GRE® Quantitative Comparison Q4

The GRE maths sample question given below is a hard Quantitative Comparison question in Set Theory. This question tests the concept of Subsets and a very preliminary understanding of Odd and Even numbers.

Question 4: 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.

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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Video Explanation

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Explanatory Answer | GRE Set Theory Quantitative Comparison Q4

Step 1: Evaluate Quantity A

Quantity A: Number of subsets of A comprising of at least 2 elements, sum of whose elements is odd.

A = {3, 5, 7, 11, 13}
Set A has 5 elements and all of them are odd.
The sum will be odd if the subset comprises of 3 or 5 elements.
Number of 3 element subsets = 5C₃ = 10
Number of 5 element subsets = 5C₅ = 1
Quantity A = 10 + 1 = 11 subsets.

Step 2: Evaluate Quantity B

Quantity B: Number of subsets of B comprising of at least 2 elements, sum of whose elements is even.

B = {2, 3, 4, 5}
Set B has 4 elements.
2 element subsets with even sum = {2, 4}, {3, 5}. When elements are both odd or both even.
3 element subsets with even sum = {3, 5, 2}, {3, 5, 4}. Two odd and one even.
4 element subsets with even sum = {2, 3, 4, 5}
Quantity B = 2 + 2 + 1 = 5 subsets.

Step 3: The comparison

Quantity A: Number of subsets of A comprising of at least 2 elements, sum of whose elements is odd.
Quantity B: Number of subsets of B comprising of at least 2 elements, sum of whose elements is even.
Quantity A = 11
Quantity B = 5
Quantity A is greater

Choice A is the correct answer.