If a and b are integers, and a not= b, is |a|b > 0? (1) : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 06:43

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a and b are integers, and a not= b, is |a|b > 0? (1)

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 04 Nov 2006
Posts: 268
Location: California
Followers: 1

Kudos [?]: 192 [2] , given: 0

If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

Show Tags

20 Dec 2006, 14:21
2
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:13) correct 44% (01:18) wrong based on 608 sessions

HideShow timer Statistics

If a and b are integers, and a not= b, is |a|b > 0?

(1) |a^b| > 0

(2) |a|^b is a non-zero integer
[Reveal] Spoiler: OA
SVP
Joined: 01 May 2006
Posts: 1797
Followers: 9

Kudos [?]: 149 [5] , given: 0

Show Tags

20 Dec 2006, 14:37
5
KUDOS
(E) for me.

|a|*b > 0 ?
<=> b > 0 ?

From (1)
|a^b| > 0

o If b=-1 and a=1, 1 > 0 and b < 0
o If b=1 and a=-1, 1 > 0 and b > 0

INSUFF.

From (2)
|a|^b is a non zero integer implies that b must be positive or equal to 0 in order to not create a real number such as 2^-1.

So, we remains with the cases of b = 0 and b > 0.

INSUFF.

Both (1) and (2)
It brings nothing more.

INSUFF.
Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait
Followers: 14

Kudos [?]: 272 [0], given: 0

Show Tags

20 Dec 2006, 17:10
1
This post was
BOOKMARKED

Given: a , b are ints. and a is different from b
asking: |a| * b > 0

what the question is really asking if b > 0 [ |a| is always >0 ]

(1) |a^b| >0
----------------
says nothing, cuz |x| is always > 0
statement 1 is insufficient

(2) |a|^b is not zero
-------------------------
also says nothing .. we know |a|^b > 0
b could be -ve or +ve
statement 2 is insufficient

(1) and (2) together
------------------------
both statements really say nothing about b

Senior Manager
Joined: 12 Mar 2006
Posts: 366
Schools: Kellogg School of Management
Followers: 3

Kudos [?]: 70 [0], given: 3

Show Tags

16 Jan 2007, 20:49
is |a|b > 0 is same as, is b > 0

stat 1 is not sufficient since all it says is that a <> 0

from stat 2 b>= 0 since a only negative value of b can cause |a|^b to be not a non zero integer

so E ?
Senior Manager
Joined: 24 Nov 2006
Posts: 350
Followers: 1

Kudos [?]: 25 [0], given: 0

Re: DS_If a and b.... [#permalink]

Show Tags

16 Jan 2007, 21:39
mm007 wrote:
If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

First of all, the question is equivalent to: is a<>0 AND b>0?

(1) For |a^b| > 0, a could be <>0 but b could be <0 OR b>0 => insuff => B, C, or E.

(2) This is a similar case to (1): b, similarly to a, could be <>0 => insuff => C or E.

(1&2) Again, similar case to (1) and (2): b could be +ve or -ve => insuff => E.
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 117 [0], given: 1

Show Tags

16 Jan 2007, 23:03
Quote:
If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer

E2

I rephrased the stem to "is |a|>0 and is b -ve, 0 or +ve?"

1) |a^b| will always be +ve. But here, b can be greater than or equal to 0 and |a^b| will still be +ve
INS

2) |a|^b. Here, |a| cannot be 0 but B can be 0 or 1. b can't be -ve b/c |a|^b will become a non-integer, 1/a^b.
INS

Taken together, we're still not told anything about b. If we can't figure what b is we can't do much with this prob.
INS
Manager
Joined: 31 Aug 2009
Posts: 58
Followers: 0

Kudos [?]: 43 [0], given: 0

Show Tags

10 Sep 2009, 03:55
Can anybody chime in? Although I agree with the answer, I don't think the bold statement below is correct. B does not have to be
0 or greater. It can be -4 if A is 1.

If b= -4 and a=1. this satisfiies the conditions: 1) a,b are integers 2) a is not equal to b 3) statement 2; 1^(-4)=1. that is a non-zero integer. So you can't say B is definitely positive or 0. Combining statement 1 and 2. You can't determine if A is a 1 or not so E.

Please correct me if I am wrong. Thanks.

Fig wrote:
(E) for me.

|a|*b > 0 ?
<=> b > 0 ?

From (1)
|a^b| > 0

o If b=-1 and a=1, 1 > 0 and b < 0
o If b=1 and a=-1, 1 > 0 and b > 0

INSUFF.

[b]From (2)
|a|^b is a non zero integer implies that b must be positive or equal to 0 in order to not create a real number such as 2^-1.

So, we remains with the cases of b = 0 and b > 0.[/b]
INSUFF.

Both (1) and (2)
It brings nothing more.

