MathematicsThe 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 100z+10y+x  .
    We can say that, y 2 =xz  , where xz   is a square number.
    By using the trial-and-error method, we have
    If xz=1  , then y=1  . The number will be 111. So, we cannot subtract 400 from 111. Again, if xz=4  , then y=2  . The number will be 421. So, 421400=21  , which is not a three-digit number. Again, if xz=9  , then y=3  . The number will be 931. So, 931400=531  , which is a three-digit number.
    Then, the sum is 931+531=1462  .
    Hence, the correct option is 3.
     
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