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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

In a sample of college students, 40 percent are third...

by Vincen » Fri Sep 08, 2017 3:04 pm

In a sample of college students, 40 percent are third year students and 70 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?

(A) 3/4
(B) 2/3
(C) 4/7
(D) 1/2
(E) 3/7

OA is D.

The problems that involve percentages are very difficult to me. Experts, how can I solve these kind of problems in a way easy to understand?

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Source: Beat The GMAT — Problem Solving | Fri Sep 08, 2017 3:04 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 » Fri Sep 08, 2017 11:53 pm

Vincen wrote:In a sample of college students, 40 percent are third year students and 70 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?

(A) 3/4
(B) 2/3
(C) 4/7
(D) 1/2
(E) 3/7

OA is D.

The problems that involve percentages are very difficult to me. Experts, how can I solve these kind of problems in a way easy to understand?

Say there are a total of a total of 100 students ( I year, II year, and III year)

Number of III year students = 40% of 100 = 40

Number of students who are not II year students = 70% of 100 = 70
=> Number of II year students = 100 - 70 = 30
=> Number of I year and III year students combined = 70

=> Number of I year students = 70 - Number of III year students = 70 - 40 = 30

Thus, the number of I year and II year students combined = 30 + 30 = 60

Thus, (Number of II year students) / (Number of I year and II year students combined) = 30 / 60 = 1/2.

The correct answer: D

Hope this helps!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: In a sample of college students, 40 percent are third...

by Scott@TargetTestPrep » Sun Feb 09, 2020 4:26 am

Vincen wrote: ↑
Fri Sep 08, 2017 3:04 pm
In a sample of college students, 40 percent are third year students and 70 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?

(A) 3/4
(B) 2/3
(C) 4/7
(D) 1/2
(E) 3/7

OA is D.

The problems that involve percentages are very difficult to me. Experts, how can I solve these kind of problems in a way easy to understand?

We can let the total number of students be 100. Since 40% are third-year students, 40 students are third-year. Thus, 60 students are not third-year. Since 70% are not second-year, 70 students are not second-year. Thus, 100 - 70 = 30 students are second-year.

Since 60 students are not third-year and 30 students are second-year, the fraction of students who are not third-year but are second-year is:

30/60 = 1/2

Answer: D

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