knight247 wrote:The digits of a positive integer having 3 digits when taken in order are in arithmetic progression and their sum is 18. The number obtained by reversing the digits is 396 less than the original number. Find the number
(A)468
(B)594
(C)792
(D)822
(E)864
OA is E
Detailed explanations would be appreciated. Thanks
We can plug in the answer choices, which represent the 3-digit integer.
The sum of the digits must be 18.
Eliminate D (since 8+2+2≠18).
When the digits are taken in order, they must be in arithmetic progression.
Thus, the 3 digits must be equally spaced.
Eliminate B (since 4-5-9 is not equally spaced).
Eliminate C (since 2-7-9 is not equally spaced).
When the digits are reversed, the result must be 396 less than the original number.
Thus, the units digit must be smaller than the hundreds digit.
Eliminate A (since the units digit 8 is larger than the hundreds digit 4).
The correct answer is
E.
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