Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 23:42 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A school has 60 students. Each student studies either Cantonese or Fre

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56268
A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

1
1 00:00

Difficulty:   15% (low)

Question Stats: 80% (01:01) correct 20% (01:27) wrong based on 163 sessions

### HideShow timer Statistics A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

_________________
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

NF + NC = 0 (as each student learns either cantonese or french)

Text in black: given values
Text in red: calculated values

From statement 1, we can see x/4 +x= 60 . Thus this statement is sufficient

From statement 2, we see that 2x-36=60. Thus this statement is sufficient as well. Thus both statements are sufficient and hence D is the correct answer.
Attachments image.jpg [ 44.1 KiB | Viewed 2408 times ]

Manager  B
Joined: 26 Dec 2011
Posts: 115
Schools: HBS '18, IIMA
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

Solution -

From the given information, C + F = 60.

Stmt1 - The number of students who study French is 4 times the number of the students who study Cantonese. --> F = 4C.
Substitute F = 4C in C + F = 60 --> C + (4C) = 60 --> 5C = 60 --> C = 12 and F = 48. Sufficient.

Stmt2 - The number of students who study Cantonese is 36 fewer than the number who study French. --> C = F – 36.
Again, substitute C in the original equation C + F = 60 --> (F – 36) + F = 60 --> 2F – 36 = 60 --> F = 48. Sufficient.

ANS D.
_________________
Thanks,
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

This question doesn't need to be solved by double matrix or Venn diagram because two of the catagories are already known as zero

Students who don't study either of the Cantonese and French = 0
Students who study Both Cantonese and French = 0

i.e. only categories are

Students studying Cantonese (C)
Students studying French (F)
and F + C = 60

Question : Students studying French = ?

Statement 1: The number of students who study French is 4 times the number of the students who study Cantonese

i.e. F = 4*C and F+C = 60
i.e. C = 12 and F = 48
SUFICIENT

Statement 2: The number of students who study Cantonese is 36 fewer than the number who study French.

C = F-36 and F+C = 60
i.e. C = 12 and F = 48
SUFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
SVP  B
Joined: 06 Nov 2014
Posts: 1877
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

1
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

c = Cantonese f= French => c + f =60

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
f=4c => c=4/f This can be plugged into the value for c in c+f=60 to solve for f. Sufficient.

(2) The number of students who study Cantonese is 36 fewer than the number who study French.
c=f - 36 This can be plugged into the value for c in c + f = 60 to solve for f. Sufficient.

D
Intern  Joined: 04 Nov 2013
Posts: 28
Concentration: Finance, Strategy
GPA: 4
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

Because each student must take a language, and no student can take both, this makes the question easier.
1. 4x + x = 60
5x=60
x=12

There are 48 French students. Sufficient.

2. (x-36) + x = 60
2x=96
x=48
Again, there are 48 French students. Sufficient.

D
_________________
Please kudos if you found this post helpful. I am trying to unlock the tests Manager  Joined: 20 Jul 2011
Posts: 79
GMAT 1: 660 Q49 V31 Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

Given : F + C = 60---- Eq 1

St 1: F = 4C => Can be solved with eq 1. Sufficient

St 2: C = F-36 => Can be solved with eq 1. Sufficient.

Hence Option D
Director  P
Joined: 21 May 2013
Posts: 655
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

Statement 1:The number of students who study French is 4 times the number of the students who study Cantonese.
C+4C=60. Find the value of C and F. Sufficient.
Statement 2:The number of students who study Cantonese is 36 fewer than the number who study French
F+F-36=60. Sufficient Joined: 24 Oct 2012
Posts: 167
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

1
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Given : Each student studies either Cantonese or French, but not both
C + F = 60 -- Equation 1

Statement 1: F = 4c - Sufficient to solve equation 1

Statement 2: C = F - 36 --
So F-36 + F = 60 -- Sufficient to solve equation 1

Hence Option D
Senior Manager  B
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

(1): f = 4c. f+c = 60. so, 4c+c = 60, therefore c = 12, f = 48. Sufficient.

(2): f - c = 36. f+c = 60. Solving we get f = 48, c = 12. Sufficient.

Ans (D).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Math Expert V
Joined: 02 Sep 2009
Posts: 56268
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.

800score Official Solution:

Use C to represent the number of students studying Cantonese and F to represent the number of students studying French. The given information tells us that the number of students adds up to 60, or C + F = 60.

Statement (1) gives us another equation: F = 4C. Now we can substitute F with 4C in the original equation:
C + F = 60
C + (4C) = 60
5C = 60
C = 60/5 = 12.

Since we are told that 4C = F, we know that:
F = 12 × 4 = 48.

Therefore, Statement (1) is sufficient.

Statement (2) tells us that F – 36 = C. Again, we can substitute this into the original equation:
C + F = 60.
(F – 36) + F = 60
2F – 36 = 60
2F = 96
F = 48.

Since, either statement alone is sufficient to solve for F, the correct answer is choice (D).
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 11705
Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

### Show Tags

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.
_________________ Re: A school has 60 students. Each student studies either Cantonese or Fre   [#permalink] 22 Dec 2018, 16:35
Display posts from previous: Sort by

# A school has 60 students. Each student studies either Cantonese or Fre  