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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?

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1356

1648

1462

1000

answer is C.

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Detailed Solution

Let the three-digit number be x, y, and z. Then, the number is

100 z + 10 y + x

.
We can say that,

y 2 = x z

, where

x z

is a square number.
By using the trial-and-error method, we have
If

x z = 1

, then

y = 1

. The number will be 111. So, we cannot subtract 400 from 111. Again, if

x z = 4

, then

y = 2

. The number will be 421. So,

421 − 400 = 21

, which is not a three-digit number. Again, if

x z = 9

, then

y = 3

. The number will be 931. So,

931 − 400 = 531

, which is a three-digit number.
Then, the sum is

931 + 531 = 1462

.
Hence, the correct option is 3.

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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?

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