Question

Find the missing character in the given table: 

16	210	14
14	156	12
12	?	10

• A. 90
• B. 100
• C. 110
• D. 120

Hint:

Another way to see this pattern is $C_2 = (C_1 - 1) \times C_3$. For Row 1: $(16 - 1) \times 14 = 15 \times 14 = 210$. For Row 3: $(12 - 1) \times 10 = 11 \times 10 = 110$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In matrix-based reasoning puzzles, we look for a mathematical relationship between the numbers in each row or column. Usually, the outer numbers are manipulated to result in the central number.

Step 2: Key Formula or Approach:
We check the relationship between the first and third columns to derive the second column. Let the numbers be $C_1, C_2,$ and $C_3$. We observe the pattern: \[ C_2 = (C_1 \times C_3) - (C_1 + C_3) \] Alternatively, \[ C_2 = (C_1 - 1) \times (C_3 + 1) \text{ or } C_1 \times C_3 - \text{adjustment} \] Let's test $C_2 = C_1 \times (C_3 + 1)$: Row 1: $16 \times (14 + 1) = 16 \times 15 = 240$ (No) Let's test $C_2 = (C_1 \times C_3) - (C_1 + C_3)$: Row 1: $(16 \times 14) - (16 + 14) = 224 - 30 = 194$ (No) Let's try: $C_2 = (C_1 + C_3) \times \frac{(C_1 + C_3)}{2} - \text{constant}$? No. Correct Pattern: $C_2 = (C_1 \times C_3) - \text{something}$. Row 1: $16 \times 14 = 224$. $224 - 14 = 210$. Row 2: $14 \times 12 = 168$. $168 - 12 = 156$.

Step 3: Detailed Explanation:
The pattern identified is: $\text{Middle Number} = (\text{First Number} \times \text{Third Number}) - \text{Third Number}$. Row 1: $(16 \times 14) - 14 = 224 - 14 = 210$
Row 2: $(14 \times 12) - 12 = 168 - 12 = 156$
Applying this to Row 3: \[ ? = (12 \times 10) - 10 \] \[ ? = 120 - 10 = 110 \]

Step 4: Final Answer:
The missing character is 110.