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

 It is currently 19 Sep 2019, 18:36 ### 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 < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2

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

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58117
If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags 00:00

Difficulty:   75% (hard)

Question Stats: 53% (01:54) correct 47% (02:07) wrong based on 141 sessions

### HideShow timer Statistics

If a < b, is a > 0?

(1) a^2 < b^2

(2) a^2 < ab < b^2

_________________
Manager  B
Joined: 06 May 2018
Posts: 58
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

1
If a < b, is a > 0?

(1) a^2 < b^2

(2) a^2 < ab < b^2

Choosing different values for (1): a=-2 < b=3 or a=2 < b=3 Hence, not sufficient

Choosing different values for (2): a=2 < 2*3 < 3 but a=-2 <-2*3 <3 violates the statement. Hence, B is sufficient
Intern  B
Joined: 23 Aug 2017
Posts: 26
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

1
Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2

(2) a^2 < ab < b^2

1) any square number hide its signal. Not sufficient
2) ab > 0, so a > 0. Sufficient
Manager  P
Joined: 04 Oct 2018
Posts: 161
Location: Viet Nam
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2

(2) a^2 < ab < b^2

(1) |a| < |b|
a = 5, b = 7 =>|a| < |b| => a > 0
a = -5, b = 7 => |a| < |b| => a < 0
=> Stm1 insufficient.
(2) a^2 < ab < b^2 => ab > 0 => a & b are both negative or positive
a = 5, b = 7 => a^2 < ab < b^2 => a > 0
a= -5, b = -3 ( a<b) => this violates a^2 < ab < b^2 (since 25 can't < 15 can't < 9) => This case can not be existed...
=> a & b are only positive => a > 0 => Sufficient
Hence B
_________________
"It Always Seems Impossible Until It Is Done"
Senior Manager  G
Joined: 24 Nov 2016
Posts: 447
Location: United States
If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2
(2) a^2 < ab < b^2

$$a<b…a-b<0$$

(1) $$a^2 < b^2…|a|<|b|$$:
if $$a<0$$ then $$b>0$$ ($$b$$ ≠ negative because $$a<b$$ and $$|a|<|b|$$)
if $$a>0$$ then $$b>0$$
both cases are possible, insufi.

(2) $$a^2 < ab < b^2…a^2 < ab…a^2-ab<0…a(a-b)<0$$:
if $$a<0$$ then $$a-b>0…or…a>b$$: but given $$a<b$$ this is not possible
if $$a>0$$ then $$a-b<0…or…a<b$$: this is sufi.

Originally posted by exc4libur on 20 Aug 2019, 04:59.
Last edited by exc4libur on 21 Aug 2019, 03:51, edited 1 time in total.
SVP  P
Joined: 03 Jun 2019
Posts: 1525
Location: India
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2

(2) a^2 < ab < b^2

Given: a < b

Asked: Is a > 0?

(1) $$a^2 < b^2$$
|a|<|b|
a can be +ve or -ve and b must be +ve
NOT SUFFICIENT

(2) a^2 < ab < b^2
ab > a^2 > 0
ab>0
a & b have same sign
$$a^2 < ab < b^2$$ => |a|<|b|
a can be +ve or -ve and b must be +ve
But a & b have same sign
b = +ve => a = +ve
a>0
SUFFICIENT

IMO B
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9643
Location: Pune, India
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

exc4libur wrote:
Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2
(2) a^2 < ab < b^2

VeritasKarishma hey how are you, could you check this out?

$$a<b…a-b<0$$

(1) $$a^2 < b^2…|a|<|b|$$:
if $$a<0$$ then $$b<0…or…b>0$$
if $$a>0$$ then $$b>0$$
both cases are possible, insufi.

(2) $$a^2 < ab < b^2…a^2 < ab…a^2-ab<0…a(a-b)<0$$:
if $$a<0$$ then $$a-b>0…or…a>b$$: but given $$a<b$$ this is not possible
if $$a>0$$ then $$a-b<0…or…a<b$$: this is sufi.

In stmnt 1, in the highlighted part, b cannot be negative.
a can be positive or negative, as you mentioned.

Rest all is good.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Senior Manager  G
Joined: 24 Nov 2016
Posts: 447
Location: United States
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

exc4libur wrote:
Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2
(2) a^2 < ab < b^2

VeritasKarishma hey how are you, could you check this out?

$$a<b…a-b<0$$

(1) $$a^2 < b^2…|a|<|b|$$:
if $$a<0$$ then $$b<0…or…b>0$$
if $$a>0$$ then $$b>0$$
both cases are possible, insufi.

(2) $$a^2 < ab < b^2…a^2 < ab…a^2-ab<0…a(a-b)<0$$:
if $$a<0$$ then $$a-b>0…or…a>b$$: but given $$a<b$$ this is not possible
if $$a>0$$ then $$a-b<0…or…a<b$$: this is sufi.

In stmnt 1, in the highlighted part, b cannot be negative.
a can be positive or negative, as you mentioned.

Rest all is good.

ah yes, bc of the $$|a|<|b|$$
thank you! GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4748
Location: India
Concentration: Sustainability, Marketing
Schools: INSEAD, HEC '22, IIM
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2  [#permalink]

### Show Tags

Bunuel wrote:
If a < b, is a > 0?

(1) a^2 < b^2

(2) a^2 < ab < b^2

test with values ;
a,b ; 2,3 , 1/4,1,3 , -2,-1

#1
a^2 < b^2
not sufficeint as a >0 as 1/4 and -ve as -2
#2a^2 < ab < b^2
can be re written as ; a<1<b
sufficient to say that a is -ve
IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions. Re: If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2   [#permalink] 23 Aug 2019, 08:07
Display posts from previous: Sort by

# If a < b, is a > 0? (1) a^2 < b^2 (2) a^2 < ab < b^2

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

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