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. |

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- Cannot be determined

From INR 2999

**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 = 5C_{3} = 10

Number of 5 element subsets = 5C_{5} = 1

Quantity A = 10 + 1 = 11 subsets.

**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.

**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**

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