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If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) and the M101 (Mathematics for Computer Science) classes, how many of the CS103 students are not enrolled in M101?

Statement (1) by itself is insufficient. We don't know anything about the number of students taking CS103.

Statement (2) by itself is sufficient. S2 tells us that 59 students take CS103. We know that 53 of these 59 students take M101 as well. Thus, we find that \(59 - 53 = 6\) students are not enrolled in M101.

Hello Bunuel, The question stem is silent about the number of students who did not enroll in any of the course. From the solution, it can be seen that that value is taken ZERO.

How can we assume this as such ? Is it a convention that in a set theory question , if the stem is silent about this fact we assume it to be zero ?

Hello Bunuel, The question stem is silent about the number of students who did not enroll in any of the course. From the solution, it can be seen that that value is taken ZERO.

How can we assume this as such ? Is it a convention that in a set theory question , if the stem is silent about this fact we assume it to be zero ?

Thanks.

The question asks "how many of the CS103 students are not enrolled in M101", so we are not interested in students who are not enrolled in any of the classes. It may or may not be 0 but we don't care.
_________________

I used a venn diagram with two overlapping circle to approach this question, one circle each for the two classes. The intersection of the two circles is 53 as 53 students take both classes.

Statement 1 does not tell us anything about the circle for CS students so nut sufficient. Statement 2 tells us the total circle for CS is 59 as we know 53 already overlaps the remainder must be CS only which gives us 59 - 53 = 6. Sufficient.