GRE® Set Theory Question Bank

Step 1: Let Set A comprise all 3-digit numbers that are multiples of 6.
Step 2: Let Set B comprise all 3-digit numbers that are odd multiples of 4.
Step 3: Find Set A ∪ B to find the answer to the question.

Step 1: Let Set A comprise all numbers less than 200 that are multiples of 3. Find n(A).
Step 2: Let Set B comprise all numbers less than 200 that are odd multiples of 5. Find n(B).
Step 4: Find Set A ∩ B to find the number of numbers less than 200 that are multiples of 3 and are odd multiples of 5.
Step 3: Find Set A ∪ B to find the answer to the question.

Step 1: Assign a variable for the total length of the vacation. Let it be n days.
Step 2: Express number of days they played together in the mornings in temrs of n.
Step 3: Express number of days they played together in the evenings in temrs of n.
Step 4: Add expressions in steps 2 and 3 and equate it to the number of days they played during the vacation and solve for n.

Step 1: All elements of set A are odd. Sum will be odd when the subset comprises either 3 or 5 elements. Compute number of such subets.
Step 2: Set B comprises 4 elements. List down possible scenarios when the subset has 2, 3, and 4 elements when the sum will be even and count the number of such subsets.
Step 3: Compare the two quantities and determine the answer.

Step 1: Shortlist the values that n can take such that 34/n is an integer as the number of people watching both La Liga and EPL has to be an integer.
Step 2: For each of the shortlisted values, find out the number of people watching only La Liga, EPL and both and determine whether that is a feasible combination. If it is, the value is a possible answer.