If x=y^a, y=z^b and z= x^c, then abc=?

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Chinn_asama: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Sat Jun 02, 2012 7:14 pm; Thanked: 1 times

by Chinn_asama » Sat Jun 23, 2012 11:41 am

If x=y^a, y=z^b and z= x^c, then abc=?

can anyone explain why the answer is 1?

Thanx

Source: Beat The GMAT — Problem Solving | Sat Jun 23, 2012 11:41 am

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Sat Jun 23, 2012 12:00 pm

Chinn_asama wrote:If x=y^a, y=z^b and z= x^c, then abc=?

x = y^a
y = z^b --> z = y^(1/b)
z = x^c = (y^a)^c = y^(ac)

So, y^(1/b) = y^(ac)
--> 1/b = ac
--> abc = 1

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