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In a factory that produces computer circuit boards, 4.5

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In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post Updated on: 12 Jun 2012, 14:31
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In a factory that produces computer circuit boards, 4.5 percent of all boards produced are found to be defective and are repaired before being sold, but 10 percent of all defective boards are sold without being repaired. What percentage of boards produced in the factory are defective?

A. 4.5%
B. 5.0%
C. 6.0%
D. 10.0%
E. 14.5%

Originally posted by perseverant on 18 May 2010, 16:59.
Last edited by Bunuel on 12 Jun 2012, 14:31, edited 1 time in total.
Edited the question and added the OA.
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 27 Aug 2013, 02:52
5
1
perseverant wrote:
In a factory that produces computer circuit boards, 4.5 percent of all boards produced are found to be defective and are repaired before being sold, but 10 percent of all defective boards are sold without being repaired. What percentage of boards produced in the factory are defective?

A. 4.5%
B. 5.0%
C. 6.0%
D. 10.0%
E. 14.5%


1. 10% of defective boards are not repaired . Therefore 90% of defective boards are repaired
2. 90% of defective boards is equal to 4.5% of all boards produced
3 Total percentage of defective boards produced = 4.5/90 * 100 = 5%
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Re: In a factory that produces computer circuit boards  [#permalink]

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New post 18 May 2010, 23:01
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2
Total Boards = X
Total Defective Boards = Y

Out of this Y "Defective" boards 10% "Escaped" (GIVEN) and 90% "Get caught and fixed"

We know that "Get Caught and fixed" = 4.5% of X. This implies

90% of Y = 4.5% of X.


(90/100) * Y = (4.5/100) * X ===> Y = 0.05 * X ===> 5% of X.

Hope this helps.

What is the OA? Is it B?
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Re: In a factory that produces computer circuit boards  [#permalink]

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New post Updated on: 18 Jun 2013, 14:40
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Just for the sake of some intuition one should consider this:

That actual 4.5 percent figure that got fixed from the entire amount is equal to 90 percent that got fixed. The 4.5 percent here is adjusted to the 10 percent that gets escaped. So the 4.5 percent of all boards that are found to be defective already includes the adjustment that 10 percent escaped. So in other words after 10 percent escapes that figure is 4.5 percent of total boards. So we need to figure out what the original defective boards in percentage were.

As we know 10% escaped and wasn't caught,
We also know that when we originally found 4.5% of boards and fixed them before selling them
So that 4.5% was in reality only 90% of all defective board since we missed 10%
So, 90% of all defective boards = 4.5% of all boards

So, (10% of y + 4.5% of x) = total number of defective boards = y

Key word here "found"

Originally posted by iNumbv on 12 Jun 2012, 13:22.
Last edited by iNumbv on 18 Jun 2013, 14:40, edited 1 time in total.
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Re: In a factory that produces computer circuit boards  [#permalink]

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New post 12 Jun 2012, 13:49
i think total cb and defective cb are not required because (X/Y)*(Y/total) is the answer where x is defective and not repaired and y is defective and total is total no of bulbs.
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 17 Jun 2012, 17:26
Answer: B

X = all boards
4.5% * X = all boards that are DEFECTIVE and repaired before being sold

Y = all DEFECTIVE boards
100% all boards - 10% all DEFECTIVE boards that are NOT being repaired before being sold = 90%

90% * Y = all DEFECTIVE boards that are repaired before being sold

.9*Y = .045*X
Y = (.045/.9) * X
Y = .05
Y = 5%
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 26 Aug 2013, 22:22
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As 10% of all defective boards are sold without being repaired, (100 - 10)% = 90% of all defective boards are sold after being repaired

So, 90% of all defective boards = 4.5% of all boards
--> 100% of all defective boards = (4.5/90)*100% = 5% of all boards
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 07 Feb 2014, 07:05
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T - total boards
D - ALL defective boards.

\(\frac{90}{100}*D=\frac{4.5}{100}* T\)

D = 5% of Total.

B is answer.
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 12 Feb 2014, 14:17
SravnaTestPrep wrote:
perseverant wrote:
In a factory that produces computer circuit boards, 4.5 percent of all boards produced are found to be defective and are repaired before being sold, but 10 percent of all defective boards are sold without being repaired. What percentage of boards produced in the factory are defective?

