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

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.

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.

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

Answer: Option D

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

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

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
Answer D

(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).

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).

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

Let the number of students studying Cantonese be C and number of students studying French be F.
C + F = 60

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
F = 4C; F+C=60
5C = 60; C = 12; F = 48
SUFFICIENT

(2) The number of students who study Cantonese is 36 fewer than the number who study French.
C = F-36 = 60 - F
2F = 96; F = 48; C = 12
SUFFICIENT

IMO D