The concepts tested include union and intersection of 2 or 3 sets, subsets, proper subsets, and complementary sets. Sample GRE practice questions from set theory is given below. Attempt these questions and check whether you have got the correct answer. If you are not able to solve the question, go to the explanatory answer or the video explanations to learn how to solve this GRE sample question.
Set A comprises all 3-digit numbers that are multiples of 6. Set B comprises all 3-digit numbers that are multiples of 4 but are not multiples of 8. How many elements does (A ∪ B) comprise?
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.
Set A comprises all multiples of 3 less than 200. Set B comprises of all odd multiples of 5 less than 200. How many elements does A∪B have?
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.
Last summer vacation John played with Sam either in the evening or in the morning, never once playing both in the morning and the evening on the same day. On a few days, John did not play with Sam. If they did not play in the mornings for 18 days and did not play in the evenings on 21 days and played together 27 days, how long was the summer vacation?
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.
A = {3, 5, 7, 11, 13}, B = {2, 3, 4, 5}
Quantity A | Quantity B |
---|---|
Number of subsets of A comprising of at least 2 elements, sum of whose elements is odd. | Number of subsets of B comprising of at least 2 elements, sum of whose elements is even. |
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.
In a group of people, n watched only La Liga and 2n watched EPL. If 34/n watched both La Liga and EPL, how many watched La Liga?
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.
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