GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 01:38

### GMAT Club Daily Prep

#### 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

# The present ratio of students to teachers at a certain

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Dec 2011
Posts: 50
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

Updated on: 07 Dec 2012, 06:59
9
61
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:50) correct 17% (02:30) wrong based on 2198 sessions

### HideShow timer Statistics

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

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

Originally posted by Impenetrable on 26 Mar 2012, 03:48.
Last edited by Bunuel on 07 Dec 2012, 06:59, edited 1 time in total.
Renamed the topic and edited the question.
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 58409
Re: Slightly embarrasing  [#permalink]

### Show Tags

26 Mar 2012, 04:02
24
19
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 $$x$$ --> $$x=15$$ --> $$t=x=15$$.

Answer: E.

Hope it helps.
_________________
##### Most Helpful Community Reply
Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 197
Location: India
Concentration: General Management, Entrepreneurship
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

26 Mar 2012, 04:16
11
5
+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'.
##### General Discussion
Manager
Joined: 14 Dec 2011
Posts: 50
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

26 Mar 2012, 04:14
How stupid of me. I should slap myself.

Thanks a lot!
Manager
Joined: 13 Feb 2012
Posts: 129
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

25 Oct 2012, 02:28
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.
_________________
"The Burnout" - My Debrief

Kudos if I helped you

Andy
Intern
Joined: 21 Mar 2014
Posts: 3
The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

02 Aug 2014, 04:23
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.

Thanks,

P.
Math Expert
Joined: 02 Sep 2009
Posts: 58409
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

02 Aug 2014, 10:05
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.

Does this make sense?
_________________
Intern
Joined: 21 Mar 2014
Posts: 3
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

02 Aug 2014, 10:32
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.

Cheers
Math Expert
Joined: 02 Sep 2009
Posts: 58409
The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

02 Aug 2014, 10:44
2
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.

Hope it's clear.
_________________
Intern
Joined: 21 Mar 2014
Posts: 3
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

02 Aug 2014, 10:56
Great, now it's crystal clear. Thanks again
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

06 Aug 2014, 22:19
2
$$\frac{s}{t} = \frac{30}{1}$$

$$\frac{s+50}{t+5} = \frac{25}{1}$$

Placing s=30t in the above equation

30t+50 = 25t+125

5t = 75

t=15

Answer = E
_________________
Kindly press "+1 Kudos" to appreciate
Manager
Joined: 09 Aug 2015
Posts: 83
GMAT 1: 770 Q51 V44
GPA: 2.3
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

10 Aug 2015, 13:01
Hi, is there a quicker way to do this like using Alligation or something that would not involve setting up algebraic equations?
CEO
Joined: 20 Mar 2014
Posts: 2596
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

10 Aug 2015, 13:09
1
ggurface wrote:
Hi, is there a quicker way to do this like using Alligation or something that would not involve setting up algebraic equations?

You can try plugging in the values from the options.

Lets say T = 10 ---> S = 300 ---> 350/15 = a bit less than 25 (A and B will only make this ratio lesser, eliminate A and B)

Go for T = 12 --> S = 30*12 = 360 ---> 360+50 / 12+5 = less than 25. Either you can now go further with T = 15 or mark E as the answer .

Check: T = 15 ---> S = 30*15=450 ---> 450+50/20 = 25.
Intern
Joined: 11 Oct 2013
Posts: 23
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

11 Aug 2015, 03:26
s:t = 30:1
s= 30x
t = x

(30x + 50)/(x+5) = 25

So, we just solve for x

(30x + 50) = 25x + 125
5x = 75
x=15
Senior Manager
Joined: 28 Jun 2015
Posts: 283
Concentration: Finance
GPA: 3.5
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

11 Aug 2015, 04:48
$$\frac{s}{t} = \frac{30}{1}$$ => $$s = 30t$$ => $$s-30t = 0$$ ---> (i)

$$\frac{s+50}{t+5} = \frac{25}{1}$$

$$s + 50 = 25t + 125$$

$$s - 25t = 75$$ ---> (ii)

from (i) and (ii), $$t = 15$$.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

09 Jun 2016, 14:10
2
2
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?

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

We are given that the ratio of students to teacher is 30 to 1. We can rewrite this using variable multipliers.

students : teachers = 30x : x

We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:

Students/Teachers  25/1 = (30x + 50)/(x + 5)

If we cross multiply we have:

25(x + 5) = 30x + 50

25x + 125 = 30x + 50

75 = 5x

15 = x

Since x is the present number of teachers, currently there are 15 teachers.

Answer E.
_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 03 Jan 2017
Posts: 134
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

25 Mar 2017, 06:18
ratio problems are always tricky for me

i tried to approach it this way:

(30x+50)/x+5=25/1
x=15
E is the answer
Manager
Joined: 02 Jan 2017
Posts: 67
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
WE: Business Development (Accounting)
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

17 Dec 2017, 10:51
The wording is quite confusing, i calculated 15 and then read [ Present number of teachers ]. Question starts with [ Present number] i adjusted for change of 5 teachers :/.
Manager
Joined: 31 Jul 2017
Posts: 197
Location: Tajikistan
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

22 Jun 2018, 07:42
1
Lets set an equation,
30x+50/x+5=25x/1x OR
x(30x+50)=25x(x+5)
30x^2=50x=25x^2+125x
5x^2=75x
x^2=15x
x(x-15)=0
x=15 (E)
_________________
Please press kudos, if I was able to help you. Thank you.
Intern
Joined: 26 Apr 2017
Posts: 9
Re: The present ratio of students to teachers at a certain  [#permalink]

### Show Tags

27 Oct 2018, 11:32
Here the eqation

st=301st=301

s+50t+5=251s+50t+5=251

Placing s=30t in the above equation

5t = 75

t=15

Easy
Re: The present ratio of students to teachers at a certain   [#permalink] 27 Oct 2018, 11:32

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

# The present ratio of students to teachers at a certain

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne