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Operation F means “take the square root,� operation G me

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Operation F means “take the square root,� operation G me

by guerrero » Sun May 05, 2013 12:00 pm
Operation F means "take the square root," operation G means "multiply by constant c," and operation H means "take the reciprocal." For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) -1

(B) -½

(C) 0

(D) ½

(E) 1

Is it GMAT type question ? If yes , I need some help in understanding the approach .

thanks in advance .

OAE
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by Atekihcan » Sun May 05, 2013 12:09 pm
F(x) = √x
G(x) = cx
H(x) = 1/x

Now, F(G(H(x))) = √(c/x)
And, F(H(G(x))) = √(1/cx)

As the result should be same for any order of the operations, √(c/x) = √(1/cx)
Clearly both c and x must be positive.

So, c/x = 1/cx
--> c = 1/c
--> c = 1

Answer : E
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