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# In which of the following pairs are the two numbers reciproc

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Joined: 02 Sep 2009
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In which of the following pairs are the two numbers reciproc  [#permalink]

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26 Dec 2013, 08:56
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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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Re: In which of the following pairs are the two numbers reciproc  [#permalink]

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26 Dec 2013, 08:56
1
SOLUTION

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 $$\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$$.

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

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26 Dec 2013, 21:51
1
Solution:

I. The reciprocal of 3 is 1/3. So, I is correct.
II. The reciprocal of 1/17 is 17. So, II is incorrect.
III. The reciprocal of \sqrt{3} = 1/\sqrt{3} = \sqrt{3}/(\sqrt{3} * \sqrt{3} = \sqrt{3}/3. So, III is correct.

Ans is (D).
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Posts: 55804
Re: In which of the following pairs are the two numbers reciproc  [#permalink]

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30 Dec 2013, 03:33
1
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 $$\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$$.

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

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30 Dec 2013, 05:19
2
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 $$\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$$.

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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30 Dec 2013, 05:22
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 $$\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$$.

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]

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08 Jan 2014, 08:08
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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09 Jul 2017, 08:13
2
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

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

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14 Aug 2018, 03:50
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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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11 Sep 2018, 23:43
1
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] 11 Sep 2018, 23:43
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