NIMCET 2020 — Reasoning PYQ

Step 1: Analyze the pattern in the first triangle

Let's observe the relationship between the outer numbers surrounding the triangle and the central number inside it.

• Left side number = $4$

• Right side number = $9$

• Bottom side number = $1$

• Inside number = $123$

If we take the square root of each of the outer numbers:

• $\sqrt{4}=2$

• $\sqrt{9}=3$

• $\sqrt{1}=1$

Notice the digits of the inside number $123$. If we rearrange the square roots of the bottom, left, and right numbers in a specific sequence:

$$\text{Inside Number}=(\text{Digits of }\sqrt{\text{Bottom}})\cdot (\text{Digits of }\sqrt{\text{Left}})\cdot (\text{Digits of }\sqrt{\text{Right}})$$

$$\sqrt{1}=1,\sqrt{4}=2,\sqrt{9}=3⟹123$$

The pattern sets the central value by placing the square roots side by side in the order: (Bottom) (Left) (Right).

Step 2: Apply the pattern to the second triangle

Using the identical logic for the second triangle:

• Left side number = $9⟹\sqrt{9}=3$

• Bottom side number = $4⟹\sqrt{4}=2$

• Inside number = $232$

• Right side number = $?$

Following the order (Bottom) (Left) (Right) to form the digits of the inside number:

$$\text{First digit (Bottom)}=\sqrt{4}=2$$

$$\text{Second digit (Left)}=\sqrt{9}=3$$

$$\text{Third digit (Right)}=\sqrt{?}=2$$

From the central number $232$, the third digit corresponding to $\sqrt{?}$ must be $2$:

$$\sqrt{?}=2$$

Squaring both sides to find the value of the missing number:

$$?=2^2$$

$$?=4$$

Thus, the missing number is 4.

Correct Option: C