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 Concept:
In number grid puzzles, we look for arithmetic relationships across rows or down columns. Often, the numbers in the first two rows combine to form the value in the third row, or there is a relationship involving square roots or squares.
Step 2: Key Formula or Approach:
Let the rows be $R_1, R_2, R_3$. Check the relationship: $R_3 = 2 \times R_1 + R_2$ or similar combinations. In this specific grid, the logic involves the sum of the components.
Step 3: Detailed Explanation:
1. Column 1: \(64 \times 2 + 25 + 11 = 164\) (This doesn't quite fit). Let's try: \( (64 \times 2) + 36 = 164 \).
2. Column 2: \( (80 \times 1) + (11 \times 4) + 1 = 125 \).
3. Alternative Logic (Sum of squares):
Notice the first numbers are perfect squares: \(\sqrt{64}=8, \sqrt{25}=5, \sqrt{16}=4\).
Column 1: \(64 + 25 \times 4 = 164\).
Column 2: \(80 + 11 \times 4 + 1 = 125\).
4. Correct Vertical Pattern:
Row 3 = Row 1 + (Row 2 \(\times\) 4).
Col 1: \(64 + (25 \times 4) = 64 + 100 = 164\).
Col 2: \(80 + (11 \times 4) + 1 = 125\) (Mismatch).
Final Logic:
Sum of elements in Row 1: \(6+4+8+0+1+2 = 21\)
Sum of elements in Row 2: \(2+5+1+1+6 = 15\)
Let's try: \(R_1 + R_2 \times 2\):
Col 3: \((12 \times 1) + (6 \times 0.5) + \dots\)
Applying Column Logic \(2 \times R_1 + R_2 = R_3\):
Col 1: \(2(64) + 25 + 11 = 164\) (Wait, 25 and 11 are in Row 2? No).
Let's use: \(2 \times R_1 + R_2 = R_3\).
Col 1: \(2(64) + 25 = 128 + 25 = 153\) (No).
Col 1: \(2.5 \times 64 + 4 = 164 \implies 160 + 4 = 164\).
Col 2: \(1.5 \times 80 + 5 = 125 \implies 120 + 5 = 125\).
Col 3: \(1 \times 12 + 5 = 17\).
Step 4: Final Answer:
The missing number is 17.