Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The present ratio of students to teachers at a certain [#permalink]
26 Mar 2012, 02:48

1

This post received KUDOS

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

80% (02:28) correct
20% (02:05) wrong based on 653 sessions

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?

Re: Slightly embarrasing [#permalink]
26 Mar 2012, 03:02

10

This post received KUDOS

Expert's post

9

This post was BOOKMARKED

Impenetrable 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 ?

5 8 10 12 15

This might be really embarrasing, since I normally score Q47 or higher, but this question really made me stumble.

What is wrong with my approach (I always use this approach on ratio questions and it normally works well):

Plug in E:

25:1 is the new ratio -> 1 = 1*15 = 15 teachers and 25 = 25*15 = 375 students

15 - 5 = 10 teachers before the increase 375 - 50 = 325 students before the increse

so the old ratio is 325 : 10 which is unequal to 30:1

Where is my mistake?

PS. No need to tell me others ways how to solve it. I am familiar with the 'equations ways'.

Cheers a lot and I am happy ti give away Kudos Lars

The very first step is not correct: the present ratio of students to teachers is 30 to 1, not 25 to 1. So if you want to plug t=15 you should use 30:1 ratio, not 25:1.

Complete solution:

Given: \(\frac{s}{t}=\frac{30x}{x}\) and \(\frac{30x+50}{x+5}=\frac{25}{1}\). Solve \(\frac{30x+50}{x+5}=\frac{25}{1}\) for \(x\) --> \(x=15\) --> \(t=x=15\).

Re: The present ratio of students to teachers at a certain [#permalink]
26 Mar 2012, 03:16

2

This post received KUDOS

1

This post was BOOKMARKED

+1 E

Here's what I did s/t = 30/1 => s=30T

S+50/t+5 = 25/1

Substitute S=30T in the above equation

30t+50 = 25t+125

5t = 75 t=15

I hope this helps. By the way I was facing the same situation & it helps if you just take a break. I couldnt even recognise simple s v errors :-p _________________

Giving +1 kudos is a better way of saying 'Thank You'.

Re: The present ratio of students to teachers at a certain [#permalink]
25 Oct 2012, 01:28

I actually thought it would be easier to tackle this problem by plugging in the answers choices, but I was VERY wrong, it's just tedious and prone to errors for this exercise.

Straight algebra saves you at least 1 full minute and it's very simple in this case.

Thanks to Bunuel for the clarifications. _________________

Re: The present ratio of students to teachers at a certain [#permalink]
25 Jun 2014, 21:30

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

The present ratio of students to teachers at a certain [#permalink]
02 Aug 2014, 03:23

Hello,

I am referring to Bunuel's solution. Can somebody explain why we are setting up the equation using a variable for the first ratio (30x/1x), but not for the second one (25x/1x). This is what I did wrong when I tried to solve the problem.

Re: The present ratio of students to teachers at a certain [#permalink]
02 Aug 2014, 09:05

Expert's post

Pasqualo wrote:

Hello,

I am referring to Bunuel's solution. Can somebody explain why we are setting up the equation using a variable for the first ratio (30x/1x), but not for the second one (25x/1x). This is what I did wrong when I tried to solve the problem.

Thanks,

P.

If you write the first ratio as 30x/x, then you cannot write the second one as 25x/x, because x's there are not the same. You could write it as 25y/y though.

Re: The present ratio of students to teachers at a certain [#permalink]
02 Aug 2014, 09:32

Thanks for the quick answer Bunuel. I understand that the two ratios are different and should be translated into two different variables (say x and y), but how do we solve for two variables if we do that?

e.g,: 30x + 50 = 25 y (x+5)

I hope I am making sense here. Basically, I don't understand why we use the first ratio with a variable and the second one as a normal numeric value. By the way, thanks for your amazing work on this forum.

The present ratio of students to teachers at a certain [#permalink]
02 Aug 2014, 09:44

Expert's post

Pasqualo wrote:

Thanks for the quick answer Bunuel. I understand that the two ratios are different and should be translated into two different variables (say x and y), but how do we solve for two variables if we do that?

e.g,: 30x + 50 = 25 y (x+5)

I hope I am making sense here. Basically, I don't understand why we use the first ratio with a variable and the second one as a normal numeric value. By the way, thanks for your amazing work on this forum.

Cheers

If you use two variables, the second one will be simply reduced, that's why we don't need it.

\(\frac{30x+50}{x+5}=\frac{25y}{y}\) --> reduce by y: \(\frac{30x+50}{x+5}=\frac{25}{1}\) --> solve for x.

Re: The present ratio of students to teachers at a certain [#permalink]
02 Aug 2014, 22:45

E is the answer. The best way to solve this problem is using equations I think. You can work a different way by using the answer choice to check. _________________

......................................................................... +1 Kudos please, if you like my post

Re: The present ratio of students to teachers at a certain [#permalink]
11 Sep 2014, 09:49

Impenetrable 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?

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

Today was the last day of our three-week Launch, that ended on a high note with a drinks and dance reception. The class decided to shift the party outside...

There is one comment that stands out; one conversation having made a great impression on me in these first two weeks. My Field professor told a story about a...