Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 03 May 2016, 21:40

### 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: 65
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
Followers: 1

Kudos [?]: 24 [2] , given: 24

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

### Show Tags

26 Mar 2012, 03:48
2
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

80% (02:28) correct 20% (02:08) wrong based on 818 sessions

### HideShow timer Statictics

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, 06:59, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 32602
Followers: 5649

Kudos [?]: 68564 [10] , given: 9815

### Show Tags

26 Mar 2012, 04:02
10
KUDOS
Expert's post
10
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.
_________________
Manager
Joined: 14 Dec 2011
Posts: 65
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
Followers: 1

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

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!
Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 291
Location: India
Concentration: General Management, Entrepreneurship
Followers: 2

Kudos [?]: 185 [2] , given: 16

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

### Show Tags

26 Mar 2012, 04:16
2
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'.

Manager
Joined: 13 Feb 2012
Posts: 147
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Followers: 4

Kudos [?]: 6 [0], given: 85

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

Manager
Joined: 17 Jul 2010
Posts: 124
Followers: 1

Kudos [?]: 32 [0], given: 43

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

### Show Tags

09 May 2013, 19:51
the first part seems to be the trickiest,$$\frac{S}{T}$$ = $$\frac{30}{1}$$, then cross multiply to get 30T=S
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9274
Followers: 455

Kudos [?]: 115 [0], given: 0

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

### Show Tags

25 Jun 2014, 22:30
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.
_________________
Intern
Joined: 21 Mar 2014
Posts: 3
Followers: 0

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

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: 32602
Followers: 5649

Kudos [?]: 68564 [0], given: 9815

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

### Show Tags

02 Aug 2014, 10:05
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.

Does this make sense?
_________________
Intern
Joined: 21 Mar 2014
Posts: 3
Followers: 0

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

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: 32602
Followers: 5649

Kudos [?]: 68564 [0], given: 9815

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

### Show Tags

02 Aug 2014, 10:44
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.

Hope it's clear.
_________________
Intern
Joined: 21 Mar 2014
Posts: 3
Followers: 0

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

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
Manager
Joined: 22 Feb 2009
Posts: 230
Followers: 5

Kudos [?]: 92 [0], given: 148

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

### Show Tags

02 Aug 2014, 23:45
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

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 35

Kudos [?]: 1473 [0], given: 193

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

### Show Tags

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

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

Placing s=30t in the above equation

30t+50 = 25t+125

5t = 75

t=15

_________________

Kindly press "+1 Kudos" to appreciate

Manager
Joined: 07 Apr 2014
Posts: 147
Followers: 1

Kudos [?]: 19 [0], given: 81

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

### Show Tags

11 Sep 2014, 10:49
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?

(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

I have resolved using plug in method & got E.. worst method for this question ..
Manager
Joined: 09 Aug 2015
Posts: 99
GMAT 1: 770 Q51 V44
GPA: 2.3
Followers: 0

Kudos [?]: 17 [0], given: 6

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?
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2605
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 95

Kudos [?]: 1069 [0], given: 777

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

### Show Tags

10 Aug 2015, 13:09
Expert's post
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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Intern
Joined: 11 Oct 2013
Posts: 30
Followers: 0

Kudos [?]: 1 [0], given: 3

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
Manager
Joined: 28 Jun 2015
Posts: 139
Concentration: Finance, Economics
GPA: 3.5
Followers: 0

Kudos [?]: 48 [0], given: 19

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.

Re: The present ratio of students to teachers at a certain   [#permalink] 11 Aug 2015, 04:48
Similar topics Replies Last post
Similar
Topics:
The ratio of the present ages of a man and his wife is 5 : 4 2 19 Feb 2016, 10:38
1 A teacher grades students’ tests by subtracting twice the number of in 6 13 Dec 2015, 04:49
14 A certain organization presents reward to some people... 4 15 Oct 2012, 19:37
19 At a certain university, the ratio of the number of teaching 17 04 Jun 2009, 21:11
4 A certain college has a student-to-teacher ratio of 11 to 1. 13 27 Jan 2008, 10:39
Display posts from previous: Sort by