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In a certain school, the ratio of the number of first graders to the
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05 Aug 2022, 01:30
05 Aug 2022, 01:30
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Question Stats:
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In a certain school, the ratio of the number of first graders to the number of third-graders is 12 to 5 and the ratio of the number of fourth-graders to the number of first-graders is 8 to 9. If the ratio of the number of second graders to the number of third-graders is 16 to 15, what is the ratio of the number of second graders to the number of fourth graders?
A. 1 to 2
B. 225 to 512
C. 25 to 72
D. 2 to 1
E. 72 to 25
Are You Up For the Challenge: 700 Level Questions
A. 1 to 2
B. 225 to 512
C. 25 to 72
D. 2 to 1
E. 72 to 25
Are You Up For the Challenge: 700 Level Questions
Re: In a certain school, the ratio of the number of first graders to the
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05 Aug 2022, 05:15
05 Aug 2022, 05:15
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Given :
1st / 3rd = 12/5, …..Ratio 1
4th/1st = 8/9 ………ratio 2
3rd/2nd = 15/16 (Reciprocal of what is given in Q ) ……..Ratio 3
2nd/ 4th =?
Multiply num and den of Ratio 1 by 3 and get = 1st/3rd = 36/15
Now using modified ratio 1 and Ratio 3 we get
1st : 2nd : 3rd : 4th = 36 : 16 : 15 : __.........(Equation 1 )
Now we know 4th/1st = 8/9 (from Q) , multiply den and num by 4 to get 4th/1st = 32/36
Substitute in equation 1 and get ratio of 2nd / 4th = ½
1st / 3rd = 12/5, …..Ratio 1
4th/1st = 8/9 ………ratio 2
3rd/2nd = 15/16 (Reciprocal of what is given in Q ) ……..Ratio 3
2nd/ 4th =?
Multiply num and den of Ratio 1 by 3 and get = 1st/3rd = 36/15
Now using modified ratio 1 and Ratio 3 we get
1st : 2nd : 3rd : 4th = 36 : 16 : 15 : __.........(Equation 1 )
Now we know 4th/1st = 8/9 (from Q) , multiply den and num by 4 to get 4th/1st = 32/36
Substitute in equation 1 and get ratio of 2nd / 4th = ½
Re: In a certain school, the ratio of the number of first graders to the
[#permalink]
05 Aug 2022, 10:29
05 Aug 2022, 10:29
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Expert Reply
Bunuel wrote:
In a certain school, the ratio of the number of first graders to the number of third-graders is 12 to 5 and the ratio of the number of fourth-graders to the number of first-graders is 8 to 9. If the ratio of the number of second graders to the number of third-graders is 16 to 15, what is the ratio of the number of second graders to the number of fourth graders?
A. 1 to 2
B. 225 to 512
C. 25 to 72
D. 2 to 1
E. 72 to 25
A. 1 to 2
B. 225 to 512
C. 25 to 72
D. 2 to 1
E. 72 to 25
First:Third = 12:5
First:Fourth = 9:8
Second:Third = 16:15
We need to figure out multiples of those such that we can link them together. That is, if we multiply First:Third by 3, we get 36:15, which matches up with the 15 Thirds in Second:Third. Now, if we multiply First:Fourth by 4, we get 36:32, which matches up with the 36 Firsts in First:Third. We now have:
First:Third = 36:15
First:Fourth = 36:32
Second:Third = 16:15
36 first-graders, 16 second-graders, 15 third-graders, and 32 fourth-graders satisfies our ratios.
16:32 = 1:2
Answer choice A.
