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Of the final grades received by the students in a certain

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Of the final grades received by the students in a certain [#permalink] New post 26 Dec 2012, 06:04
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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?

(A) 80
(B) 110
(C) 160
(D) 200
(E) 400
[Reveal] Spoiler: OA
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Re: Of the final grades received by the students in a certain [#permalink] New post 26 Dec 2012, 06:08
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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.

Answer: D.
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Re: Of the final grades received by the students in a certain [#permalink] New post 17 Mar 2014, 22:00
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Let total number of students be t.

Then
1/5t + 1/4t + 1/2t + 10 = t
solve
10 = t - 1/5t - 1/4t - 1/2t
10 = 1/20t
200 = t

Answer D.
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Of the final grades received by the students in a certain [#permalink] New post 20 Jan 2015, 04:04
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
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Of the final grades received by the students in a certain [#permalink] New post 20 Jan 2015, 19:58
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HI All,

If you plan to take a "math approach" to this question, you might find that converting the fractions to decimals saves you some work:

1/5 = .2 are As
1/4 = .25 are Bs
1/2 = .5 are Cs
X = Total grades given

Sub-Total = .95(X) of the grades are A/B/C, so the other .05(X) are Ds

.05(X) = 10
5X = 1,000
X = 200

Final Answer:
[Reveal] Spoiler:
D


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Re: Of the final grades received by the students in a certain [#permalink] New post 20 May 2015, 11:44
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] New post 22 May 2015, 22:33
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.

Final Answer:
[Reveal] Spoiler:
D


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Re: Of the final grades received by the students in a certain   [#permalink] 22 May 2015, 22:33
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