply to the existing post. If the question is not discussed before, create a new thread.
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Re: One-fifth of the light switches produced by a certain factory are defe [#permalink]

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New post 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%


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aimtoteach

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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%
[Reveal] Spoiler:
B

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Thanks,
aimtoteach


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

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

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

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New post 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%
[Reveal] Spoiler:
B





RejectedNot Rejected
Defectiveabc
Not Defectivedef
ghi


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




RejectedNot Rejected
Defective16420
Not Defective4e80
2080100


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!
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Screen Shot 2016-09-01 at 11.33.23 AM.png
Screen Shot 2016-09-01 at 11.33.23 AM.png [ 29.23 KiB | Viewed 1247 times ]

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

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New post 01 Sep 2016, 13:48
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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?

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

switches.png
switches.png [ 24.47 KiB | Viewed 1075 times ]

One-fifth of the light switches produced by a certain factory are defe   [#permalink] 01 Sep 2016, 13:48
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