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At a certain school, the ratio of the number of second grade [#permalink]
27 Feb 2012, 09:02

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Difficulty:

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Question Stats:

78% (03:11) correct
21% (02:27) wrong based on 197 sessions

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

Re: At a certain school, the ratio of the number of second grade [#permalink]
27 Feb 2012, 12:17

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Expert's post

BANON 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

Let # of first, second, third and fourth graders be A, B, C and D respectively. Question: \frac{A}{C};

Given: \frac{B}{D}=\frac{8}{5}, \frac{A}{B}=\frac{3}{4}, and \frac{C}{D}=\frac{3}{2};

Re: At a certain school, the ratio of the number of second grade [#permalink]
22 Apr 2012, 01:31

Expert's post

BN1989 wrote:

How can you solve this with an unknown multiplier?

let a=1st b=2nd c=3rd and d=4th graders

b/d=8/5 or b=8x and d=5x

so we get a=3/4*(8x)=6x and c=15/2*x

which obviously is not correct, why can't I apply this concept here?

Actually it's a perfectly valid approach. You've done everything right, there is just one final step missing: A/C=(6x)/(15x/2)=12/15=4/5.
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Re: At a certain school, the ratio of the number of second grade [#permalink]
12 Jun 2013, 00:36

1

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BANON 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 / Four = 8/5 First / Second = 3/4 Third / Four = 3/2

==> First = 3/4 Second = 3/4 (8/5 four) = 3/4 * 8/5 * (2/3 Third) = 4//5 Third ==> First / Third = 4/5

E is correct
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