A < 1 min read

Is the sum of four particular integers even?

1. Two of the integers are odd and two are even.
2. The average (arithmetic mean) of the four integers is an integer.

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are asked to determine

• Whether the sum of four particular integers even or not.

To determine this, we need to know either the values of the integers, or the even-odd nature of them.

With this understanding, let us now analyse the individual statement.

 

Step 3: Analyse Statement 1

As per the information given in statement 1, two of the integers are odd and two are even.

• Therefore, the sum of the four integers = (odd + odd) + (even + even) = even + even = even

As we can determine that the sum of the four integers is even, statement 1 is sufficient to answer the question.

 

Step 4: Analyse Statement 2

As per the information given in statement 2, the average (arithmetic mean) of the four integers is an integer.

• Hence, we can say, sum of the four integers = average of the four integers × 4
• As any multiple of 4 is an even number, the sum of the four integers is also an even number

Hence, statement 2 is sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer choice is option D.