Question

In a secret code, if 3 becomes 1312, 4 becomes 1716, 5 becomes 2120, 6 becomes 2524, 7 becomes 2928 and 8 becomes 3332 then what would 9 become?

• A. 3736
• B. 3637
• C. 3534
• D. 3835

Hint:

When the output in a coding problem is a multi-digit number, always try splitting it into smaller, more manageable parts. Often, simple arithmetic operations relate these parts to the input.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a coding-decoding problem where an input number \(X\) is transformed into a four-digit number based on a hidden rule. We need to deduce this rule from the given examples.
Step 2: Key Formula or Approach:
A common strategy for such problems is to look for patterns by splitting the output number into parts. Since the output is a four-digit number, let's split it into two two-digit numbers and analyze each part separately in relation to the input number \(X\).
Step 3: Detailed Explanation:
Let's write down the transformations and split the output: - \(X=3 \rightarrow 1312 \implies 13 \text{ and } 12\) - \(X=4 \rightarrow 1716 \implies 17 \text{ and } 16\) - \(X=5 \rightarrow 2120 \implies 21 \text{ and } 20\) - \(X=6 \rightarrow 2524 \implies 25 \text{ and } 24\) - \(X=7 \rightarrow 2928 \implies 29 \text{ and } 28\) - \(X=8 \rightarrow 3332 \implies 33 \text{ and } 32\) Now, let's find the rule for each part.
Rule for the second part (last two digits): - For \(X=3\), the part is 12. \(12 = 4 \times 3\). - For \(X=4\), the part is 16. \(16 = 4 \times 4\). - For \(X=5\), the part is 20. \(20 = 4 \times 5\). The pattern is consistent. The rule is: Second Part = \(4 \times X\). Rule for the first part (first two digits): - For \(X=3\), the part is 13. Notice that \(13 = 12 + 1\). - For \(X=4\), the part is 17. Notice that \(17 = 16 + 1\). - For \(X=5\), the part is 21. Notice that \(21 = 20 + 1\). The pattern is that the first part is one more than the second part. So, the rule is: First Part = (Second Part) + 1 = \(4 \times X + 1\). Let's apply these rules to find the code for \(X=9\).
- Second Part = \(4 \times 9 = 36\). - First Part = \(4 \times 9 + 1 = 36 + 1 = 37\). Combining the two parts, the number becomes 3736.
Step 4: Final Answer:
The code for 9 is 3736.