All trainees in a certain aviator training program must take

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

All trainees in a certain aviator training program must take

by BTGmoderatorDC » Tue Dec 10, 2019 2:59 pm

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All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?

(1) 10 percent of the trainees did not pass either test.
(2) 20 percent of the trainees passed only the flight test.

OA D

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Tue Dec 10, 2019 2:59 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Dec 12, 2019 9:58 pm

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BTGmoderatorDC wrote:All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?

(1) 10 percent of the trainees did not pass either test.
(2) 20 percent of the trainees passed only the flight test.

OA D

Source: Official Guide

Since the data are given in percents, the total no. of trainees = 100.

Say x trainees passed both tests. We have to get the value of x.

Let's take each statement one by one.

(1) 10 percent of the trainees did not pass either test.

=> 90% passed at least one of the two tests.

=> 90 = Only the flight test passed trainees + Only the flight test passed trainees + Both the tests passed trainees

=> 90 = (80 - x) + (70 - x) + x

=> x = 60. Sufficient.

(2) 20 percent of the trainees passed only the flight test.

=> 20 = 80 - x => x = 60. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Fri Dec 20, 2019 9:19 pm

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Let the percentage of trainees that passes both tests = x
Trainees that passed written test = 70 - x
Trainees that passed flight test = 80 - x
Now, we are to find the percentage of the trainees that passed both tests.
Since the information provided is expressed as a percentage, then the percentage of the total trainee = 100

Statement 1: 10% of trainee did not pass either test.
100 = (70-x) + (80-x) + x + 10
100 = 160 - x
x = 160 - 100 = 60
Therefore, statement 1 is SUFFICIENT.

Statement 2: 20 percent of the trainees passed only the flight test.
This means that 80 - x = 20
80 - 20 = x
x = 60
Statement 2 is also SUFFICIENT.

Since each statement alone is sufficient, then option D is the correct answer.

Thanks

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8088; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: All trainees in a certain aviator training program must take

by Scott@TargetTestPrep » Sun Sep 06, 2020 1:23 pm

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BTGmoderatorDC wrote: ↑
Tue Dec 10, 2019 2:59 pm
All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 80 percent of the trainees passed the flight test, what percent of the trainees passed both tests?

(1) 10 percent of the trainees did not pass either test.
(2) 20 percent of the trainees passed only the flight test.

OA D

Source: Official Guide

Solution:

Question Stem Analysis:

We can use the formula:

Total = Pass Written + Pass Flight - Pass Both + Pass Neither

With “Total” = 100, we are given “Pass Written” = 70 and “Pass Flight” = 80, and we need to find “Pass Both.” That is,

100 = 70 + 80 - B + N

B = 50 + N

If we know the value of N (“Pass Neither”), then we can determine the value of B (“Pass Both”).

Statement One Only:

10 percent of the trainees did not pass either test.

Since we are given that N = 10, we have:

B = 50 + 10 = 60

Statement one alone is sufficient.

Statement Two Only:

20 percent of the trainees passed only the flight test.

This means “Pass Only Flight” = 20. Since Pass Both = Pass Flight - Pass Only Flight, we have B = 80 - 20 = 60.

Statement two alone is sufficient.

Answer: D

Scott Woodbury-Stewart
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