Question

7.
Which 4 digit number multiplied by 4 gives the same number in reverse?
abcd x 4 = dcba
WH​

Answer 1

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8712

Step-by-step explanation:

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

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

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

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

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

☆From [5], D is either 8 or 9.

☆However, since D times 4 would end in 2, D is 8.Using [2], 4000a+400b+40c+4d = 1000d+100c+10b+a, which would simplify to 2c-13b = 1 after substituting A = 2 and D = 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 ither 1 or 3.

☆The answer you're looking for is 2178, multiplied by 4 gives 8712.

Hopes it help you✌️✌️