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

It is currently 19 Aug 2018, 14:14

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 and b are real numbers, is a < b?

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

Hide Tags

Intern
Intern
avatar
B
Joined: 20 Nov 2017
Posts: 26
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
CAT Tests
If a and b are real numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jul 2018, 19:35
2
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (02:27) correct 71% (01:48) wrong based on 41 sessions

HideShow timer Statistics

If a and b are real numbers, is a < b?


(1) \(a^b < b^a\)

(2) \(\frac{a}{b} > 1\)
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
If a and b are real numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jul 2018, 21:08
1
If a and b are real numbers, is a < b?


(1) \(a^b < b^a\)..
a) let a be 4 and b be 3......a>b
\(a^b<b^a........4^3<3^4........64<81\)
b) let a be -2 and b be -1......a<b
\((-2)^{-1}<(-1)^{-2}...........-1/2<1\)
So insufficient

(2) \(\frac{a}{b} > 1\)
This means |a|>|b|...
a=4, and b=3..........4/3>1 and a>b
a=-4, and b=-1..........(-4)/(-1)=4>1 and a<b
So insufficient

Combined
Both cases remain..
a=4, and b=3......a>b
a=-2, and b =-1.....a<b
Insufficient

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
avatar
B
Joined: 11 Mar 2018
Posts: 65
Re: If a and b are real numbers, is a < b?  [#permalink]

Show Tags

New post 17 Jul 2018, 21:45
Karthik200 wrote:
If a and b are real numbers, is a < b?


(1) \(a^b < b^a\)

(2) \(\frac{a}{b} > 1\)



(1) \(a^b < b^a\)
\(a=2\), \(b=3\) \(a<b\)
\(8<9\) True

\(a=-3\), \(b=-2\) \(a<b\)
\(9<\frac{-1}{8}\) False

Insufficient.

(2) \(\frac{a}{b} > 1\)

\(\frac{a}{b} > 1\)
\(a>b\)
However
\(\frac{-a}{-b} >1\)
\(-a<-b\)
Eg: \(a=+-5\), \(b=+-4\)

Insufficient.

(1) and (2) Insufficient.

Hence, E
_________________

Regards
AD
---------------------------------
A Kudos is one more question and its answer understood by somebody !!!

Intern
Intern
avatar
B
Joined: 20 Nov 2017
Posts: 26
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
CAT Tests
If a and b are real numbers, is a < b?  [#permalink]

Show Tags

New post 18 Jul 2018, 02:17
chetan2u wrote:
If a and b are real numbers, is a < b?


(1) \(a^b < b^a\)..
a) let a be 4 and b be 3......a>b
\(a^b<b^a........4^3<3^4........64<81\)
b) let a be -2 and b be -1......a<b
\((-2)^{-1}<(-1)^{-2}...........-1/2<1\)
So insufficient

(2) \(\frac{a}{b} > 1\)
This means |a|>|b|...
a=4, and b=3..........4/3>1 and a>b
a=-4, and b=-1..........(-4)/(-1)=4>1 and a<b
So insufficient

Combined
Both cases remain..
a=4, and b=3......a>b
a=-2, and b =-1.....a<b
Insufficient

E


Hi chetan2u,

In these kinds of problems where plugging in of numbers required, I am finding it difficult to try out all the possibilities to disprove the given statements under two minutes. Is there any strategy to plug in the smart numbers that work best, especially for number property DS questions? I hope it will benefit many others as well.

Thanks & Regards,
Karthik
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
Re: If a and b are real numbers, is a < b?  [#permalink]

Show Tags

New post 18 Jul 2018, 02:26
Karthik200 wrote:
chetan2u wrote:
If a and b are real numbers, is a < b?


(1) \(a^b < b^a\)..
a) let a be 4 and b be 3......a>b
\(a^b<b^a........4^3<3^4........64<81\)
b) let a be -2 and b be -1......a<b
\((-2)^{-1}<(-1)^{-2}...........-1/2<1\)
So insufficient

(2) \(\frac{a}{b} > 1\)
This means |a|>|b|...
a=4, and b=3..........4/3>1 and a>b
a=-4, and b=-1..........(-4)/(-1)=4>1 and a<b
So insufficient

Combined
Both cases remain..
a=4, and b=3......a>b
a=-2, and b =-1.....a<b
Insufficient

E


Hi chetan2u,

In these kinds of problems where plugging in of numbers required, I am finding it difficult to try out all the possibilities to disprove the given statements under two minutes. Is there any strategy to plug in the smart numbers that work best, especially for number property DS questions? I hope it will benefit many others as well.

Thanks & Regards,
Karthik


If I were to do this problem, I'll pick up the statement II as it is more friendly...
a/b>1 means a and b are of same sign and numeric value of a is more than that of b.. hence |a|>|b|
And |a|>|b| means a>b if both positive and a<b if both negative

So check for the same cases in statement I too..
Both negative and a<b.....-4<-3....(-4)^{-3}<(-3)^{-4}.....-1/64<1/81
Both positive and a>b......4>3.....4^3<3^4.........64<81
So insufficient
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
B
Joined: 20 Nov 2017
Posts: 26
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
CAT Tests
Re: If a and b are real numbers, is a < b?  [#permalink]

Show Tags

New post 18 Jul 2018, 02:42
chetan2u wrote:
Karthik200 wrote:
chetan2u wrote:
If a and b are real numbers, is a < b?


(1) \(a^b < b^a\)..
a) let a be 4 and b be 3......a>b
\(a^b<b^a........4^3<3^4........64<81\)
b) let a be -2 and b be -1......a<b
\((-2)^{-1}<(-1)^{-2}...........-1/2<1\)
So insufficient

(2) \(\frac{a}{b} > 1\)
This means |a|>|b|...
a=4, and b=3..........4/3>1 and a>b
a=-4, and b=-1..........(-4)/(-1)=4>1 and a<b
So insufficient

Combined
Both cases remain..
a=4, and b=3......a>b
a=-2, and b =-1.....a<b
Insufficient

E


Hi chetan2u,

In these kinds of problems where plugging in of numbers required, I am finding it difficult to try out all the possibilities to disprove the given statements under two minutes. Is there any strategy to plug in the smart numbers that work best, especially for number property DS questions? I hope it will benefit many others as well.

Thanks & Regards,
Karthik


If I were to do this problem, I'll pick up the statement II as it is more friendly...
a/b>1 means a and b are of same sign and numeric value of a is more than that of b.. hence |a|>|b|
And |a|>|b| means a>b if both positive and a<b if both negative

So check for the same cases in statement I too..
Both negative and a<b.....-4<-3....(-4)^{-3}<(-3)^{-4}.....-1/64<1/81
Both positive and a>b......4>3.....4^3<3^4.........64<81
So insufficient


Thanks chetan2u. I will try to apply this from my next DS problem onwards.
Re: If a and b are real numbers, is a < b? &nbs [#permalink] 18 Jul 2018, 02:42
Display posts from previous: Sort by

If a and b are real numbers, is a < b?

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.