In a factory that produces computer circuit boards, 4.5 percent of all boards produced are found to be defective and are

[BTGmoderatorDC]

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%


OA B

Source: Official Guide

[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%

OA B

Source: Official Guide

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 \(X\).

\(\dfrac{90}{100} \cdot Y = \dfrac{4.5}{100} \cdot X \Longrightarrow Y = 0.05 \cdot X \Longrightarrow 5\%\) of \(X\).

Hence, 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%


OA 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