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

It is currently 22 Nov 2019, 15:40

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

The sum of a certain number and its reciprocal is equal to 2.9

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 03 Nov 2016, 12:42
3
8
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

58% (02:34) correct 42% (02:39) wrong based on 163 sessions

HideShow timer Statistics

The sum of a certain number and its reciprocal is equal to 2.9. What is the absolute value of the difference of this number and its reciprocal ?

A. 2.2

B. 1.2

C. 0.3

D. 0.4

E. 2.1

_________________
Manager
Manager
avatar
B
Joined: 28 Jun 2016
Posts: 205
Location: Canada
Concentration: Operations, Entrepreneurship
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 03 Nov 2016, 13:11
2
ReussirleGMAT wrote:
The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?

A. 2,2 B. 1,2 C. 0,3 D. 0,4 E. 2,1


x + 1/x = 2.9

x-1/x = y


Add two equations

2x = 2.9 + y

So when 2.9 and correct answer choice are added, the final digit should be even

So eliminate A, B and D

Substitute y=0.3

x=1.6

1.6+1/1.6 is not equal to 2.9


Substitute y = 2.1

So x=2.5


2.5+1/2.5 =2.9

E


Sent from my iPhone using GMAT Club Forum mobile app
Manager
Manager
User avatar
P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 03 Nov 2016, 13:33
Nice method acegmat123

There is another way to solve this problem, could you find it?

Anis
_________________
Intern
Intern
avatar
B
Joined: 10 Oct 2016
Posts: 2
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 03 Nov 2016, 19:20
x+1/x = 2.9. We need to find x-1/x.

We know that \((x+1/x)^2-4\) = \((x-1/x)^2\) \* using relation \((a+b)^2\) = \(a^2+b^2+2ab\) and \((a-b)^2\) = \(a^2+b^2-2ab\) \*

Therefore 8.41-4 =\((x-1/x)^2\) and,

abs(x-1/x) =\sqrt{(4.41)} i.e. 2.1

Answer choice E
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1221
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 03 Nov 2016, 23:14
1
1
ReussirleGMAT wrote:
The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?

A. 2,2 B. 1,2 C. 0,3 D. 0,4 E. 2,1



x+1/x=2.9
x^2-2.9x+1=0
10x^2-29x+10=0
(5x-2)(2x-5)=0
5x=2
x=2/5=.4
1/.4-.4=2.1
E
Manager
Manager
User avatar
P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 03 Nov 2016, 23:45
Nice Method seneca04 but it is not the best way, please check how gracie did it.
_________________
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 417
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 08 Sep 2017, 05:33
a+1/a = 2.9
\(a^2\)-2.9a+1=0
10\(a^2\)-29a+10=0
(5a-2) ( a-5) =0
a cant be 5 as sum is less
a=2/5

so 1/a-a => 5/2-2/5 =21/10 =2.1 = option E
_________________
Give Kudos for correct answer and/or if you like the solution.
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 417
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 08 Sep 2017, 05:50
1
ANOTHER METHOD

(a+1/a)^2 = a^2 +1/a^2 +2
2.9^2 = y+2 where y= a^2+1/a^2

(a-1/a)^2 = a^2 + 1/a^2 -2
z^2 = y-2 WHERE z= a-1/a

z^2 - 2.9^2 = -4
z^2 = 2.9^2-4
z^2 = 8.41-4
Z^2 = 4.41
Z= 2.1 OPTION E
_________________
Give Kudos for correct answer and/or if you like the solution.
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 417
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 08 Sep 2017, 05:52
AnisMURR wrote:
Nice Method seneca04 but it is not the best way, please check how gracie did it.



check my method, How i did it apart from gracie 'S method.
_________________
Give Kudos for correct answer and/or if you like the solution.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13633
Re: The sum of a certain number and its reciprocal is equal to 2.9  [#permalink]

Show Tags

New post 06 Feb 2019, 12:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________
GMAT Club Bot
Re: The sum of a certain number and its reciprocal is equal to 2.9   [#permalink] 06 Feb 2019, 12:13
Display posts from previous: Sort by

The sum of a certain number and its reciprocal is equal to 2.9

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne