If a, b and c are different real numbers such that a+1/b = b+1/c = c+1

**Edited

OK! Not sure a GMAT question or not? Definitely took me > 2 min

Given,
\(a+\frac{1}{b}\) = \(b+\frac{1}{c}\)
--> \(a - b\) = \(\frac{1}{c}\) - \(\frac{1}{b}\) = \(\frac{(b - c)}{bc}\) ....... (1)

\(b+\frac{1}{c}\) = \(c+\frac{1}{a}\)
--> \(b - c\) = \(\frac{1}{a}\) - \(\frac{1}{c}\) = \(\frac{(c - a)}{ac}\) ....... (2)

\(a+\frac{1}{b}\) = \(c+\frac{1}{a}\)
--> \(a - c\) = \(\frac{1}{a}\) - \(\frac{1}{b}\) = \(\frac{(b - a)}{ab}\) ....... (3)

Multiply (1), (2) & (3)
--> \((a - b)*(b - c)*(a - c)\) = (\(\frac{(b - c)}{bc}\))*(\(\frac{(c - a)}{ac}\))*(\(\frac{(b - a)}{ab}\))
--> \((a - b)*(b - c)*(a - c)\) = \(\frac{(b - c)*(c - a)*(b - a)}{(abc)^2}\)

The above equation is only possible when (abc)^2 = 1
--> a*b*c can be 1 or -1

So, possible value = 1

IMO Option A

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