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totals 510
The ratio of students to teachers is 16 to 1.
Total students = 480
Total Teachers = 30
Kindergarten students = 480/5 =>96
fifth and sixth graders = 480-96=>384/3 =>128
first and second grades = 480/4 = 120
third and fourth grades=(480-(128+120+96))/2 =>68
so its 28 fewer

C

/Prabu
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C
Good one, but took me a while...
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crejoc
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

A. 12 greater
B. 17 fewer
C. 28 fewer
D. 36 fewer
E. 44 fewer

This problem is way too long. I don't know if we will see something like this on GMAT. But just in case, has anyone found a shorter/faster way to solve this?

Cheers!
J :)
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Ans C.

Took time for the calculations. Exceeded 2min. :(
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crejoc
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

A. 12 greater
B. 17 fewer
C. 28 fewer
D. 36 fewer
E. 44 fewer

Official Explanation:
We know that the student to teacher ratio at the school is 16 to 1, and the total number of people is 510.
Therefore: Number of students = (16/17)(510) = 480 and Number of teachers = (1/17)(510) = 30
Kindergarten students make up 1/5 of the student population, so: Number of kindergarten students = (1/5)(480) = 96

Fifth and sixth graders account for 1/3 of the remainder (after kindergarten students are subtracted from the total),
therefore: Number of 5th and 6th grade students = (1/3)(480 – 96) = (1/3)(384) = 128 Students

first and second grades account for 1/4 of all the students,
so: Number of 1st and 2nd grade students = (1/4)(480) = 120

So far, we have accounted for every grade but the 3rd and 4th grades, so they must consist of the students left over:
Number of 3rd and 4th grade students = Total students – students in other grades
Number of 3rd and 4th grade students = 480 – 96 – 128 – 120 = 136

If there are an equal number of students in the third and fourth grades, then: Number of 3rd grade students = 136/2 = 68

The number of students in third grade is 68, which is fewer than 96, the number of students in kindergarten.
The number of students in 3rd grade is thus 96 – 68 = 28 fewer than the number of kindergarten students.
The correct answer is C.
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17x=510
x=30

30 teachers
480 students
- 96 kindergarten
- 4/15*480=128 fifth and sixth graders
- 120 first and second grades
- 68 third graders
- 68 fourth graders

Answer C
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crejoc
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

A. 12 greater
B. 17 fewer
C. 28 fewer
D. 36 fewer
E. 44 fewer

We can let x = the number of teachers; thus, 16x = the number of students, and we have:

x + 16x = 510

17x = 510

x = 30

So there are 16(30) = 480 students at the school. We see that 1/5(480) = 96 are kindergarten students and 1/3(480 - 96) = 1/3(384) = 128 are 5th and 6th graders.

Furthermore, 1/4(480) = 120 are 1st and 2nd graders.

So we have 480 - 96 - 128 - 120 = 136 3rd and 4th graders.

Since 3rd and 4th graders have an equal number of students, there are 136/2 = 68 3rd graders.

Thus, there are 96 - 68 = 28 fewer 3rd graders than kindergarten students.

Answer: C
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It took me 5 minutes to solve this problem crejoc, Is there a faster way and how much others have taken?

crejoc
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

A. 12 greater
B. 17 fewer
C. 28 fewer
D. 36 fewer
E. 44 fewer
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