Three distinct single digit numbers A, B, C are in GP. If abs(x) for real x is…
2026
Three distinct single digit numbers A, B, C are in GP. If abs(x) for real x is the absolute value of x(x if x is +ve or zero, -x if x is -ve), then the number of different possible values of abs(A+B-C) is:
- A.
5
- B.
4
- C.
6
- D.
3
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Correct answer: A
Solution: Enumerate all three-term geometric progressions with distinct positive single-digit integer terms (1 through 9) and compute |A+B-C|.
(1, 2, 4) → |1 + 2 - 4| = 1
(2, 4, 8) → |2 + 4 - 8| = 2
(1, 3, 9) → |1 + 3 - 9| = 5
(4, 2, 1) → |4 + 2 - 1| = 5
(8, 4, 2) → |8 + 4 - 2| = 10
(9, 3, 1) → |9 + 3 - 1| = 11
The computed absolute values are 1, 2, 5, 5, 10, 11, so the distinct values are 1, 2, 5, 10, 11.
Therefore, the number of different possible values of |A + B - C| is 5.