50% of students' study science and 30% of science students

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AAPL: Moderator; Posts: 2749; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Sat Sep 29, 2018 4:54 am

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e-GMAT

50% of students' study science and 30% of students score more than 80% marks in the exam. If 40% of all students (science + non-science) get more than 80% marks in the exam, what percentage of non-science students score less than 80% marks?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

OA C

Source: Beat The GMAT — Problem Solving | Sat Sep 29, 2018 4:54 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 29, 2018 6:54 am

AAPL wrote:e-GMAT

50% of students' study science and 30% of students score more than 80% marks in the exam. If 40% of all students (science + non-science) get more than 80% marks in the exam, what percentage of non-science students score less than 80% marks?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

Let the total number of students = 100.

Since 50% of the students study science, the number of science students = (50/100)(100) = 50, implying that the number of non-science students = 100-50 = 50.

Since 30% of the 50 science students score more than 80%, the number of science students who score more than 80% = (30/100)(50) = 15.
Since 40% of all 100 students score more than 80%, the total number of students who score more than 80% = (40/100)(100) = 40.
Thus, the number of non-science students who score more than 80% = 40-15 = 25.

Since 25 of the 50 non-science students score more than 80%, the remaining 25 non-science students score 80% or less.
Thus:
Percentage of non-science students who score 80% or less = 25/50 = 1/.2 = 50%.

The correct answer is C.

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by Scott@TargetTestPrep » Fri Oct 19, 2018 2:27 pm

AAPL wrote:e-GMAT

50% of students' study science and 30% of students score more than 80% marks in the exam. If 40% of all students (science + non-science) get more than 80% marks in the exam, what percentage of non-science students score less than 80% marks?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

We can let the total number of students = 100. So 50 students are science students and the other 50 students are non-science students. Furthermore, 0.3 x 50 = 15 science students and 0.4 x 100 = 40 of all students score more than 80% on the exam. Therefore, 40 - 15 = 25 non-science students score more than 80% on the exam. That means 50 - 25 = 25 non-science students score less than 80% on the exam (assuming no one scores exactly 80% on the exam). So 25/50 = 50% of the non-science students score less than 80% on the exam.

Answer: C

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