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Of the final grades received by the students in a certain [#permalink]

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26 Dec 2012, 07:04

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Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 10 grades are D's. What is the number of students in the course?

Re: Of the final grades received by the students in a certain [#permalink]

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26 Dec 2012, 07:08

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Expert's post

Walkabout wrote:

Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 10 grades are D's. What is the number of students in the course?

(A) 80 (B) 110 (C) 160 (D) 200 (E) 400

1/5+1/4+1/2=19/20 of the grades are A, B, or C.

Thus the remaining 10 grades represent 1/20 of the grades. Theretofore there are 20*10=200 students.

Of the final grades received by the students in a certain [#permalink]

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20 Jan 2015, 05:04

I guess the more staightforward way to do this is giving a variable for the total number of students, say T:

Then: (1/5)T + (1/4)T + (1/2)T + 10 = T T/5 + T/4 + T/2 + 10 = T (4T + 5T + 10T) / 20 = T - 10 --> we multiplied with the LCM and moved 10 to the other side. 19T = 20 (T - 10) 19T = 20T - 200 T = 200, ANS D

Re: Of the final grades received by the students in a certain [#permalink]

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20 May 2015, 12:44

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I would rather use decimals for this question. Grades A:0,2, B:0,25, C:0,5 and the remaining(0,2+0,25+0,5=0,95) 0,05*X=10 --> So, X=200 (D) _________________

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Re: Of the final grades received by the students in a certain [#permalink]

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22 May 2015, 23:33

Expert's post

Hi All,

This question can also be solved by TESTing THE ANSWERS.

We're given data on the "breakdown" of grades in a course: 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 10 grades are D's. We're asked for the total number of students in the course.

Let's TEST Answer C: 160 students

Total = 160 1/5 are A's = 32 1/4 are B's = 40 1/2 are C's = 80 Sub-total = 152, which leaves 8 students with D's. This is TOO LOW (there are supposed to be 10 students with D's). Thus we need MORE total students. Eliminate Answers A, B and C.

Since 8 is relatively close to 10, we probably don't need that many more students, so let's TEST D next....

Answer D: 200 students

Total = 200 1/5 are A's = 40 1/4 are B's = 50 1/2 are C's = 100 Sub-total = 190, leaving 10 for D's. This is a MATCH for what we were told, so this MUST be the answer.

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