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

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Senior Manager
Joined: 28 Jun 2007
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At a certain school, the ratio of the number of second [#permalink]  02 Sep 2007, 09:24
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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
Manager
Joined: 02 Jul 2007
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I get E

Second/Fourth=8/5 ----> 5(Second)=8(Fourth)
First/Second=3/4 -----> 4(First)=3(Second)
Third/Fourth=3/2 -----> 2(Third)=3(Fourth)

Want to find First/Third

2(Third)=3(Fourth) -> 2(Third)/3=Fourth
5(Second)=8(Fourth)-> 5(Second)=8[2(Third)/3] -> Second=16(Third)/15
4(First)=3(Second) -> 4(First)=3[16(Third)/15]

4(First)=[16(Third)/5]
First=[4(Third)/5]
First/Third=4/5
GMAT Club Legend
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This question can be broken down as:
2nd:4th = 8:5
1st:2nd = 3:4
3rd:4th = 3:2
1st:3rd = ?:?

Then 1st/2nd * 2nd/4th = 1st/4th = 6/5
1st/4th * 4th/3rd = 1st/3rd = 6/5 * 2/3 = 4/5

Ans E
Manager
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Q: 1st __ 2nd __ 3rd __ 4th

1) - __ 8 __ - __ 5
2) 3 __ 4 __ - __ - [to receive 2) from 1) we should devide 1) by 2]
so 3 __ 4 __ - __ 2*1/2
3) - __ - __ 3 __ 2 [to equalize 2) and 3) we need to *4/5 in order to receive 2 from 2*1/2]
so 12/5 __ 16/5 __ 3 __ 2 [multiplying by 5]
so 12 __ 16 __ 15 __ 10

1st/3rd = 12/15 = 4/5

Anw. is E
Director
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Let
N1 = Number of first graders
N2 = Number of second graders
N3 = Number of third graders
N4 = Number of fourth graders
Given:
N2 / N4 = 8/5
N1/N2 = 3/4
N3/N4 = 3/2
N1/N3 = N1/N2 * N2/N4 * N4/N3
= 3/4 * 8/5 * 2/3 = 4/5

Director
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Re: PS - Set 1, Math 33 [#permalink]  03 Sep 2007, 01:08
gluon 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

I got E

There is very good explanation above with N1, N2......s
Senior Manager
Joined: 28 Jun 2007
Posts: 320
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OA is indeed E

That is an excellent explanation Hanumayamma. I have no idea why my brain froze while trying to do such a simple problem.
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