GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 03:20

### 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

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

# In the following pairs of numbers, which are reciprocals of each other

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58400
In the following pairs of numbers, which are reciprocals of each other  [#permalink]

### Show Tags

Updated on: 07 Jul 2019, 00:03
00:00

Difficulty:

(N/A)

Question Stats:

76% (00:42) correct 24% (00:43) wrong based on 78 sessions

### HideShow timer Statistics

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

I. 1 and 1
II. 1/11 and −11
III. 5 and $$\frac{\sqrt{5}}{5}$$

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

Source: Nova GMAT
Difficulty Level: 600

_________________

Originally posted by Bunuel on 24 Jun 2017, 08:19.
Last edited by SajjadAhmad on 07 Jul 2019, 00:03, edited 1 time in total.
Senior SC Moderator
Joined: 22 May 2016
Posts: 3544
Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

### Show Tags

24 Jun 2017, 08:35
Bunuel wrote:
In the following pairs of numbers, which are reciprocals of each other?

I. 1 and 1
II. 1/11 and −11
III. 5 and $$\frac{\sqrt{5}}{5}$$

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

The product of a number and its reciprocal is 1.

I. 1 and 1. Yes. 1*1 = 1. Or remember that the only two numbers that are their own reciprocals are 1 and -1. Keep.

II. 1/11 and -11. No. 1/11 * -11 = -1. Reject.

III. 5 and $$\frac{\sqrt{5}}{5}$$. No. 5 * $$\frac{\sqrt{5}}{5}$$ = $$\frac{\sqrt{5}}{1}$$. The reciprocal of 5 is 1/5. The reciprocal of $$\frac{\sqrt{5}}{5}$$ is $$\frac{5}{\sqrt{5}}$$. Reject.

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Director
Joined: 04 Dec 2015
Posts: 745
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

### Show Tags

24 Jun 2017, 08:56
Bunuel wrote:
In the following pairs of numbers, which are reciprocals of each other?

I. 1 and 1
II. 1/11 and −11
III. 5 and $$\frac{\sqrt{5}}{5}$$

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

Reciprocals multiplied to each other will always be $$= 1$$.

Lets check this rule on the options.

I. 1 and 1

$$1 * \frac{1}{1} = 1$$ ---------- (Reciprocals)

II. $$\frac{1}{11}$$ and −11

$$\frac{1}{11} * - 11 = -1$$ --------- (Not reciprocals)

III. 5 and $$\frac{\sqrt{5}}{5}$$

$$5 *$$ $$\frac{\sqrt{5}}{5}$$ $$= \sqrt{5}$$ ---------- (Not reciprocals)

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

### Show Tags

24 Jun 2017, 09:39
A number is a reciprocal of another number, if the numbers can be represented as x and $$\frac{1}{x}$$
Lets look at the answer options,
I. 1 and 1 (These are reciprocal numbers)
II. 1/11 and −11 (Two numbers can never be reciprocal if they are of the opposite sign)
III. 5 and $$\frac{\sqrt{5}}{5}$$

Since 5 = $$\sqrt{5}*\sqrt{5}$$
$$\frac{\sqrt{5}}{5}$$ = $$\frac{\sqrt{5}}{\sqrt{5}*\sqrt{5}}$$ = $$\frac{1}{\sqrt{5}}$$

5 and $$\frac{\sqrt{5}}{5}$$ are not reciprocals.
Hence Option A(I only) is the only option which has reciprocal numbers.
_________________
You've got what it takes, but it will take everything you've got
Manager
Joined: 30 May 2012
Posts: 198
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

### Show Tags

14 Jul 2017, 13:18
Bunuel Could you please modify the answer? Seems to most of us the answer is A. If not, please provide an explanation. Thank you.
Re: In the following pairs of numbers, which are reciprocals of each other   [#permalink] 14 Jul 2017, 13:18
Display posts from previous: Sort by