For how many three-digit numbers can you subtract 297 and obtain a second three-digit number which is the original three-digit number reversed?
A. 5
B. 10
C. 20
D. 40
E. 60
E. 60
Suppose that ‘pqr’ is a three-digit number whose digits are reversed when 297 is subtracted.Since ‘pqr’ represents the number 100p + 10q + r and ‘rqp’ represents 100r + 10q + p, we have 100p + 10q + r − 297 = 100r + 10q + p. This equation can be rearranged to give 99p − 99r = 297 and hence we have p − r = 3. Since we know that ‘rqp’ is a three-digitnumber, r ≠ 0. Therefore there are six possibilities for the pair (p, r), namely (4, 1), (5, 2),(6, 3), (7, 4), (8, 5) and (9, 6). The middle digit, q, can be any one of the 10 digits. Thereforethe number of possible values for the original three-digit number is 6 × 10 = 60.
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