In this coding system, two two-digit numbers are combined by interleaving their digits. For example: 53 34 becomes 5334, and 65 46 becomes 6456. Using the same digit-interleaving pattern, what will 75 24 become?

Introduction / Context:This question tests pattern recognition in number coding. Two two-digit numbers are being combined into a four-digit output using a consistent arrangement of digits. The goal is to identify that arrangement and apply it to a new pair.

Given Data / Assumptions:

• 53 34 = 5334
• 65 46 = 6456
• Find: 75 24 = ?
• Assume the same digit placement rule applies to all cases.

Concept / Approach:Break each two-digit number into tens and ones digits. Check how the four digits appear in the output. A common pattern is interleaving: first tens digit, then tens digit of second, then ones digit of first, then ones digit of second.

Step-by-Step Solution: Take 65 and 46: 65 has digits: 6 (tens), 5 (ones) 46 has digits: 4 (tens), 6 (ones) Output is 6456 = 6,4,5,6 So the rule is: (tens of first), (tens of second), (ones of first), (ones of second). Now apply to 75 and 24: 75 gives 7 (tens), 5 (ones) 24 gives 2 (tens), 4 (ones) Interleave: 7,2,5,4 → 7254

Verification / Alternative check:Check 53 and 34: tens digits 5 and 3, ones digits 3 and 4, giving 5,3,3,4 → 5334. This matches, confirming the same rule, so 7254 is correct.

Why Other Options Are Wrong: 7542: keeps first number then reversed second, not interleaving. 7524: concatenates numbers directly. 7452: mixes tens/ones order incorrectly. 7245: swaps the last two digits incorrectly.

Common Pitfalls:Concatenating without interleaving, reversing one number, or interleaving in the wrong sequence (ones first instead of tens first) are typical errors.

Final Answer:7254