Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
8 schools sent a total of 96 students to a math club competition, with each school sending at least one student. If one school sent the third most number of students to the competition (and no two schools sent the same number of students), did that school send at least 15 students?
(1) The most number of students that were sent by any one school was 34.
(2) The second most number of students that were sent by any school was 33.
There are 8 variables (8 schools) and 2 equations (total=96, at least=min=1) in the original condition, but only 2 equations are given by the conditions, so there is high chance (E) will be our answer.
Looking at the conditions together,
if we let T be the school that is the third from top sending students,
1+2+3+4+5+15+33+34=97>96, so T cannot be 15, so it is always 'no' and the conditions is sufficient, making the answer seem like (C); this is an integer type of question, question with commonly made mistakes, so if we apply mistake type 4(A),
For condition 1, 1+2+3+4+5+14+33+34(no), 1+2+3+4+5+16+31+34 (yes), so this is insufficient.
For condition 2, the answer is always 'no' in 1+2+3+4+5+15+33+34, so this is also sufficient, and the answer becomes (B).
For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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