Average of 3 positive integer a,b,c is 111 b is 2 more than c then whi

We know the average and the number of values which will help us find the sum of the values. Knowing the sum will eventually help us in determining the nature of the numbers since we can use the property of odds and evens when we know the sum of values.

There are 3 numbers and their average is 111. Therefore, sum of values

a+b+c = 3 * 111 = 333.

Note that 333 is an odd number. If the sum of three numbers is an odd number, then it means that all the three are odd OR it could also be that two are even and one is odd.


We know that b=c+2, from the question data. Therefore, b + c = 2c+2 which will definitely be even. Since the sum of b and c is even, a HAS to be odd. This means that option A has to be true always.
Answer options B, C, D and E can be eliminated.

If c is even, b will be even. Answer option B can be eliminated since we got b to be even.
If c is odd, be will be odd. Answer option D can be eliminated.
We have already proved that a HAS to be odd, therefore, answer option C is always FALSE.
If c is odd, a+c will be even. If c is even, a+c will be odd. Answer option E can be eliminated.

The correct answer option is A.

Hope that helps!

Solution

Given
In this question, we are given that

• Average of 3 positive integers a, b, and c is 111.
• The value of b is 3 more than c

To find
We need to determine

• From the given choices, which one is true

Approach and Working out
Sum of the integers = a + b + c = 111 x 3 = 333
Also, b = 2 + c

Hence, we can write,

• a + 2 + c + c = 333
Or, a + 2c = 331

Now, 2c is always even
Hence, a = 331 – even = odd – even = odd

Thus, option A is the correct answer.

Correct Answer: Option A