# Quantitative Aptitude – Square – Rahul has just made a 3 x 3 magic square

## XAT 2021 Exam Paper – Quantitative Aptitude – Square – Rahul has just made a 3 x 3 magic square

Q. Rahul has just made a 3 x 3 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. 1. 21
2. 36
3. 12
4. 40
5. 24

Solutions:
Given , Sum of the cells along any row, column or diagonals are same.
Thus
Second column = diagonal
2x + 4y + (3x+2z) = (y+z)+4y + (2x+y+z)
Or 3x – 2y =0
Or 3x = 2y ————-1)
Also
2x + 4y + (3x+2z) = (3x+4y) + 4y + z-1
2x – 4y +z +1=0 —————2)
And
(3x+4y) + 4y + z-1 = y+z + 3x+2z + z-1
7y = 3z ———3)
From eq 1 and eq 3,
21x = 14y = 6z ———–4)
On solving eq 2 and eq 4)
X= 2, y = 3 and z = 7
So N = 2x + 4y + (3x+2z) = 5x + 4y + 2z = 36

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