There is a 4 digit number that when multiplied by 4 is the reverse.

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Mathematics

2 May, 00:27

There is a 4 digit number that when multiplied by 4 is the reverse.

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Howard Weber · Answer 1

2178 that the answer

Nico · Answer 2

The answer is 2178, if you multiply it by 4, you would get 8717

Step-by-step explanation:

HERE ARE THE STEPS IF YOU NEED THEM!

1. Lets say the number is written as ABCD (1000a+100b+10c+d).

2. Multiplying it by 4, gives you DCBA (1000d+100c+10b+a)

3. By divisibility of 4, BA is a two-digit number divisible by 4.

4. Now, the largest possible value of ABCD is 2499, because anything more will result in a five digit number when multiplied by 4.

5. Out of the two possibilites 1 and 2 for A, [3] follows that A is even, so 2.

6. From [5], D is either 8 or 9. However, since D times 4 would end in 2, D is 8.

7. Using [2], 4000a+400b+40c+4d = 1000d+100c+10b+a, which would simplify to 2c-13b = 1 after substituting A = 2 and D = 8.

8. The only possible value of (b, c) where they would both be single digit integers is (1,7). Also to note from [3], B is odd. And from [4], B is either 1 or 3.