INSUFF.
Manager
Joined: 24 Sep 2009
Posts: 111
Followers: 1

Kudos [?]: 15 [0], given: 2

Re: DS_If a and b.... [#permalink]

Show Tags

26 Nov 2009, 19:34
mm007 wrote:
If a and b are integers, and a not= b, is |a|b > 0?

(1) |a^b| > 0

(2) |a|^b is a non-zero integer

Clearly E.
|a^b| and |a|^b are always >0, no matter what b is, because absolute value is always greater than 0.
Thus, we can't know if b>0 or not.
_________________

http://www.online-stopwatch.com/
http://gmatsentencecorrection.blogspot.com/

Manager
Joined: 05 Dec 2009
Posts: 127
Followers: 2

Kudos [?]: 87 [0], given: 0

Re: DS_If a and b.... [#permalink]

Show Tags

21 Dec 2009, 08:22
mm007 wrote:
If a and b are integers, and a not= b, is |a|b > 0?

(1) |a^b| > 0

(2) |a|^b is a non-zero integer

Question is |a|b>0 this can be proved if we can prove that a not=0 and b>0.
1. |a^b| > 0 implies that a not = 0. a can be +ve or -ve, and be can be 0, +ve or -ve....but we are sure that a not=0 else |a^b| = 0.
Statement 1 itself is insuff.

2. |a|^b is a non zero integer.
we already know a,b both are integers....|a| is > 0, so b >= 0.
No clear value of b...

So ans E.
Intern
Joined: 12 Sep 2010
Posts: 10
Followers: 0

Kudos [?]: 51 [0], given: 0

Show Tags

15 Sep 2010, 08:15
Mishari wrote:

Given: a , b are ints. and a is different from b
asking: |a| * b > 0

what the question is really asking if b > 0 [ |a| is always >0 ]

(1) |a^b| >0
----------------
says nothing, cuz |x| is always > 0
statement 1 is insufficient

(2) |a|^b is not zero
-------------------------
also says nothing .. we know |a|^b > 0
b could be -ve or +ve
statement 2 is insufficient

(1) and (2) together
------------------------
both statements really say nothing about b

>>Please tell me how can |a| be taken as positive in the above steps without knowing its sign..I mean if a is negative,then |a| wil be negative..Right?Am i missing anythin badly?
Math Expert
Joined: 02 Sep 2009
Posts: 36597
Followers: 7093

Kudos [?]: 93432 [1] , given: 10563

Show Tags

15 Sep 2010, 08:39
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
ravitejapandiri wrote:
>>Please tell me how can |a| be taken as positive in the above steps without knowing its sign..I mean if a is negative,then |a| wil be negative..Right?Am i missing anythin badly?

Absolute value of of an expression is alway non-negative: $$|some \ expression|\geq{0}$$. Please check Walker's post on Absolute Value at: math-absolute-value-modulus-86462.html

As for the question:

If a and b are integers, and a does not equal to b, is |a|*b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer.

$$|a|*b>0$$ is true when $$b>0$$ and $$a$$ does not equal to zero.

(1) $$|a^b| > 0$$ --> $$a$$ does not equal to zero, but we don't know about $$b$$, it can be any value, positive or negative. Not sufficient.

(2) $$|a|^b$$ is a non-zero integer --> $$a$$ can be 1 and $$b$$ any integer, positive or negative. Not sufficient.

(1)+(2) If $$a=1$$ and $$b=2$$, then $$|a|*b>0$$, but if $$a=1$$ and $$b=-2$$, then $$|a|*b<0$$. Not sufficient.

Other discussion of this question at: good-set-of-ds-85413.html
Similar question: the-power-of-absolutes-manhattan-challenge-problem-101661.html

Hope it helps.
_________________
Intern
Joined: 26 Mar 2010
Posts: 48
Followers: 0

Kudos [?]: 8 [0], given: 5

Re: DS question : need help [#permalink]

Show Tags

28 Oct 2010, 18:20
Basically just need to find out if b is positive or negative, since a will always be positive as it is inside of the | |.

1) Doesn't give you anything because everything is inside of the | |, so you can't tell if b is positive or negative, so insufficient.

2) Tells you that b is not negative since that would result in a non-integer. However, b could be 0 since a number raised to the 0 is 1, which is a non-integer number. Also insufficient.

Using both statements still doesn't provide anything because b can still be equal to 0, in which case |a|b > 0 is false. However, b can also be any positive number which would make |a|b > 0 true. Thus E.
Manager
Joined: 07 May 2013
Posts: 109
Followers: 0

Kudos [?]: 24 [0], given: 1

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

Show Tags

04 Jun 2014, 18:35
The reason why s2 alone or taken together with s1 is not sufficient bcos we need info on the signs that is, a is +ve or -ve and whether b is +ve or -ve & not wether they are zero or non-zero integers.
Intern
Joined: 05 Feb 2014
Posts: 26
Followers: 0

Kudos [?]: 2 [0], given: 65

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

Show Tags

02 Sep 2014, 03:43
Bunuel wrote:
ravitejapandiri wrote:
>>Please tell me how can |a| be taken as positive in the above steps without knowing its sign..I mean if a is negative,then |a| wil be negative..Right?Am i missing anythin badly?

