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In a factory that produces computer circuit boards, 4.5 perc

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by gmatter2012 » Mon Jul 09, 2012 3:37 am
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%
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by Anurag@Gurome » Mon Jul 09, 2012 4:03 am
gmatter2012 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?
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

The correct answer is B.
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by Anurag@Gurome » Mon Jul 09, 2012 4:08 am
Algebraic Approach:

Say, number of boards produced = x and number of defective boards produced = y
Now, 4.5% of x boards are defective and sold after repair.
And 10% of y defective boards are sold without repair.

So, (10% of y + 4.5% of x) = total number of defective boards = y
--> (0.1y + 0.045x) = y
--> 0.9y = 0.045x
--> y = (45/900)*x = x/20 = 5% of x

The correct answer is B.
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by gmatter2012 » Mon Jul 09, 2012 5:12 am
The language was a bit twisted for this question

but after explanation its clear
Great !!
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by Jeff@TargetTestPrep » Wed Nov 22, 2017 11:23 am
gmatter2012 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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by [email protected] » Wed Nov 22, 2017 1:01 pm
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.

Final Answer: B

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Rich
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