A: 2178
If the number is still 4 digits when multiplied by 4, then the number has to be less than 2500 (as 2500 x 4 = 10000 and you would then have 5 digits).
That makes w = 1 or 2
But when multiplying by 4, the last digit will never be 1 so when we reverse to zyxw, the w must be 2 so that the last digit will then be 2. The multiples of 4 that have a last digit of 2 are 3 x 4 and 8 x 4.
Since we are multiplying a number in the 2000s by 4, the number is becomes will start with an 8.
w = 2 and z = 8
The second digit x must be 4 or less as it says above, the number must be less than 2500.
Because 2250 x 4 = 9000, x must be 0 1 or 2
Through some trial and error, you can find that the number is 2178 and its reverse is 8712.
If the number is still 4 digits when multiplied by 4, then the number has to be less than 2500 (as 2500 x 4 = 10000 and you would then have 5 digits).
That makes w = 1 or 2
But when multiplying by 4, the last digit will never be 1 so when we reverse to zyxw, the w must be 2 so that the last digit will then be 2. The multiples of 4 that have a last digit of 2 are 3 x 4 and 8 x 4.
Since we are multiplying a number in the 2000s by 4, the number is becomes will start with an 8.
w = 2 and z = 8
The second digit x must be 4 or less as it says above, the number must be less than 2500.
Because 2250 x 4 = 9000, x must be 0 1 or 2
Through some trial and error, you can find that the number is 2178 and its reverse is 8712.
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