Did not understand the solution to this Ratio problem

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madhan_dc: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Mon Jan 24, 2011 1:37 pm

by madhan_dc » Fri Jan 28, 2011 6:13 pm

Problem: A students grade in a course is determined by 4 quizzes and one exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade if determined by the exam?

can someone please explain a solution.

answer is 1/3

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Source: Beat The GMAT — Problem Solving | Fri Jan 28, 2011 6:13 pm

stormier: Master | Next Rank: 500 Posts; Posts: 139; Joined: Fri Nov 26, 2010 4:45 pmFollowed by: 1 member; Location: Boston; Thanked: 20 times; GMAT Score:720

by stormier » Fri Jan 28, 2011 6:33 pm

madhan_dc wrote:Problem: A students grade in a course is determined by 4 quizzes and one exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade if determined by the exam?

can someone please explain a solution.

answer is 1/3

The problem says that an exam counts twice as much as a quiz. In other words, the weighting for exam is twice that of the quiz.

So if the student takes total of 4 quizzes and 1 exam, one can say that he took 6 quizzes (all of equal importance or weighting)

Out of these 6 quizzes which count equally towards the grade, 2 are determined by the exam.

Thus required fraction = 2q/(4q+1e) = 2q/(4q+2q) = 1/3

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jan 29, 2011 12:48 am

madhan_dc wrote:Problem: A students grade in a course is determined by 4 quizzes and one exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade if determined by the exam?

One exam is equivalent to two quizzes.
Hence, total = (1 exam + 4 quizzes) = 6 quizzes

Required fraction = (1 exam)/(total) = (2 quizzes)/(6 quizzes) = 1/3

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pesfunk: Master | Next Rank: 500 Posts; Posts: 286; Joined: Tue Sep 21, 2010 5:36 pmFollowed by: 5 members; Location: Kolkata, India; Thanked: 11 times

by pesfunk » Sat Jan 29, 2011 2:57 am

Let the weight of one quiz be X

So total weight of all 4 quizzes = 4X

Weight of Exam = 2X (Given)

So total weight = 4X + 2X = 6X

Answer = 2X / 6X = 1/3

madhan_dc wrote:Problem: A students grade in a course is determined by 4 quizzes and one exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade if determined by the exam?

can someone please explain a solution.

answer is 1/3

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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 Jan 29, 2011 3:57 am

madhan_dc wrote:Problem: A students grade in a course is determined by 4 quizzes and one exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade if determined by the exam?

can someone please explain a solution.

answer is 1/3

An easy and efficient approach would be to plug in values that satisfy the conditions given.

Let quiz = 1 point, exam = 2 points.
Quiz points = 4*1 = 4.
Exam points = 1*2 = 2.
Total points = 4+2 = 6.
Exam/total = 2/6 = 1/3.

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madhan_dc: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Mon Jan 24, 2011 1:37 pm

by madhan_dc » Sat Jan 29, 2011 5:47 am

Thank you all.

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