Find a $4$ -digit odd number using each of the digits $1, 2, 4$ and $5$ only once such that when the first and the last digits are interchanged, it is divisible by $4$

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Solution

a number is divisible by $4$ if the last $2$ digits are 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 b used at last
$⟹$ the numbers are $4521, 2451, 4125, 2415$

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Find a 4-digit odd number using each of the digits 1,2,4 and 5 only once such that when the first and the last digits are interchanged, it is divisible by 4

a number is divisible by 4 if the last 2 digits are 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 b used at last⟹ the numbers are 4521,2451,4125,2415

Find a $4$ -digit odd number using each of the digits $1, 2, 4$ and $5$ only once such that when the first and the last digits are interchanged, it is divisible by $4$

a number is divisible by $4$ if the last $2$ digits are 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 b used at last
$⟹$ the numbers are $4521, 2451, 4125, 2415$