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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 BTGmoderatorLU » Thu May 31, 2018 1:53 pm

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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. -1/2
C. 0
D. 1/2
E. 1

The OA is E.

Please, can anyone assist me with this PS question? I don't have it clear. Thanks in advance.
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by Jay@ManhattanReview » Thu May 31, 2018 9:45 pm
BTGmoderatorLU wrote: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. -1/2
C. 0
D. 1/2
E. 1

The OA is E.

Please, can anyone assist me with this PS question? I don't have it clear. Thanks in advance.
-1 and -2 cannot be correct since the square root of negative numbers is not real.

0 cannot be correct since the reciprocal of 0 is indeterminable.

1/2 cannot be correct since √(1/2) ≠ 1/2 x 2 ≠ 1/(1/2).

1 is correct since √1 = 1 x 1 = 1/1.

The correct answer: E

Hope this helps!

-Jay
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by Jeff@TargetTestPrep » Sun Jun 03, 2018 5:35 pm
BTGmoderatorLU wrote: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. -1/2
C. 0
D. 1/2
E. 1
Let x be a positive constant. Let's apply the operations F, G and H to x in various orders:

F(G(H(x))) = F(G(1/x)) = F(c/x) = √(c/x)

H(G(F(x))) = H(G(√x)) = H(c√x) = 1/(c√x)

Since we are looking for a value of c which produces the same result when the operations are applied in any order, let's equate these two values:

√(c/x) = 1/(c√x)

(√c)/(√x) = 1/(c√x)

Since x is positive, we can multiply each side of this equation by √x:

√c = 1/c

c√c = 1

Let's square each side:

c^3 = 1

c = 1

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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