In a factory that produces computer circuit boards, 4.5 percent of all boards

[BTGModeratorVI]

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%

Answer: B
Source: Official guide

[Brent@GMATPrepNow]

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%

Answer: B
Source: Official guide

One approach is to use the Double Matrix Method.
This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of circuit boards, and the two characteristics are:
- defective or not defective
- repaired or not repaired

Since we're looking for a certain percentage, let's make things easy on ourselves and examine a population of 100 circuit boards.
We're told that 4.5 percent of all boards produced are found to be defective AND are repaired
4.5% of 100 = 4.5
So, we'll place 4.5 in the top-left box, since it represents circuit boards that are defective and have been repaired.



Next, we're told that 10 percent of all defective boards are sold without being repaired
Since we aren't told how many defective boards there are, let's let x = the total number of defective boards among the 100 boards
If there are x defective boards, then 0.1x represents the number of defective boards that are NOT repaired.
We get the following:


At this point, recognize that the two boxes in the top row must add to x
So, we can write: 4.5 + 0.1x = x
Subtract 0.1x from both sides to get: 4.5 = 0.9x
Divide both sides by 0.9 to get: 5 = x

If x = 5, then we know that there are 5 defective circuit boards out of a population of 100 circuit boards.

5/100 = 5%, so 5% of the circuit boards are defective.

Answer: B

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
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- https://www.beatthegmat.com/motel-t271938.html
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- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

[swerve]

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%

Answer: B
Source: Official guide

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 \(= \dfrac{4.5}{90} \cdot 100 = 5\%\)

Therefore, B

[Scott@TargetTestPrep]

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%

Answer: B
Source: Official guide

Solution:

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