Xavier Aptitude Test 2021 Paper

Question : 10 of 100

Marks: +1, -0

Rahul has just made a $3×3$ 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 $\N$ ?

$3x + 4y$	$2x$	$2x + y+ z$
$2x^2$	$4y$	$y^2 +z$
$y+z$	$3x + 2z$	$z-1$

Validate

Solution:

Sum of

3^{\rd}

row

=

sum of

2^{\nd}

column

⇒2x+4y = y+2z-1

⇒ 2x+3y-2z= -1

...(A)

Sum of diagonals are also equal

⇒ 3x+4y+z-1 = y+z+2x+y+z

⇒ x+2y-z=1

...(B)

Solving equation A and B we get

y= 3

Putting it in A, we get

x-z = -5

...(C)

Sum of

1^{\st}

row

=

sum of

2^{\nd}

column

5x+5y+z = 3x+4y+2z

⇒ 2x +y - z =0

Since

y=3

2x-z = -3

...(D)

Solving C and D we get

x=2

and

z=7

Hence

\N = 36

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