NIMCET 2020 — Reasoning PYQ

Step 1: Analyze the pattern in the columns

Let us observe the relationship between the numbers in each column from top to bottom. Let the rows be $R_1$, $R_2$, and $R_3$.

For Column 1:

The numbers are $1$, $2$, and $3$.

If we add the first two rows and multiply by the first row, or look for a combined arithmetic logic:

$$(R_1+R_2)\times R_1\text{ does not fit everything perfectly.}$$

Let's look at another common matrix pattern:

$$(R_2+R_3)÷R_1\to (2+3)/1=5$$

Let's try a direct algebraic combination for the column values:

$$\text{Pattern: }(R_2\times R_1)+\text{something?}$$

Let's re-verify the exact mathematical logic linking the row values vertically:

$$\text{For Column 1: }1\times (2+1)=3$$

$$\text{For Column 2: }7\times (14+1)=105$$

Wow! Let's check this exact column-wise logic:

$$\text{Column 1: }{R}_1\times (R_2+1)=1\times (2+1)=1\times 3=3=R_3$$

$$\text{Column 2: }{R}_1\times (R_2+1)=7\times (14+1)=7\times 15=105=R_3$$

The pattern holds perfectly for both columns!

Step 2: Apply the pattern to Column 3

Following the exact logic established above:

$$R_1\times (R_2+1)=R_3$$

Substitute the known values from the third column ($R_1=9$ and $R_3=117$, with $R_2=?$):

$$9\times (?+1)=117$$

Divide both sides by $9$:

$$?+1=\frac{117}{9}$$

$$?+1=13$$

Subtract $1$ from both sides:

$$?=13-1$$

$$?=12$$

Thus, the missing number is 12.

Correct Option: D