Last visit was: 24 Apr 2026, 04:08 It is currently 24 Apr 2026, 04:08
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
Sub 505 (Easy)|   Arithmetic|                           
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,809
Own Kudos:
Given Kudos: 105,869
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,809
Kudos: 810,934
 [38]
4
Kudos
Add Kudos
34
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,809
Own Kudos:
Given Kudos: 105,869
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,809
Kudos: 810,934
 [10]
4
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
General Discussion
User avatar
nutshell
Joined: 21 Mar 2011
Last visit: 04 Jul 2019
Posts: 95
Own Kudos:
311
 [1]
Given Kudos: 104
Status:GMATting
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
GMAT 1: 590 Q45 V27
Posts: 95
Kudos: 311
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,809
Own Kudos:
810,934
 [2]
Given Kudos: 105,869
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,809
Kudos: 810,934
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
WoundedTiger
Joined: 25 Apr 2012
Last visit: 03 Jan 2026
Posts: 520
Own Kudos:
2,584
 [2]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Products:
Posts: 520
Kudos: 2,584
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,809
Own Kudos:
Given Kudos: 105,869
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,809
Kudos: 810,934
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WoundedTiger
Bunuel
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.
avatar
masokaz
Joined: 14 Nov 2012
Last visit: 10 Jan 2014
Posts: 1
Given Kudos: 2
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
easy question.. wish all GMAT could be this simple
User avatar
ydmuley
User avatar
Retired Moderator
Joined: 19 Mar 2014
Last visit: 01 Dec 2019
Posts: 807
Own Kudos:
916
 [3]
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
shashankism
Joined: 13 Mar 2017
Last visit: 19 Feb 2026
Posts: 608
Own Kudos:
Given Kudos: 88
Affiliations: IIT Dhanbad
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy)
Posts: 608
Kudos: 712
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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:
1. Please provide your solutions to the questions;
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
avatar
care05
Joined: 07 Sep 2018
Last visit: 08 Jun 2019
Posts: 2
Own Kudos:
1
 [1]
Given Kudos: 1
Posts: 2
Kudos: 1
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone please tell me how 1/sqr3 is equal to sqr3/3? Thanks!

Posted from my mobile device
User avatar
WM88
User avatar
Current Student
Joined: 20 Jun 2019
Last visit: 16 Apr 2021
Posts: 43
Own Kudos:
28
 [1]
Given Kudos: 15
Location: United States (DC)
GRE 1: Q159 V162
GPA: 3.4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ydmuley
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?
User avatar
Prasannathawait
Joined: 10 Aug 2018
Last visit: 15 Jun 2020
Posts: 215
Own Kudos:
152
 [1]
Given Kudos: 179
Location: India
Concentration: Strategy, Operations
WE:Operations (Energy)
Products:
Posts: 215
Kudos: 152
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
D is the right answer. I think the level of question is in the 300's.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
avatar
sahuanamika
Joined: 22 May 2021
Last visit: 05 Oct 2021
Posts: 44
Own Kudos:
Given Kudos: 107
Posts: 44
Kudos: 21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
totaltestprepNick
Joined: 25 Aug 2014
Last visit: 23 Apr 2026
Posts: 469
Own Kudos:
Given Kudos: 2
GMAT 1: 750 Q49 V42
GMAT 1: 750 Q49 V42
Posts: 469
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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





Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

[email protected]
Moderators:
Math Expert
109809 posts
Tuck School Moderator
853 posts