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Arithmetic Ratio and Proportion (OG 12th Prob. Solving #66)

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by dheaven1 » Tue Mar 16, 2010 9:08 pm
66. 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

The OG explanation is extremely complicated...is there any easier way to do this?
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by kstv » Tue Mar 16, 2010 9:37 pm
Try to bring them to a common level. Eg 1) Ratio of II grade to IV is 8 : 5.
2) I grade to II grade is 3 : 4 no harm in saying 6: 8 (multiplying by 2) so that in (1) & (2) Grade II is 8 and we can combine (1) & (2) and say
3) I : II : IV = 6: 8: 5
4) III : IV is 3 : 2 how to compare II and IV multiply 3) with 2 and IV with 5
3) I:II:IV = 12:16:10 and 4) III : IV is 15 : 10 combine (3) and (4)
5) I:II:III:IV = 12:16:15:10 so I: II is 12:15
12/15 = 4 to 5
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by papgust » Tue Mar 16, 2010 9:44 pm
Moved to Problem Solving!
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by halai82 » Wed Mar 17, 2010 9:31 am
You could use proportional method (similar Percentage).

I drew a table and filled up the empty boxes using above method (It keeps me on track), TIME is important.

My workings are:

1) 2nd : 4th = 8:5
2) 1st : 2nd = 3:4
3) 3rd : 4th = 3:2

need, 1st : 3rd.

Get 2nd : 3rd using (5/2) i.e 8/(5/2) = 16/5. Ratio 16/5:3
Get 1st : 2nd using (4/3) i.e (16/5)/(4/3) = 48/20

which is give us, 1st : 3rd ratio of (48/20):3
Take 20 on the other side making it 48:60 and then just remove the common factors => 4:5.

Thanks
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by this_time_i_will » Wed Mar 17, 2010 6:49 pm
took me 1.30 minutes.
what should be the average time to sove these type of questions.
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by rameshbec » Thu Mar 18, 2010 4:36 am
this_time_i_will wrote:took me 1.30 minutes.
what should be the average time to sove these type of questions.

less than 30 sec
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by rameshbec » Thu Mar 18, 2010 4:37 am
this_time_i_will wrote:took me 1.30 minutes.
what should be the average time to sove these type of questions.

less than 30 sec
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by halai82 » Thu Mar 18, 2010 10:40 am
Everyone is unique and have different weakness and strenght. I would suggest you should spend slightly more time on your weak topics and slightly less time on your strenght topics.

But try to practise more questions on your weaker topics to gain speed. Difficult questions will be taken care off in this way too.

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by Cb » Thu Apr 22, 2010 5:57 am
@dheaven1...

hii.. :)
Try this...

a:b:c:d be the no. of graders...

now we have....
1)a:b=3:4
2)c:d=3:2
3)b:d=8:5

what we want is.. a:c

and a:c=(a:b)*(d:c)*(b:d)=(3:4)*(2:3)*(8:5)=4:5....

its the ans...if u r good at calculation it will just take 15 sec to solve this....near about the the time as much i took... :D
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by ps63739 » Thu Apr 22, 2010 6:05 pm
Cb wrote:@dheaven1...

hii.. :)
Try this...

a:b:c:d be the no. of graders...

now we have....
1)a:b=3:4
2)c:d=3:2
3)b:d=8:5

what we want is.. a:c

and a:c=(a:b)*(d:c)*(b:d)=(3:4)*(2:3)*(8:5)=4:5....

its the ans...if u r good at calculation it will just take 15 sec to solve this....near about the the time as much i took... :D
Can we do what you mentioned for similar type of questions? Or in better terms, is it proven to be true in all type of questions, where we have to manipulate ratios?
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by tpr-becky » Thu Apr 22, 2010 8:47 pm
yes, when you manipulate ratios you can cross cancel in the same way you would do with fractions.
Becky
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