Q. A Question is given followed by two Statements I and II. Consider the Question and the Statements.

# Question: What are the unique values of x and y, where x, y are distinct natural numbers?

Statement-I: **x / y is odd.**

Statement-II: **xy = 12**

Which one of the following is correct in respect of the above Question and the Statements?

a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

b) The Question can be answered by using either Statement alone.

c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

d) The Question cannot be answered even by using both the Statements together.

Correct answer: c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

Let’s approach this step-by-step:

## 1. First, let’s consider Statement I alone: x / y is odd

This statement alone doesn’t give us enough information to determine unique values for x and y. There are many pairs of natural numbers that satisfy this condition (e.g., 3/1, 5/1, 7/1, 9/3, etc.).

## 2. Now, let’s consider Statement II alone: xy = 12

This statement also doesn’t give us unique values for x and y. The possible pairs of natural numbers are (1,12), (2,6), (3,4), (4,3), (6,2), and (12,1).

### 3. Now, let’s consider both statements together:

– From Statement II, we know the possible pairs are (1,12), (2,6), (3,4), (4,3), (6,2), and (12,1).

– From Statement I, we know that x/y must be odd.

– Checking each pair:

(1,12): 1/12 is not odd

(2,6): 2/6 is not odd

(3,4): 3/4 is not odd

(4,3): 4/3 is not odd

(6,2): 6/2 is not odd

(12,1): 12/1 is odd

Therefore, the only pair that satisfies both statements is (12,1).

Given this analysis, we can conclude that:

The correct answer is c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

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