At Jefferson Elementary School, the number of teachers and s

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

C
Good one, but took me a while...

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

Ans C.

Took time for the calculations. Exceeded 2min.

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.

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

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