OG 13 question 66. Ratio and Proportion

[red217]

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

( i would appreciate if someone could help me solve it the way Manhattan Gmat Guide 1 tells us to)
Thanks

[nephicheng]

I would suggest you read the Manhattan Guide #4, Word Translations. It goes in to great detail on how to solve ratio problems. This ratio problem is easier to solve if you create a matrix.

Here is an example with the given information:

First graders | Second graders | Third graders | Fourth grader
----------------------8--------------------------------5------
-------3--------------4---------------------------------------
---------------------------------------3---------------2------
--------------------------------------------------------------
From here we can change the numbers but keep the same ratios. Since 3 to 4 is the same as 6 to 8 we can consolidate.

First graders | Second graders | Third graders | Fourth grader
------6---------------8--------------------------------5------
--------------------------------------3----------------2------
Then we can consolidate.

First graders | Second graders | Third graders | Fourth grader
------6---------------8--------------------------------5------
--------------------------------------15--------------10------
This then turns to:

First graders | Second graders | Third graders | Fourth grader
-----12---------------16--------------15---------------10-----

First graders = 12 and Third graders = 15. 12/15 = 4/5, E.

I hope this helps.

[GMATGuruNY]

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

1st/3rd = 1st/2nd * 2nd/4th * 4th/3rd.

In the equation above, all of the values in red cancel out.
Thus:
1st/3rd = 3/4 * 8/5 * 2/3 = 4/5.

The correct answer is E.