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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri May 22, 2020 7:36 pm

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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%

OA B

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Fri May 22, 2020 7:36 pm

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Sat May 23, 2020 10:00 am

BTGmoderatorDC wrote: ↑
Fri May 22, 2020 7:36 pm
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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

by Scott@TargetTestPrep » Sat May 30, 2020 1:48 pm

BTGmoderatorDC wrote: ↑
Fri May 22, 2020 7:36 pm
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

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