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# Ratio problems - quick & easy method to solve - need verification!

Author Message
Intern
Joined: 04 Oct 2017
Posts: 1
Ratio problems - quick & easy method to solve - need verification!  [#permalink]

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04 Oct 2017, 09:26
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 3 sessions

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As I was practicing I came across the following question:

At a certain school, the ratio of students to teachers is 3:5, and the ratio of teachers to administrators is 4:5. Which of the following could be the total number of students at the school? (Indicate all that apply):

A. 150
B. 180
C. 200
D. 240
E. 300

I got the right answer, but my method was somewhat convoluted. The explanation offered by the website seems much easier (especially because these types of ratio problems confuse me). This their explanation:

The Correct answers are B, D, and E. Whenever a question provides multiple ratios with a common element, manipulate the ratios so that the common element has the same value in both ratios. In this case, the common element is teachers, so we should manipulate the ratios so that the number of teachers is the least common multiple of 5 and 4: 20. In the first ratio: students/teachers = 3/5 = 12/20. In the second ratio: teachers/administrators = 4/5 = 20/25. The ratio of students to teachers to administrators is thus 12:20:25. The number of students must therefore be a multiple of 12. Any choice that is a multiple of 12 is a potential value for the number of students. The correct answer is B, D, and E.

The bold part of the explanation is the part that I don't fully buy because I can't come up with the logic for why that must be the case. Can anyone verify (and perhaps attempt to explain why) that this is a valid method and will always work for this type of question.

Much appreciated!

--== Message from the GMAT Club Team ==--

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This discussion does not meet community quality standards. It has been retired.

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Math Expert
Joined: 02 Sep 2009
Posts: 50670
Re: Ratio problems - quick & easy method to solve - need verification!  [#permalink]

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04 Oct 2017, 09:41
tkfull wrote:
As I was practicing I came across the following question:

At a certain school, the ratio of students to teachers is 3:5, and the ratio of teachers to administrators is 4:5. Which of the following could be the total number of students at the school? (Indicate all that apply):

A. 150
B. 180
C. 200
D. 240
E. 300

I got the right answer, but my method was somewhat convoluted. The explanation offered by the website seems much easier (especially because these types of ratio problems confuse me). This their explanation:

The Correct answers are B, D, and E. Whenever a question provides multiple ratios with a common element, manipulate the ratios so that the common element has the same value in both ratios. In this case, the common element is teachers, so we should manipulate the ratios so that the number of teachers is the least common multiple of 5 and 4: 20. In the first ratio: students/teachers = 3/5 = 12/20. In the second ratio: teachers/administrators = 4/5 = 20/25. The ratio of students to teachers to administrators is thus 12:20:25. The number of students must therefore be a multiple of 12. Any choice that is a multiple of 12 is a potential value for the number of students. The correct answer is B, D, and E.

The bold part of the explanation is the part that I don't fully buy because I can't come up with the logic for why that must be the case. Can anyone verify (and perhaps attempt to explain why) that this is a valid method and will always work for this type of question.

Much appreciated!

Please post GRE questions on GRE site: http://greprepclub.com/

GRE quantitative section: http://greprepclub.com/forum/gre-quanti ... section-3/

Hope it helps.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: Ratio problems - quick & easy method to solve - need verification! &nbs [#permalink] 04 Oct 2017, 09:41
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