Find four-digit odd numbers using each of the digits $1, 2, 4$ and $5$ only once such that when the first and last digits are interchange , it becomes exactly divisible by $4 .$

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Solution

Since as we know that last two digits of number is divisible by $4$ .Then the number is also divisible by $4$ .
The last two digits must be $24$ or $12$ or $52$ after interchanging and for the number to be odd $1$ or $5$ should be used at last.
Hence, the numbers are $4521, 2451, 4125, 2415$

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Find four-digit odd numbers using each of the digits 1,2,4and 5 only once such that when the first and last digits are interchange , it becomes exactly divisible by 4.

Since as we know that last two digits of number is divisible by 4.Then the number is also divisible by 4. The last two digits must be 24 or 12 or 52 after interchanging and for the number to be odd 1 or 5 should be used at last.Hence, the numbers are 4521,2451,4125,2415

Find four-digit odd numbers using each of the digits $1, 2, 4$ and $5$ only once such that when the first and last digits are interchange , it becomes exactly divisible by $4 .$

Since as we know that last two digits of number is divisible by $4$ .Then the number is also divisible by $4$ .
The last two digits must be $24$ or $12$ or $52$ after interchanging and for the number to be odd $1$ or $5$ should be used at last.
Hence, the numbers are $4521, 2451, 4125, 2415$