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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Operation F means “take the square root,” operation G means “multiply
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19 Jul 2021, 02:32
19 Jul 2021, 02:32
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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
(A) –1
(B) –1/2
(C) 0
(D) 1/2
(E) 1
Operation F means “take the square root,” operation G means “multiply
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29 Jan 2022, 20:41
29 Jan 2022, 20:41
2
Positive integer \(x\)
Operation \(F\) - Square root \(= \sqrt{x}\)
Operation \(G\) - multiply by \(c\) \(= cx\)
Operation \(H\) - reciprocal \(= \frac{1}{x}\)
For example,
\(H(G(F(x)) = \frac{1}{c\sqrt{x}}\)
\(H(F(G(x)) = \frac{1}{\sqrt{cx}}\)
For both of these to remains the same, let's compare them
\(\frac{1}{c\sqrt{x}} = \frac{1}{\sqrt{cx}}\)
\(c = \sqrt{c}\)
\(c\) can be \(0\) or \(1\)
But \(c\) can't be \(0\) as the reciprocal will be undefined.
\(c = 1\)
Answer E
Operation \(F\) - Square root \(= \sqrt{x}\)
Operation \(G\) - multiply by \(c\) \(= cx\)
Operation \(H\) - reciprocal \(= \frac{1}{x}\)
For example,
\(H(G(F(x)) = \frac{1}{c\sqrt{x}}\)
\(H(F(G(x)) = \frac{1}{\sqrt{cx}}\)
For both of these to remains the same, let's compare them
\(\frac{1}{c\sqrt{x}} = \frac{1}{\sqrt{cx}}\)
\(c = \sqrt{c}\)
\(c\) can be \(0\) or \(1\)
But \(c\) can't be \(0\) as the reciprocal will be undefined.
\(c = 1\)
Answer E
Re: Operation F means take the square root, operation G means multiply
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06 Sep 2025, 22:16
06 Sep 2025, 22:16
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
