Question

Find the missing number in the square: 

 

• A. 15
• B. 16
• C. 17
• D. 18
• E. 19

Hint:

When column logic is inconsistent, check if Row 3 is related to the previous rows via a multiplier that decreases or increases across columns (e.g., $\times 2.5, \times 1.5, \times 1$).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to identify the pattern or relationship between the numbers in the 3x3 grid to find the value of the missing number marked with a question mark.
Step 2: Key Formula or Approach:
The pattern can be row-wise, column-wise, or diagonal. We need to test simple arithmetic operations (+, -, *, /) or other mathematical relations (squares, cubes) for each row and column to find the governing rule.
Step 3: Detailed Explanation:
Let's analyze the numbers in each row. Let the columns be C1, C2, and C3.
Row 1: The numbers are 64, 80, and 12.
Let's check the relationship:
\[ 64 + 80 = 144 \] We can observe that 144 is the square of 12.
\[ 144 = 12^2 \] So, the pattern for the first row is: C1 + C2 = (C3)$^2$.
Row 2: The numbers are 25, 11, and 6.
Let's apply the same pattern to check if it holds true:
\[ 25 + 11 = 36 \] We can observe that 36 is the square of 6.
\[ 36 = 6^2 \] The pattern C1 + C2 = (C3)$^2$ is consistent for the second row as well.
Row 3: The numbers are 164, 125, and ?.
We can now apply the established pattern to find the missing number. Let the missing number be \(x\).
\[ 164 + 125 = x^2 \] \[ 289 = x^2 \] \[ x = \sqrt{289} \] \[ x = 17 \] Step 4: Final Answer:
The missing number in the square is 17.