It is currently 16 Jan 2018, 14:53

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The present ratio of students to teachers at a certain

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Dec 2011
Posts: 61

Kudos [?]: 52 [3], given: 24

GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
The present ratio of students to teachers at a certain [#permalink]

### Show Tags

26 Mar 2012, 02:48
3
KUDOS
28
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:32) correct 16% (02:03) wrong based on 1371 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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Dec 2012, 05:59, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 52 [3], given: 24

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139207 [12], given: 12779

### Show Tags

26 Mar 2012, 03:02
12
KUDOS
Expert's post
16
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 $$x$$ --> $$x=15$$ --> $$t=x=15$$.

Hope it helps.
_________________

Kudos [?]: 139207 [12], given: 12779

Manager
Joined: 14 Dec 2011
Posts: 61

Kudos [?]: 52 [0], given: 24

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, 03:14
How stupid of me. I should slap myself.

Thanks a lot!

Kudos [?]: 52 [0], given: 24

Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 268

Kudos [?]: 338 [5], given: 16

Location: India
Concentration: General Management, Entrepreneurship
Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

26 Mar 2012, 03:16
5
KUDOS
2
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'.

Kudos [?]: 338 [5], given: 16

Manager
Joined: 13 Feb 2012
Posts: 143

Kudos [?]: 11 [0], given: 85

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, 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.
_________________

"The Burnout" - My Debrief

Kudos if I helped you

Andy

Kudos [?]: 11 [0], given: 85

Intern
Joined: 21 Mar 2014
Posts: 3

Kudos [?]: [0], given: 98

The present ratio of students to teachers at a certain [#permalink]

### Show Tags

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.

Thanks,

P.

Kudos [?]: [0], given: 98

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139207 [0], given: 12779

Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

02 Aug 2014, 09:05
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?
_________________

Kudos [?]: 139207 [0], given: 12779

Intern
Joined: 21 Mar 2014
Posts: 3

Kudos [?]: [0], given: 98

Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

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.

Cheers

Kudos [?]: [0], given: 98

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139207 [2], given: 12779

The present ratio of students to teachers at a certain [#permalink]

### Show Tags

02 Aug 2014, 09:44
2
KUDOS
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.

Hope it's clear.
_________________

Kudos [?]: 139207 [2], given: 12779

Intern
Joined: 21 Mar 2014
Posts: 3

Kudos [?]: [0], given: 98

Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

02 Aug 2014, 09:56
Great, now it's crystal clear. Thanks again

Kudos [?]: [0], given: 98

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1844

Kudos [?]: 2859 [2], given: 193

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, 21:19
2
KUDOS
$$\frac{s}{t} = \frac{30}{1}$$

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

Placing s=30t in the above equation

30t+50 = 25t+125

5t = 75

t=15

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2859 [2], given: 193

Current Student
Joined: 09 Aug 2015
Posts: 94

Kudos [?]: 31 [0], given: 7

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, 12:01
Hi, is there a quicker way to do this like using Alligation or something that would not involve setting up algebraic equations?

Kudos [?]: 31 [0], given: 7

Current Student
Joined: 20 Mar 2014
Posts: 2685

Kudos [?]: 1843 [0], given: 800

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, 12:09
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.

Kudos [?]: 1843 [0], given: 800

Intern
Joined: 10 Oct 2013
Posts: 32

Kudos [?]: 2 [0], given: 3

Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

11 Aug 2015, 02:26
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

Kudos [?]: 2 [0], given: 3

Senior Manager
Joined: 28 Jun 2015
Posts: 299

Kudos [?]: 114 [0], given: 47

Concentration: Finance
GPA: 3.5
Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

11 Aug 2015, 03:48
$$\frac{s}{t} = \frac{30}{1}$$ => $$s = 30t$$ => $$s-30t = 0$$ ---> (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.

Kudos [?]: 114 [0], given: 47

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1044 [0], given: 5

Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

09 Jun 2016, 13:10
Expert's post
1
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?

(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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1044 [0], given: 5

Manager
Joined: 03 Jan 2017
Posts: 194

Kudos [?]: 11 [0], given: 4

Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

25 Mar 2017, 05:18
ratio problems are always tricky for me

i tried to approach it this way:

(30x+50)/x+5=25/1
x=15

Kudos [?]: 11 [0], given: 4

Manager
Joined: 02 Jan 2017
Posts: 90

Kudos [?]: 2 [0], given: 23

Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41
Re: The present ratio of students to teachers at a certain [#permalink]

### Show Tags

17 Dec 2017, 09:51
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 :/.

Kudos [?]: 2 [0], given: 23

Re: The present ratio of students to teachers at a certain   [#permalink] 17 Dec 2017, 09:51
Display posts from previous: Sort by
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6546595096588135, "perplexity": 4529.138444104244}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886758.34/warc/CC-MAIN-20180116224019-20180117004019-00714.warc.gz"}