A. 4.5%
B. 5.0%
C. 6.0%
D. 10.0%
E. 14.5%


1. 10% of defective boards are not repaired . Therefore 90% of defective boards are repaired
2. 90% of defective boards is equal to 4.5% of all boards produced
3 Total percentage of defective boards produced = 4.5/90 * 100 = 5%


Or similarly one can use smart numbers:

Let's say total produced were 1000

So we have that 45 were defective and repaired
Since 10% were not repaired, 90% of boards were defective and repaired
The 9/10x = 45, where 'x' is the total number of defective boards.

x = 50

Therefore percentage defective 50/1000 = 5%

Hope this clarifies
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 15 Apr 2016, 11:06
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Total production = 1000
Defective goods sold without repairing = 100
Non defective ( Ready for sale ) = 900
Defective and repaired before sold = 45

Thus out of 900 Good items produced in the factory 45 are found defective

Percentage of defective goods = 45/900 * 100 =>5%
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 07 May 2017, 01:09
Alternatively, this question can be viewed as an overlapping set with 2 variables.

Defective Not defective
Repaired 4.5
Not repaired 0.1x
Total x

Thus, 4.5 + 0.1x = x
Solve for x:
x=5
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 07 May 2017, 02:24
defective=100
defective & sold=10% 0f defective
defective & not sold=90%
90%=4.5
100%=5
ans: B
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 19 Nov 2017, 20:04
Here's what I did. Say, Total produced= 100 and Total defective=x. Repaired and sold 4.5% of 100=4.5, sold without repair=.10x, then .10x+4.5=x. We can solve for X=5, that is (5/100)%= 5%. Answer choice B.
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 22 Nov 2017, 12:23
perseverant wrote:
In a factory that produces computer circuit boards, 4.5 percent of all boards produced are found to be defective and are repaired before being sold, but 10 percent of all defective boards are sold without being repaired. What percentage of boards produced in the factory are defective?

A. 4.5%
B. 5.0%
C. 6.0%
D. 10.0%
E. 14.5%


Since 10 percent of all defective boards are sold without being repaired, 90 percent of all defective boards are sold after being repaired, and this number is also the 4.5 percent of all boards produced. Thus if we let d = the number of defective boards and n = the total number of boards, we have:

0.9d = 0.045n

d/n = 0.045/0.9 = 45/900 = 5/100 = 5%

Answer: B
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 04 Jan 2018, 15:53
Hi All,

While this question is older - and the concept (subgroups within subgroups) is relatively rare - you can solve this problem in a couple of different ways. Here's how you can use a mix of TESTing VALUES and TESTing THE ANSWERS to get the answer:

We're told that a factory produces circuit boards and 4.5% of all boards produced are found to be defective AND then repaired before being sold. However, 10% of all defective boards are sold WITHOUT being repaired. We're asked for the percentage of boards produced in the factory are defective.

From the prompt, it's clear that not all of the defective boards are repaired, so the percentage of defective boards MUST be greater than 4.5%. Let's TEST Answer B...

Answer B: 5%

IF....
there are 1,000 total boards,
5% would be (.05)(1,000) = 50 total defective boards
4.5% would be (.045)(1,000) = 45 defective boards REPAIRED, which leaves 5 defective boards (out of 50 defective boards) NOT REPAIRED... 5/50 = 10%. This matches what we were told, so this MUST be the answer.

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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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New post 29 Sep 2018, 04:33
One way to find the percentage of defective boards would be to find the total number produced and the total number defective (including those repaired and those not repaired). But in this problem, we don't have enough information to solve it this way. We have 2 unknowns (total boards, total defective) but no way to write 2 distinct equations.

But notice that we don't actually need to solve for either of the unknowns – we only need to find the percentage that are defective, which is really just the ratio of the defective boards to the total boards. So, if we could find just one linear equation relating the 2 unknowns, we could solve it for the ratio of the 2 unknowns.

Let t = the total number of boards produced and let d = the number that are defective (including those repaired and those not repaired). We are told that 10% of all defective boards are not repaired, which implies that 90% of all defective boards are repaired.

Therefore, 90% of d = (0.90)(d) = the number of defective boards that are repaired. But we also know something else about the number of defective boards that are repaired: it is equal to 4.5% of all boards produced, or t. So we also have (0.045)(t) = the number of defective boards that are repaired. Since they both represent the same thing, we can set these two expressions equal to each other: (0.90)(d) = (0.045)(t). We can't solve for t or d but we can solve for their ratio, or d/t , which will represent the percentage of all boards that are defective. First, divide both sides by 0.90 to get d = 0.045(t)/0.90, or d = 0.05 t. Then divide both sides by t to get d/t = 0.05, or 5%. So the answer is Choice (B).
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Re: In a factory that produces computer circuit boards, 4.5  [#permalink]

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Re: In a factory that produces computer circuit boards, 4.5   [#permalink] 04 Oct 2019, 20:15
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