GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 01 Apr 2020, 10:06

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, b, and c are positive integers such that 1/a + 1/b = 1

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 10
Location: United States
GMAT 1: 740 Q50 V40
Re: If a, b, and c are positive integers such that 1/a + 1/b = 1  [#permalink]

Show Tags

New post 08 Mar 2017, 02:58
VeritasPrepKarishma wrote:
sharkr wrote:
VeritasPrepKarishma wrote:
Basically, you have to look for values such that when the numerators add up, the sum is divisible by the denominator. a and b cannot be 1 since we need the sum to be less than 1.


What are the numerators, the sum, and the denominator referring to?

Thanks in advance.



1/a + 1/b = 1/c

You have to look for values of a and b (denominators) such that when you add 1/a and 1/b, the numerator you get is divisible by the denominator of the fraction (which you get after adding)

e.g. if a = 3, b = 6

1/a + 1/b = 1/3 + 1/6 = (2 + 1)/6 = 3/6
The numerator is 3 and the denominator is 6. The numerator is divisible by the denominator such that you get 1 in the numerator after cancelling.

1/a + 1/b = 1/3 + 1/6 = 1/2

When you get 1 in the numerator, the denominator of the resulting fraction is the value of c (i.e. 2 above)


Thanks for the reply.
For clarification, don't you mean the denominator (ie. 6) is divisible by the numerator (ie. 3)?
3 / 6 = 0*6 + 3 whereas 6/3 = 3*2 (no remainder).
Intern
Intern
avatar
B
Joined: 09 May 2016
Posts: 42
CAT Tests
Re: If a, b, and c are positive integers such that 1/a + 1/b = 1  [#permalink]

Show Tags

New post 05 Apr 2017, 14:49
monsoon1 wrote:
If a, b, and c are positive integers such that 1/a + 1/b = 1/c, what is the value of c?

(1) b ≤ 4
(2) ab ≤ 15




Is there any algebric approach to be sure that B is sufficient
Manager
Manager
avatar
S
Joined: 10 Dec 2011
Posts: 78
Location: India
Concentration: Finance, Economics
GMAT Date: 09-28-2012
WE: Accounting (Manufacturing)
Re: If a, b, and c are positive integers such that 1/a + 1/b = 1  [#permalink]

Show Tags

New post 04 Jan 2018, 09:03
mau5 wrote:

From F.S 1, we know that for a to be positive, c<b. The given equation is valid for b=2,c=1 and also for b=3,c=2. Insufficient.


Now, back to your question.


We know that\(\frac{a+b}{2}\geq{\sqrt{ab}}\)

Also, from the question stem, we know that \(\frac{a+b}{ab} =\frac{1}{c}\)

Thus, \((a+b) = \frac{ab}{c}\). Replacing this in the first equation, we get \(\frac{ab}{2c}\geq{\sqrt{ab}}\)

Or,\(c\leq{\frac{\sqrt{ab}}{2}} \to c\leq{\frac{\sqrt{15}}{2}} \to c<{2}\). Thus, the only positive integer less than 2 is One and thus c=1.Sufficient.


Whoa! That's some really interesting point you are making. Never heard of this... that the average of two average of two numbers is always greather than the square root of the product of two numbers! Does this property hold always?
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14453
Re: If a, b, and c are positive integers such that 1/a + 1/b = 1  [#permalink]

Show Tags

New post 17 Jan 2020, 08:13
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: If a, b, and c are positive integers such that 1/a + 1/b = 1   [#permalink] 17 Jan 2020, 08:13

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

If a, b, and c are positive integers such that 1/a + 1/b = 1

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





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