Question

If 2 + 4 = 20 and 3 + 5 = 34, then 6 + 9 =

• A. 121
• B. 118
• C. 108
• D. 117

Hint:

For number puzzles, if the output value is significantly larger than the sum of the inputs, think of exponents (squares or cubes) or multiplication.
Here, \(2+4=6\) but the result is \(20\) (near the square of \(4\)). This immediately hints at checking squares!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question is a mathematical puzzle where the standard addition operator (+) represents a specific logical or mathematical pattern.
We are given two test cases: \(2 + 4 = 20\) and \(3 + 5 = 34\).
We need to identify this hidden pattern and apply it to find the value of \(6 + 9\).

Step 2: Key Formula or Approach:
Let us assume the operation is defined as \(a \oplus b = c\).
We need to find a function \(f(a, b) = c\) that works for both given equations.
Let us try common algebraic patterns such as:
- \((a + b) \times k\)
- \(a^2 + b^2\)
- \((a \times b) + k\)

Step 3: Detailed Explanation:

• Let us test the sum of squares hypothesis, i.e., \(f(a, b) = a^2 + b^2\).

• Testing with the first equation: \(2 + 4 = 20\)
- Here, \(a = 2\) and \(b = 4\).
- Let us calculate the sum of their squares:
\[ a^2 + b^2 = 2^2 + 4^2 \]
\[ 2^2 + 4^2 = 4 + 16 = 20 \]
- This perfectly matches the given result of \(20\).

• Testing with the second equation: \(3 + 5 = 34\)
- Here, \(a = 3\) and \(b = 5\).
- Let us calculate the sum of their squares:
\[ a^2 + b^2 = 3^2 + 5^2 \]
\[ 3^2 + 5^2 = 9 + 25 = 34 \]
- This perfectly matches the given result of \(34\).

• Since the sum of squares rule is consistent across both test cases, we can confidently apply it to the target expression: \(6 + 9\)
- Here, \(a = 6\) and \(b = 9\).
- Let us calculate the sum of their squares:
\[ 6^2 + 9^2 = 36 + 81 \]
\[ 36 + 81 = 117 \]

• Thus, the value is \(117\), which corresponds to Option (D).


Step 4: Final Answer:
The value of \(6 + 9\) based on the sum of squares logic is \(117\), which matches Option (D).