Question

If 1294 is written as 3516, how is 1385 written in the same code?

• A. 3890
• B. 2950
• C. 2049
• D. 3607
• E. 3039

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This question belongs to the category of "Positional Number Coding," where each digit of a multi-digit number is transformed independently according to a specific mathematical rule.
To solve this, we must compare the corresponding digits of the original number (1294) and the coded number (3516) to identify the underlying pattern of addition or subtraction.
Step 2: Key Formula or Approach:
We use the digit-wise shift method:
\[ \text{Digit of Code} = (\text{Digit of Original} + \text{Shift Value}) \pmod{10} \] If the result of the addition is a two-digit number, only the unit digit is retained.
Step 3: Detailed Explanation:

Analyzing the first number (1294 $\rightarrow$ 3516):
Let us break down the transformation digit by digit:
- First Digit: The original digit is 1 and the coded digit is 3. The shift is \(3 - 1 = +2\).
- Second Digit: The original digit is 2 and the coded digit is 5. The shift is \(5 - 2 = +3\).
- Third Digit: The original digit is 9 and the coded digit is 1. Here, \(9 + 2 = 11\). Taking the unit digit of 11, we get 1. Thus, the shift is \(+2\).
- Fourth Digit: The original digit is 4 and the coded digit is 6. The shift is \(6 - 4 = +2\).
The established pattern of shifts for the four positions is \((+2, +3, +2, +2)\).

Applying the pattern to the target number (1385):
Now, we apply the same sequence of shifts to each digit of 1385:
- First Digit (1): \(1 + 2 = 3\).
- Second Digit (3): \(3 + 3 = 6\).
- Third Digit (8): \(8 + 2 = 10\). We take only the unit digit, which is \(0\).
- Fourth Digit (5): \(5 + 2 = 7\).
Combining these resulting digits in order gives us the final code: \(3, 6, 0, 7\).

Step 4: Final Answer:
The number 1385, when coded using the rule established by 1294 $\rightarrow$ 3516, becomes 3607.
By comparing this result with the given options, we find that it matches option (D).