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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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In which of the following pairs are the two numbers reciprocals of each other?

I. 3 and 1/3
II. 1/17 and -1/17
III. \(\sqrt{3}\) and \(\frac{\sqrt{3}}{3}\)


(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Reciprocal for a number \(x\), denoted by \(\frac{1}{x}\) or \(x^{-1}\), is a number which when multiplied by \(x\) yields \(1\). The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). To get the reciprocal of a number, divide 1 by the number. For example reciprocal of \(3\) is \(\frac{1}{3}\), reciprocal of \(\frac{5}{6}\) is \(\frac{6}{5}\).

Reciprocal of 3 is 1/3.

Reciprocal of 1/17 is 17. Discard.

Reciprocal of \(\sqrt{3}\) is \(\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\).

Answer: D.
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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Bunuel wrote:
In which of the following pairs are the two numbers reciprocals of each other?

I. 3 and 1/3
II. 1/17 and -1/17
III. \(\sqrt{3}\) and \(\frac{\sqrt{3}}{3}\)


(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Reciprocal for a number \(x\), denoted by \(\frac{1}{x}\) or \(x^{-1}\), is a number which when multiplied by \(x\) yields \(1\). The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). To get the reciprocal of a number, divide 1 by the number. For example reciprocal of \(3\) is \(\frac{1}{3}\), reciprocal of \(\frac{5}{6}\) is \(\frac{6}{5}\).

Reciprocal of 3 is 1/3.

Reciprocal of 1/17 is 17. Discard.

Reciprocal of \(\sqrt{3}\) is \(\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\).

Answer: E.



Hi Bunuel,

We need reciprocals of given number so for 3 it will be 1/3 and for \sqrt{3} it will be 1/ \sqrt{3} or \sqrt{3}/3.

Ans should be D.

For II is not a reciprocal, reciprocal of 1/17 is 17
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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WoundedTiger wrote:
Bunuel wrote:
In which of the following pairs are the two numbers reciprocals of each other?

I. 3 and 1/3
II. 1/17 and -1/17
III. \(\sqrt{3}\) and \(\frac{\sqrt{3}}{3}\)


(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Reciprocal for a number \(x\), denoted by \(\frac{1}{x}\) or \(x^{-1}\), is a number which when multiplied by \(x\) yields \(1\). The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). To get the reciprocal of a number, divide 1 by the number. For example reciprocal of \(3\) is \(\frac{1}{3}\), reciprocal of \(\frac{5}{6}\) is \(\frac{6}{5}\).

Reciprocal of 3 is 1/3.

Reciprocal of 1/17 is 17. Discard.

Reciprocal of \(\sqrt{3}\) is \(\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\).

Answer: E.



Hi Bunuel,

We need reciprocals of given number so for 3 it will be 1/3 and for \sqrt{3} it will be 1/ \sqrt{3} or \sqrt{3}/3.

Ans should be D.

For II is not a reciprocal, reciprocal of 1/17 is 17


Yes, I and III is D, not E. Typo edited. Thank you.
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
easy question.. wish all GMAT could be this simple
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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In which of the following pairs are the two numbers reciprocals of each other?

I. 3 and 1/3

Reciprocal of \(3 = \frac{1}{3}\)

I - TRUE

II. 1/17 and -1/17

Reciprocal of \(\frac{1}{17}\) is \(17\)

II - FALSE

III. \(\sqrt{3}\) and \(\frac{\sqrt{3}}{3}\)

Reciprocal of \(\sqrt{3}\) \(= \frac{1}{\sqrt{3}}\)

Multiply and divide the above equation by \(\sqrt{3}\), we get

\(\frac{\sqrt{3}}{3}\)

III - TRUE

Hence Answer is D
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In which of the following pairs are the two numbers reciprocals of each other?

I. 3 and 1/3
II. 1/17 and -1/17
III. \(\sqrt{3}\) and \(\frac{\sqrt{3}}{3}\)

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Problem Solving
Question: 8
Category: Arithmetic Properties of numbers (reciprocals)
Page: 63
Difficulty: 600


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It is a very easy question and can be solved within 20 seconds.
We can see 3 and 1/3 are reciprocals of each other.
Reciprocal of 1/17 is 17 and not -1/17

Reciprocal of \(\sqrt{3}\) is \(\frac{1}{\sqrt{3}}\) = \(\frac{\sqrt{3}}{3}\)

So, I & III is correct and Hence option D
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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Can someone please tell me how 1/sqr3 is equal to sqr3/3? Thanks!

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Re: In which of the following pairs are the two numbers reciproc [#permalink]
ydmuley wrote:
In which of the following pairs are the two numbers reciprocals of each other?

I. 3 and 1/3

Reciprocal of \(3 = \frac{1}{3}\)

I - TRUE

II. 1/17 and -1/17

Reciprocal of \(\frac{1}{17}\) is \(17\)

II - FALSE

III. \(\sqrt{3}\) and \(\frac{\sqrt{3}}{3}\)

Reciprocal of \(\sqrt{3}\) \(= \frac{1}{\sqrt{3}}\)

Multiply and divide the above equation by \(\sqrt{3}\), we get

\(\frac{\sqrt{3}}{3}\)

III - TRUE

Hence Answer is D



Can you please tell me how you got \(\frac{\sqrt{3}}{3}\) from 1/sqr3
Why did you multiple and divide?
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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D is the right answer. I think the level of question is in the 300's.
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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Option I: 3 and 1/3 are reciprocal of each other.

Option II: 1/17 and -1/17 are not reciprocal of each other.

Option III: \(\sqrt{3}\) and \(\frac{\sqrt{3}}{ 3}\)

=> \(\frac{\sqrt{3}}{ 3}\) = \(\frac{\sqrt{3}}{ (\sqrt{3} * \sqrt{3})}\) = \(\frac{1}{ \sqrt{3}}\)

Answer D
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
Reciprocals means x * (1/x) = 1 i.e The reciprocal or multiplicative inverse of a number x is the number which, when multiplied by x , gives 1

Going by the options:
1. 3*(1/3) = 1 -- true
2. 17*(-1/17) = -1 -- not true
3. sqrt(3) * (sqrt(3)/3) = 3/3 = 1 -- true

So only 1st and 3rd options are correct.
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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Re: In which of the following pairs are the two numbers reciproc [#permalink]
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