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?
12 greater
17 fewer
28 fewer
36 fewer
44 fewer

Soln>> from the given ratio of 16:1 u can derive that ter are 480 students

KG= 1/5 * 480 =96

5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)

1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)

equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)

thus 96-68 =28>>> therfore answer is 28 fewer

C

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

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

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.

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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