Problem Solving

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

(A) 5
(B) 8
(C) 10
(D) 12
(E) 15

As with most ratio questions, the key is to express all values in terms of the same variable (the ratio multiplier). For instance, if the ratio of students to teachers is 30 to 1, we can call 30x the number of students and x the number of teachers.

The OA is E. 3 distinct solution strategies and a take-away lesson are attached. Those who cannot see the attachment can read it here. Look at the reference section of the book to ID similar OG problems.

Hope that helps,
-Patrick

Thanks for the 3 thorough explanations. please explain further how to find similar problems? I don't find such listing in the OG.

You're welcome!

Sorry I wasn't more clear. the reference section of the OG Companion has a topic/difficulty matrix for all OG questions. If you use the OG to study, you can use that matrix to organize said study. For instance if ratio questions such as the one you posted tend to give you a hard time, look up and try other ratio questions to strengthen your ability in that area; you can also use the matrix to maintain different topic/specific logs of your progress.

-Patrick

Maybe I'll checkout the GMATFix OG Companion book. seems very useful. How does it compare to Manhattan GMAT's book?

Hi Patrick

Thanks for your explanation. I have a quick Q if you dont mind.

If we set the first ratio as 30t and t why dont we use a variable in the 2nd ratio (25:1). Why do we refer to them as integers (25:1) instead of 25x:1x?

Thanks

gmatruler wrote:The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

(A) 5
(B) 8
(C) 10
(D) 12
(E) 15

We can plug in the answers, which represent the number of teachers.
Since all of the numbers in the problem are multiples of 5, the correct answer also is likely to be a multiple of 5.

Answer choice C: 10 teachers.
30:1 = 300:10, implying 300 students.
Students increased by 50 = 300+50 = 350.
Teachers increased by 5 = 10+5 = 15.
350:15 = 70:3.
The needed ratio is 25:1 = 75:3.
Since 75:3 > 70:3 -- implying more distance between the number of students and the number of teachers -- the correct answer must be bigger.

Answer choice E: 15 teachers.
30:1 = 450:15, implying 450 students.
Students increased by 50 = 450+50 = 500.
Teachers increased by 5 = 15+5 = 20.
500:20 = 25:1.
Success!

The correct answer is E.

Plugging in the answer choices is the approach that I took. It is a personal conscious decision to use the information available rather than going for the equations with the ratios.

Feels good to see that this approach has been suggested by an Expert as well.

I am not sure if I might get a response back to my query but I will go ahead and post it. While plugging in answers, I normally use C first then move to either A or E based on answer to C. Sometimes this approach takes time if I end up choosing A after C and the answer was D. Other than practice and judging from the answer of choice C is there any other way for selecting between A and E after C?