Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 21 Jul 2019, 12:24

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

If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56307
If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =  [#permalink]

Show Tags

New post 30 Jul 2018, 00:43
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (01:23) correct 13% (01:41) wrong based on 86 sessions

HideShow timer Statistics


VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1393
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =  [#permalink]

Show Tags

New post 30 Jul 2018, 01:44
Bunuel wrote:
If \(a > 0\), \(b > 0\) , and \(c > 0\) , \(a + \frac{1}{b + \frac{1}{c}}\) =


A. \(\frac{a + b}{c}\)

B. \(\frac{ac + bc + 1}{c}\)

C. \(\frac{abc + b + c}{bc}\)

D. \(\frac{a + b + c}{abc + 1}\)

E. \(\frac{abc + a + c}{bc + 1}\)



It's better to solve this one part to part:

= \(b + \frac{1}{c}\)

=\(\frac{bc + 1}{c}\)

Then

=\(\frac{1}{(bc + 1) / c}\)

= \(\frac{c}{bc + 1}\)

last part :

= a + \(\frac{c}{bc +1}\)

=\(\frac{c + abc + a}{bc +1}\)

The best answer is E.
Manager
Manager
avatar
B
Joined: 29 Jul 2018
Posts: 114
Concentration: Finance, Statistics
GMAT 1: 620 Q45 V31
GMAT ToolKit User
Re: If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =  [#permalink]

Show Tags

New post 30 Aug 2018, 13:25
assume values for a,b,c and put values of abc in options
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3857
Location: Canada
Re: If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =  [#permalink]

Show Tags

New post 30 Aug 2018, 17:25
Top Contributor
Bunuel wrote:
If \(a > 0\), \(b > 0\) , and \(c > 0\) , \(a + \frac{1}{b + \frac{1}{c}}\) =


A. \(\frac{a + b}{c}\)

B. \(\frac{ac + bc + 1}{c}\)

C. \(\frac{abc + b + c}{bc}\)

D. \(\frac{a + b + c}{abc + 1}\)

E. \(\frac{abc + a + c}{bc + 1}\)


We're looking for an expression that is equivalent to the given expression.
So, if we find the value of the given expression for certain values of a, b and c, then the correct answer choice must also equal the same value for the same value of values of a, b and c.

So, let's see what happens when a = b = c = 1

Given expression: a + 1/(b + 1/c) = 1 + 1/(1 + 1/1) =
= 1 + 1/2
= 3/2

So, when a = b = c = 1, the given expression evaluates to be 3/2
So, the correct answer choice must also evaluate to be 3/2 when we plug in a = b = c = 1

Check the answer choices....
A. (a + b)/c = (1 + 1)/1 = 2. No good. We need 3/2. ELIMINATE.

B. (ac + bc + 1)/c = (1 + 1 + 1)/1 = 3. No good. We need 3/2. ELIMINATE.

C. (abc + b + c)/bc = (1 + 1 + 1)/1 = 1. No good. We need 3/2. ELIMINATE.

D. (a + b + c)/(abc + 1) = (1 + 1 + 1)/(1 + 1) = 3/2. Perfect!! KEEP

E. (abc + a + c)/(bc + 1) = (1 + 1 + 1)/(1 + 1) = 3/2. Perfect!! KEEP


Okay, we have two possible answers: D or E.
So, we must test one more set of values.



Let's see what happens when a = b = 1 and c = 2
Here, the given expression: a + 1/(b + 1/c) = 1 + 1/(1 + 1/2) =
= 1 + 1/(3/2)
= 1 + 2/3
= 5/3

So, when a = b = 1 and c = 2 , the given expression evaluates to be 5/3
So, the correct answer choice must also evaluate to be 5/3 when we plug in a = b = 1 and c = 2

Check the REMAINING answer choices....
D. (a + b + c)/(abc + 1) = (1 + 1 + 2)/(2 + 1) = 4/3. No good. We need 5/3. ELIMINATE.

E. (abc + a + c)/(bc + 1) = (2 + 1 + 2)/(2 + 1) = 5/3. Perfect!! KEEP

Answer: E

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
Re: If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =   [#permalink] 30 Aug 2018, 17:25
Display posts from previous: Sort by

If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =

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





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