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

 It is currently 22 Mar 2019, 09:38 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b

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

### Hide Tags

Manager  Joined: 28 Aug 2010
Posts: 171
If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b  [#permalink]

### Show Tags

1
3 00:00

Difficulty:   65% (hard)

Question Stats: 57% (02:00) correct 43% (02:11) wrong based on 151 sessions

### HideShow timer Statistics

If a and b are positive, is is $$(a^{-1}+b^{-1})^{-1}$$ less than $$(a^{-1}*b^{-1})^{-1}$$?

(1) a = 2b
(2) a + b > 1

Originally posted by ajit257 on 18 Dec 2010, 14:01.
Last edited by Bunuel on 08 Oct 2017, 08:46, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 53792
Re: If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b  [#permalink]

### Show Tags

3
3
ajit257 wrote:
If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?
(1) a = 2b
(2) a + b > 1

Not sure about the ans.

Question: is $$(a^{-1}+b^{-1})^{-1}<(a^{-1}*b^{-1})^{-1}$$? --> $$(\frac{1}{a}+\frac{1}{b})^{-1}<(\frac{1}{ab})^{-1}$$ --> $$\frac{ab}{a+b}<ab$$, as $$a$$ and $$b$$ are positive we can reduce by $$ab$$ and finally question becomes: is $$a+b>1$$?

(1) a = 2b --> is $$3b>1$$ --> is $$b>\frac{1}{3}$$, we don't know that, hence this statement is not sufficient.
(2) a + b > 1, directly gives an answer. Sufficient.

P.S. ajit257 you should type the question so that it's clear which is an exponent, which is subtraction, and so on.
_________________
##### General Discussion
Manager  Joined: 21 Oct 2013
Posts: 185
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
Re: If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b  [#permalink]

### Show Tags

1
Bunuel wrote:
ajit257 wrote:
If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?
(1) a = 2b
(2) a + b > 1

Not sure about the ans.

Question: is $$(a^{-1}+b^{-1})^{-1}<(a^{-1}*b^{-1})^{-1}$$? --> $$(\frac{1}{a}+\frac{1}{b})^{-1}<(\frac{1}{ab})^{-1}$$ --> $$\frac{ab}{a+b}<ab$$, as $$a$$ and $$b$$ are positive we can reduce by $$ab$$ and finally question becomes: is $$a+b>1$$?

(1) a = 2b --> is $$3b>1$$ --> is $$b>\frac{1}{3}$$, we don't know that, hence this statement is not sufficient.
(2) a + b > 1, directly gives an answer. Sufficient.

P.S. ajit257 you should type the question so that it's clear which is an exponent, which is subtraction, and so on.

Hey Bunuel,

once again, this is a little bit fast for me.

I follow your first and third step to reduce the question, but I don't get the second.

I'd explained myself that $$(\frac{1}{ab})^{-1}$$ = $$1*(\frac{ab}{1})$$ so we have ab on the right side.

But I don't follow what you did do reduce the left side. Could you explain in detail?

Thank you!
Math Expert V
Joined: 02 Sep 2009
Posts: 53792
Re: If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b  [#permalink]

### Show Tags

unceldolan wrote:
Bunuel wrote:
ajit257 wrote:
If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?
(1) a = 2b
(2) a + b > 1

Not sure about the ans.

Question: is $$(a^{-1}+b^{-1})^{-1}<(a^{-1}*b^{-1})^{-1}$$? --> $$(\frac{1}{a}+\frac{1}{b})^{-1}<(\frac{1}{ab})^{-1}$$ --> $$\frac{ab}{a+b}<ab$$, as $$a$$ and $$b$$ are positive we can reduce by $$ab$$ and finally question becomes: is $$a+b>1$$?

(1) a = 2b --> is $$3b>1$$ --> is $$b>\frac{1}{3}$$, we don't know that, hence this statement is not sufficient.
(2) a + b > 1, directly gives an answer. Sufficient.

P.S. ajit257 you should type the question so that it's clear which is an exponent, which is subtraction, and so on.

Hey Bunuel,

once again, this is a little bit fast for me.

I follow your first and third step to reduce the question, but I don't get the second.

I'd explained myself that $$(\frac{1}{ab})^{-1}$$ = $$1*(\frac{ab}{1})$$ so we have ab on the right side.

But I don't follow what you did do reduce the left side. Could you explain in detail?

Thank you!

Sure.

$$(\frac{1}{a}+\frac{1}{b})^{-1}$$;

$$(\frac{b+a}{ab})^{-1}$$;

$$\frac{ab}{b+a}$$.

Does this make sense?
_________________
Manager  Joined: 21 Oct 2013
Posts: 185
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
Re: If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b  [#permalink]

### Show Tags

Bunuel wrote:

Sure.

$$(\frac{1}{a}+\frac{1}{b})^{-1}$$;

$$(\frac{b+a}{ab})^{-1}$$;

$$\frac{ab}{b+a}$$.

Does this make sense?

Yeah, now I see it. Guess my head was just overloaded with math --> it's really clear now! Thanks!
Non-Human User Joined: 09 Sep 2013
Posts: 10178
Re: If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b  [#permalink]

### Show Tags

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.
_________________ Re: If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b   [#permalink] 21 Feb 2019, 22:31
Display posts from previous: Sort by

# If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.  