At Jefferson Elementary School, the number of teachers and s : GMAT Problem Solving (PS)
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# At Jefferson Elementary School, the number of teachers and s

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Senior Manager
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At Jefferson Elementary School, the number of teachers and s [#permalink]

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09 Aug 2009, 07:57
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Difficulty:

55% (hard)

Question Stats:

73% (03:46) correct 27% (03:08) wrong based on 204 sessions

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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
[Reveal] Spoiler: OA
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Re: fractions school [#permalink]

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09 Aug 2009, 08:10
1
KUDOS
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
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Re: fractions school [#permalink]

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09 Aug 2009, 08:12
[quote="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?
12 greater
17 fewer
28 fewer
36 fewer
44 fewer
total = 510 , global ratio is 16:1 ie : 480 student , 30 teacher

KG = 96, 5TH+6TH = 128, 1ST+2ND = 120 THUS, 3RD+4TH = 136 EACH ACCOUNTS FOR 68

96-68= 28 FEWER
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Re: fractions school [#permalink]

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11 Aug 2009, 10:02
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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Re: fractions school [#permalink]

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04 Sep 2009, 10:13
C
Good one, but took me a while...
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Re: At Jefferson Elementary School, the number of teachers and s [#permalink]

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13 Nov 2013, 07:12
crejoc wrote:
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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Re: At Jefferson Elementary School, the number of teachers and s [#permalink]

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13 Nov 2013, 10:55
Ans C.

Took time for the calculations. Exceeded 2min.
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Re: At Jefferson Elementary School, the number of teachers and s [#permalink]

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07 Dec 2016, 15:47
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Re: At Jefferson Elementary School, the number of teachers and s   [#permalink] 07 Dec 2016, 15:47
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# At Jefferson Elementary School, the number of teachers and s

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