Question

@ (A,B) = average of A and B
*(A,B) = product of A and B
/(A,B) = A divided by 

Which expression gives the sum of A, B, and C?

• A. *(@(*( @(B, A), 2), C), 3)
• B. /(@(*( @(B, A), 3), C), 2)
• C. /(*(@(B, A), 2), C), 3)
• D. None of these

Hint:

Test expressions with concrete values to check if the structure reproduces the intended arithmetic.

Answer 1

The Correct Option is A

To solve the problem, we need to understand the given expressions:

• @(A,B): This is the average of A and B, calculated as (A + B) / 2.
• *(A,B): This is the product of A and B, calculated as A * B.
• /(A,B): This is A divided by B, calculated as A / B.

We need to find the expression that gives the sum of A, B, and C, which is A + B + C. Let's analyze each option step by step:

1. *(@(*( @(B, A), 2), C), 3)

Breaking it down:

• @(B, A) = (B + A) / 2
• *( @(B, A), 2) = ((B + A) / 2) * 2 = B + A
• @(*( @(B, A), 2), C) = (B + A + C) / 2
• *(@(*( @(B, A), 2), C), 3) = ((B + A + C) / 2) * 3 = (B + A + C) * 1.5

Clearly, this is incorrect as we need to have A + B + C, not (A + B + C) * 1.5.

2. /(@(*( @(B, A), 3), C), 2)

Breaking it down:

• @(B, A) = (B + A) / 2
• *( @(B, A), 3) = ((B + A) / 2) * 3 = (B + A) * 1.5
• @(*( @(B, A), 3), C) = ((B + A) * 1.5 + C) / 2
• /(@(*( @(B, A), 3), C), 2) = (((B + A) * 1.5 + C) / 2) / 2 = ((B + A) * 1.5 + C) / 4

This expression does not result in A + B + C.

3. /(*(@(B, A), 2), C), 3)

Breaking it down:

• @(B, A) = (B + A) / 2
• *(@(B, A), 2) = ((B + A) / 2) * 2 = B + A
• /(*( @(B, A), 2), C) = (B + A) / C
• /(*(@(B, A), 2), C), 3) = ((B + A) / C) / 3

This also does not match A + B + C.

The expression evaluated above correctly is given in:

*(@(*( @(B, A), 2), C), 3)

The correct expression for the sum A + B + C is None of these.