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.
Total students
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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
X/5 + X/4 +X/2 + 10 = X
solving for X ; X = 200
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We can let T = Total number of students in the math course and create the equation: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
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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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
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