A 4 digit number - Math Central

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Question from May, a parent:

The number is given as ABCD. The first digit is a quarter of the last digit. The second digit is one less than the first digit.
When the number ABCD is multiplied by four its digits appear in the reverse order. None of the digits are the same. What is the number. Pleas help because my child need help and I can not do this. Thank you.

Hi again May,

I can help get you started.

Since the first digit $A$ is one quarter the last digit $D,$ $D$ must be 4 times $A.$ The only digits that are multiples of 4 are 0, 4 and 8 and hence $D = 4 \times A$ is 0, 4 or 8. What can $A$ be? Now use the fact that the second digit is one less than the first digit.

Write back if you need more help,
Penny

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