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.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(D) 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).
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Can you please show me how to do this question by setting up an overlapping set matrix? Thank you.

We do NOT have any overlapping sets here. Instead, we have one set: ALL STUDENTS and two subsets: STUDY FRENCH, STUDY CANTONESE. The question statement implies that these subsets do NOT overlap (intersect).

(The proportions are yet unknown).

Statement (1) gives us:

x + 4x = 60

Statement (2) gives us:

y + (y – 36) = 60