A group of students from two schools, M and N, were surveyed to find out their preferences for three subjects: Mathematics, Science, and English. The number of students surveyed and their specific preferences are not directly known. What is the ratio of students who prefer Mathematics to those who prefer Science in School M? Statements: 1. The total number of students surveyed in School N is 60% of those surveyed in School
M. In School N, 40% of students prefer Mathematics, and 25% of the remaining students prefer Science. 2. The number of students who prefer English in School M is twice the number of students who prefer Science in School N. The ratio of students who prefer Mathematics to those who prefer English in School M is 5:4.

We learn that School N has 60% of the students that School M has.  However, this statement only gives us preferences in School N, not School M. We cannot use this information alone to determine the ratio of students who prefer Mathematics to Science in School M. Statement 1 alone is not sufficient. From Statement 2: We know that students who prefer English in School M are twice those who prefer Science in School N. Also, in School M, the ratio of students who prefer Mathematics to English is given as 5:4. But without actual numbers or the ratio of Mathematics to Science in School M, this statement alone is also insufficient. Statement 2 alone is not sufficient. Combining Statements 1 and 2: Even with both statements, we lack direct information about the ratio of Mathematics to Science preferences within School M specifically.  The statements give us indirect relationships, but they do not provide enough to determine the exact ratio needed. Correct Answer: (e) Statements 1 and 2 together are not sufficient.