Every element in the central column of the matrix has a simple arithmetic relationship with the pairs on the left and right in the corresponding row.

\(\left[\begin{array}{lllll} 17 & 12 & \mathbf{1} & 19 & 23 \\ 23 & 21 & \boldsymbol{X} & 18 & 20 \\ 24 & 17 & 3 & 32 & 36 \\ 35 & 28 & 2 & 19 & 24 \end{array}\right]\)

What would be the value of X?

  1. 2
  2. 1
  3. 0
  4. -1

Answer (Detailed Solution Below)

Option 3 : 0

Detailed Solution

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The correct answer is 0

Explanation:

Given:

Every element in the central column of the matrix has a simple arithmetic relationship with the pairs on the left and right in the corresponding row.

The matrix is

17 12 1 19 23
23 21 X 18 20
24 17 3 32 36
35 28 2 19 24

 

Calculation:

We observe that the element in the central column (1, X, 3, 2) is the difference between the sums of the pairs on the left and right in the corresponding row.

For the first row:

(17 - 12) -  (23 - 19) = 5 - 4 = 1

For the third row:

(24 - 17) - (36 - 32) = 7 - 4 = 3

For the fourth row:

(35 - 28) - (24 - 19) = 7 - 5 = 2

Now, for the second row:

(23 - 21) - (20 - 18) = 2-2= 0

Therefore, the value of X should be 0

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