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# At a certain school, the ratio of the number of second

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At a certain school, the ratio of the number of second [#permalink]  04 Feb 2008, 22:43
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5
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Re: Quants: Ratio [#permalink]  04 Feb 2008, 22:52
Ans E -> 4 to 5

First to Fourth graders is => First to Second * Second to Fourth
=> 1/2 * 2/4 => First to Fourth =>6/5

Four to Third => inverse of third to four => 2/3

First to Third is => First to Fourth * Fourth to Third
=>1/4 * 4/3=> 6/5*2/3=>4/5
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Re: Quants: Ratio [#permalink]  04 Feb 2008, 23:08
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

(A)
the overall ratio is 48 : 64 : 45 : 30
so 48 : 45 = 16 : 15
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Re: Quants: Ratio [#permalink]  05 Feb 2008, 03:48
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

Second to Fourth: 8:5
First to Second: 3:4
Third to Fourth: 3:2

First:Second:Fourth = 3:4:8:5 = 6:8:5
Third to Fourth: 3:2

First:Fourth:Third = 6:5:2:3 = 12:10:15
First to Third: 12:15 or 4:5

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Re: Quants: Ratio [#permalink]  05 Feb 2008, 06:19
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

fourth/third = 1/(third/fourth)=2/3
first/third = (first/second)*(second/fourth)*(fourth/third) = (3/4)*(8/5)*(2/3)=(3*8*2)/(4*5*3)=16/20=4/5 -> E
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Re: Quants: Ratio [#permalink]  05 Feb 2008, 08:52
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

N=1st
X=2nd
Z=3rd
Y=4th

x/y=8/5 n/x=3/4 z/y=3/2 n/z=? --> n=3x/4 z=3y/2 --> y=5x/8 ---> z=15x/16

(3x/4)/(15x/16) --> 16/5*4 --> 16/20 --> 4/5

E
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Re: Quants: Ratio [#permalink]  05 Feb 2008, 09:13
OA is E.

1:2:4:3 = 12:16:10:15

1:3 = 12:15 = 4:5
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Re: Quants: Ratio [#permalink]  05 Feb 2008, 09:18
incognito1 wrote:
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

(A)
the overall ratio is 48 : 64 : 45 : 30
so 48 : 45 = 16 : 15

Doh! Took first year students to fourth year students as 8:5.. answer is (E)
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Re: Quants: Ratio [#permalink]  06 Feb 2008, 17:29
GMATBLACKBELT wrote:
suntaurian wrote:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

N=1st
X=2nd
Z=3rd
Y=4th

x/y=8/5 n/x=3/4 z/y=3/2 n/z=? --> n=3x/4 z=3y/2 --> y=5x/8 ---> z=15x/16

(3x/4)/(15x/16) --> 16/5*4 --> 16/20 --> 4/5

E

i personally like this approach; it just makes sense to me !
Re: Quants: Ratio   [#permalink] 06 Feb 2008, 17:29
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