ratios

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mariah: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Aug 05, 2008 3:28 pm; Thanked: 2 times

by mariah » Mon Mar 21, 2011 2:03 am

In a school, the ratio of the number of second grade students to fourth grade students is 3 to 2, the ratio of the first grade students to second grade students is 1 to 3, the ratio of the third grade students to fourth grade students is 1 to 3. What is the ratio of first grade students to third grade students?

4/5
3/2
9/4
3/7
1/2

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Source: Beat The GMAT — Problem Solving | Mon Mar 21, 2011 2:03 am

gmatscottsdale: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Mon Mar 21, 2011 2:12 am; GMAT Score:740

by gmatscottsdale » Mon Mar 21, 2011 2:19 am

Here's the solution:

Second/Fourth = 3/2, First/Second = 1/3, Third/Fourth = 1/3

First/Third = ?

We need to manipulate the ratios given to get to our answer. My strategy would be to multiply the given ratios to get to our answer and cancel terms that we don't need. Since our answer needs First in numerator and Third in denominator, I start with First/Second = 1/3. I need to get rid of Second in First/Second = 1/3, so I multiply this with Second/Fourth. I need to find a suitable ratio equation where I can get rid of Fourth from the ratio we just multipled. Unfortunately, the only equation left is Third/Fourth and it has Fourth in the denominator. However, we can flip is from:

Third/Fourth = 1/3 to Fourth/Third = 3/1. Now, we could multiple Second/Fourth with Fourth/Third and we will end up canceling Fourth in the numerator and having Third in the denominator as we desired earlier.

Hence,

First/Third = First/Second * Second/Fourth * Fourth/Third = 1/3 * 3/2 * 3/1 = 9/6 = 3/2

Credited answer would be B.

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Mon Mar 21, 2011 2:20 am

Assume that there is one 1st grade student, and work the problem sentence by sentence.

ratio of first to 2nd is 1:3, so there are 3 2nd grade students.

the ratio of 2nd grade to fourth grade is 3:2, so we need 2 fourth graders for the 3 2nd graders.

The ratio of third to fourth is 1:3. If we have 2 fourth graders, then we have 2/3 thrd graders (a third of the fourth graders).

So the ratio of first to third graders is 1:2/3. Put as a fraction, that is 1/2/3 = 3/2.

Geva
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 21, 2011 3:02 am

mariah wrote:In a school, the ratio of the number of second grade students to fourth grade students is 3 to 2, the ratio of the first grade students to second grade students is 1 to 3, the ratio of the third grade students to fourth grade students is 1 to 3. What is the ratio of first grade students to third grade students?

4/5
3/2
9/4
3/7
1/2

dont have oa
[spoiler]imo 3/2[/spoiler]

To combine ratios the element common to each ratio must be represented by the same value.

2nd:4th = 3:2
3rd:4th = 1:3
Common element is 4th. Since 2*3 = 6, convert the ratios so that 4th = 6:
2nd:4th = 3:2 = 9:6.
3rd:4th = 1:3 = 2:6.
Thus, 2nd:3rd:4th = 9:2:6.

Converted 2nd:4th = 9:6.
1st:2nd = 1:3
Common element is 2nd. Convert the bottom ratio so that 2nd = 9:
1st:2nd = 1:3 = 3:9.

Thus, 1st:2nd:3rd:4th = 3:9:2:6.
1st:3rd = 3:2.

The correct answer is B.

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