The digits of a three-digit number from a G.P. If 400 is subtracted from it, then we get another three-digit number whose digits form an arithmetic series. What is the sum of these two numbers?

# The digits of a three-digit number from a G.P. If 400 is subtracted from it, then we get another three-digit number whose digits form an arithmetic series. What is the sum of these two numbers?

1. A
1356
2. B
1648
3. C
1462
4. D
1000

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### Solution:

Let the three-digit number be x, y, and z. Then, the number is  .
We can say that,  , where   is a square number.
By using the trial-and-error method, we have
If  , then  . The number will be 111. So, we cannot subtract 400 from 111. Again, if  , then  . The number will be 421. So,  , which is not a three-digit number. Again, if  , then  . The number will be 931. So,  , which is a three-digit number.
Then, the sum is  .
Hence, the correct option is 3.

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