IPMAT 2024 - Quantitative Aptitude Question 12
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IPMAT 2024 - Quantitative Aptitude
Let the sum of all three elements along any row, column or diagonal be S.
Then, f = S – (8 + 3) = S – 11 …...(i) (from the bottom row)
d = S – (7 + f) …....(ii) (from one of the diagonals)
From equations (i) and (ii), we get
d = S – (7 + S – 11)
∴ d = 4
Also, b = S – (8 + d) = S – 12 (from the middle column) …....(iii)
a = S – (b + 7) (from the first row)…....(iv)
From equations (iii) and (iv), we get a = 5 & b = 0
∴ S = 12
∴ The matrix A comes out to be 
Determinant |A| = 5(4 × 3 − 8 × 2) + 0(2 × 1 − 6 × 3) + 7(6 × 8 − 1 × 4)
= 5(12 − 16) + 0 + 7(48 − 4)
= − 20 + 0 + 308 = 288