Absolute value of of an expression is alway non-negative: $$|some \ expression|\geq{0}$$. Please check Walker's post on Absolute Value at: math-absolute-value-modulus-86462.html

As for the question:

If a and b are integers, and a does not equal to b, is |a|*b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer.

$$|a|*b>0$$ is true when $$b>0$$ and $$a$$ does not equal to zero.

(1) $$|a^b| > 0$$ --> $$a$$ does not equal to zero, but we don't know about $$b$$, it can be any value, positive or negative. Not sufficient.

(2) $$|a|^b$$ is a non-zero integer --> $$a$$ can be 1 and $$b$$ any integer, positive or negative. Not sufficient.

(1)+(2) If $$a=1$$ and $$b=2$$, then $$|a|*b>0$$, but if $$a=1$$ and $$b=-2$$, then $$|a|*b<0$$. Not sufficient.

Other discussion of this question at: good-set-of-ds-85413.html
Similar question: the-power-of-absolutes-manhattan-challenge-problem-101661.html

Hope it helps.

Hi Bunuel,
I've always struggled when to consider 0 as an integer and when not. Is there any concept that you can share? Appreciate your help!!
Math Expert
Joined: 02 Sep 2009
Posts: 36597
Followers: 7093

Kudos [?]: 93432 [1] , given: 10563

If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

Show Tags

02 Sep 2014, 03:49
1
KUDOS
Expert's post
shahPranay14 wrote:
Bunuel wrote:
ravitejapandiri wrote:
>>Please tell me how can |a| be taken as positive in the above steps without knowing its sign..I mean if a is negative,then |a| wil be negative..Right?Am i missing anythin badly?

Absolute value of of an expression is alway non-negative: $$|some \ expression|\geq{0}$$. Please check Walker's post on Absolute Value at: math-absolute-value-modulus-86462.html

As for the question:

If a and b are integers, and a does not equal to b, is |a|*b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer.

$$|a|*b>0$$ is true when $$b>0$$ and $$a$$ does not equal to zero.

(1) $$|a^b| > 0$$ --> $$a$$ does not equal to zero, but we don't know about $$b$$, it can be any value, positive or negative. Not sufficient.

(2) $$|a|^b$$ is a non-zero integer --> $$a$$ can be 1 and $$b$$ any integer, positive or negative. Not sufficient.

(1)+(2) If $$a=1$$ and $$b=2$$, then $$|a|*b>0$$, but if $$a=1$$ and $$b=-2$$, then $$|a|*b<0$$. Not sufficient.

Other discussion of this question at: good-set-of-ds-85413.html
Similar question: the-power-of-absolutes-manhattan-challenge-problem-101661.html

Hope it helps.

Hi Bunuel,
I've always struggled when to consider 0 as an integer and when not. Is there any concept that you can share? Appreciate your help!!

0 is neither positive nor negative even integer.

Check for more here: number-properties-tips-and-hints-174996.html
_________________
Current Student
Joined: 02 Jul 2012
Posts: 215
Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38
GPA: 2.6
WE: Information Technology (Consulting)
Followers: 15

Kudos [?]: 224 [0], given: 84

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

Show Tags

20 Oct 2014, 22:23
If a and b are integers, and a does not equal to b, is |a|*b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer.
to check whether |a|*b > 0, we need to identify whether b>0

1 - This statement has to be positive, irrespective of the value of a and b.
This is insufficient

2. |a|^b is non-zero integer -

Possibilities -
a = -.5 or .5 and b = -1 The value of expression would be 2
a = any number and b = 0. The value will be 1
a = any positive / negative number and b = any positive number Thus the result will be a positive number.

Thus insufficient.

Combining two,

We'll get positive values for y, and zero.

Thus combining two will not give solution.

Thus Ans - E
_________________

Give KUDOS if the post helps you...

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13500
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

Show Tags

15 Apr 2016, 06:36
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 integers, and a not= b, is |a|b > 0? (1)   [#permalink] 15 Apr 2016, 06:36
Similar topics Replies Last post
Similar
Topics:
37 If ab ≠ 0, is |a-b| > |a+b|? 22 06 May 2016, 07:46
2 If a and b are integers and a≠b, is |a|* b > 0? 3 06 Jun 2013, 10:51
2 If a > 0, is 2/(a+b) + 2/(a-b) = 1? 6 28 Apr 2013, 19:10
7 A and B are integers, is (0.5)^(AB) > 1? 4 17 Feb 2013, 19:58
2 Is a/b > 0? 3 07 Nov 2010, 12:40
Display posts from previous: Sort by