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Xavier Aptitude Test 2021 Solved Paper
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© examsnet.com
Question : 10
Total: 100
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
?
3
x
+
4
y
2
x
2
x
+
y
+
z
2
x
2
4
y
y
2
+
z
y
+
z
3
x
+
2
z
z
−
1
12
36
21
40
24
Validate
Solution:
Sum of
3
rd
row
=
sum of
2
nd
column
⇒
2
x
+
4
y
=
y
+
2
z
−
1
⇒
2
x
+
3
y
−
2
z
=
−
1
...(A)
Sum of diagonals are also equal
⇒
3
x
+
4
y
+
z
−
1
=
y
+
z
+
2
x
+
y
+
z
⇒
x
+
2
y
−
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
5
x
+
5
y
+
z
=
3
x
+
4
y
+
2
z
⇒
2
x
+
y
−
z
=
0
Since
y
=
3
,
2
x
−
z
=
−
3
...(D)
Solving C and D we get
x
=
2
and
z
=
7
Hence
N
=
36
© examsnet.com
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