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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 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
Math Expert
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Re: Of the final grades received by the students in a certain [#permalink]  26 Dec 2012, 06:08
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Expert's post
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.

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Kudos [?]: 26 [2] , given: 19

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

Senior Manager
Status: Math is psycho-logical
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GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
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Kudos [?]: 73 [0], given: 169

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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Kudos [?]: 1583 [1] , given: 152

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Expert's post
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

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

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ Director Joined: 10 Mar 2013 Posts: 602 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Followers: 7 Kudos [?]: 97 [1] , given: 200 Re: Of the final grades received by the students in a certain [#permalink] 20 May 2015, 11:44 1 This post received KUDOS 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) _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 5577 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 224 Kudos [?]: 1583 [0], given: 152 Re: Of the final grades received by the students in a certain [#permalink] 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 GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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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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