Two-digit number with digit sum 10 — Reversing the digits decreases the number by 36. Identify which statements are true: I) The number is divisible by a composite number. II) The number is a multiple of a prime number.

Introduction / Context:
This problem blends place-value reasoning with properties of primes and composites. You are told the two-digit number has digits summing to 10, and reversing the digits reduces the number by 36. From these constraints, you can determine the exact number and then evaluate the truth of the given statements regarding divisibility.

Given Data / Assumptions:

• Let the tens digit be a and the units digit be b.
• a + b = 10.
• Original number: 10a + b. Reversed: 10b + a.
• Reversing decreases the number by 36: (10a + b) - (10b + a) = 36.

Concept / Approach:
Translate the language into equations and solve the simple system for digits a and b. Then assess primality and divisibility statements. Every integer is a multiple of at least one prime (its prime factors); being divisible by a composite requires having a composite factor greater than 1, which primes do not have.

Step-by-Step Solution:
Set up the difference: (10a + b) - (10b + a) = 9a - 9b = 36 → a - b = 4.Combine with a + b = 10: add equations → 2a = 14 → a = 7; then b = 3.Number = 10a + b = 73; reversed = 37; difference = 36, as required.73 is a prime number (only factors 1 and 73).

Verification / Alternative check:
Digit-sum and reversal both check out. Quick divisibility tests show 73 has no composite divisor other than itself (which is prime), confirming its primality.

Why Other Options Are Wrong:

• only I / Both I and II / Neither I nor II: Statement I is false since 73 is not divisible by any composite number; Statement II is true because any integer is a multiple of some prime (73 * 1 = 73).

Common Pitfalls:
Assuming “multiple of a prime” means a special property—every positive integer except 1 is a multiple of at least one prime; confusing composite divisibility with primality.

Final Answer:
only II