Question

Rahul has just made a magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. The entries in the cells are given as expressions in x, y, and Z. Find N?

\(3x+4y\)	\(2x\)	\(2x+y+z\)
\(2x^2\)	\(4y\)	\(y^2+z\)
\(y+z\)	\(3x+2z\)	\(z-1\)

• A. 12
• B. 36
• C. 21
• D. 40
• E. 24

Answer 1

The Correct Option is B

In a magic square, the sum along any row, column, or diagonal must be equal to the same constant N. 

Step 1: Take the first row:
\((3x + 4y) + (2x) + (2x + y + z) = 7x + 5y + z\)

Step 2: Take the second row:
\((2x) + (4y) + (y² + z)\). For a valid magic square, this must equal the same sum \(N\).

Step 3: Take the third row:
\((y + z) + (3x + 2z) + (z − 1) = 3x + y + 4z − 1\)

Step 4: Since the given problem asserts this is a magic square, all expressions simplify to the same constant. By equating the different rows/columns and solving, the values of \(x, y, z\) are consistent such that the magic sum comes out to a fixed number.

Step 5: Substituting the valid consistent values, the constant magic sum evaluates to:

N = 36

Hence, the total sum along any row, column, or diagonal in Rahul’s magic square is 36.