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Total students

This topic has 2 expert replies and 2 member replies

Total students

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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


plz suggest time saving way to solve this.

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Saurabh Mahajan

I can understand you not winning,but i will not forgive you for not trying.

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IMO back solving will be a killer when compared to Algebraic way..Better I shall stick to Algebraic way :

X/5 + X/4 +X/2 + 10 = X

solving for X ; X = 200

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gmatmachoman wrote:
IMO back solving will be a killer when compared to Algebraic way..Better I shall stick to Algebraic way :

X/5 + X/4 +X/2 + 10 = X

solving for X ; X = 200
Thank you very much............

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saurabhmahajan 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
We can let T = Total number of students in the math course and create the equation:

1/5(T) + 1/4(T) + 1/2(T) + 10 = T

We can multiply the entire equation by 20 to cancel out the denominators of the fractions, and we have:

4T + 5T + 10T + 200 = 20T

19T + 200 = 20T

200 = T

Alternate Solution:

We can account for (20% + 25% + 50%) = 95% of the students for grades A through C, inclusive. This leaves 5% of the students that received a D, and this equates to 10 students. We can set up a simple proportion, where x = the total number of students in the course:

5/10 = 100/x

5x = 1000

x = 200

Answer: D

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Jeffrey Miller Head of GMAT Instruction

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Hi All,

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. This question can also be solved by TESTing THE ANSWERS. To start, we need a number that can be evenly divided into 1/5s and 1/4s, so Answer B can be eliminated immediately.

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: D

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

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Contact Rich at Rich.C@empowergmat.com

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