Author 
Message 
TAGS:

Hide Tags

Director
Joined: 29 Nov 2012
Posts: 813

If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
Updated on: 22 Jun 2013, 00:34
Question Stats:
66% (01:16) correct 34% (00:54) wrong based on 442 sessions
HideShow timer Statistics
If a and b are nonzero integers, and a/b > 1, then which of the following must be true? A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html
Originally posted by fozzzy on 21 Jun 2013, 22:26.
Last edited by fozzzy on 22 Jun 2013, 00:34, edited 3 times in total.




Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
22 Jun 2013, 13:43
If a and b are nonzero integers, and a/b > 1, then which of the following must be true?A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3 If b is positive, then we have that a>b>0. If b is negative, then we have that a<b<0. A. a > b. Not necessarily true. B. 2a > b. Not necessarily true. C. a^2< b^2 > a<b. Not necessarily true. D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true. E. a^3 < b^3 > a<b. Not necessarily true. Answer: D. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 68
Location: India
Concentration: Leadership, Entrepreneurship
GPA: 2.92
WE: Analyst (Computer Software)

Re: If a and b are nonzero integers, and , then which of the fo
[#permalink]
Show Tags
21 Jun 2013, 22:55
fozzzy wrote: If a and b are nonzero integers, and , then which of the following must be true?
\(a>b\)
\(2a>b\)
\(a^2< b^2\)
\(ab> b\)
\(a^3 < b^3\) A & B are non zero integers then, a>b .. Assume a = 10 & b = 20. Not true2a>b.. assume a = 10 and b =40 20>40?? Not true. B^2 > a^2. assume a = 5 and b = 2. 4 > 25?? Not true ab > b assume a = 3 and b =7 21>7?? Not true a^3 < b^3.. assume a = 3 and b = 2 9 < 8?? Not true. I guess question is not correctly worded or i am making a mistake somewhere.



Director
Joined: 29 Nov 2012
Posts: 813

Re: If a and b are nonzero integers, and , then which of the fo
[#permalink]
Show Tags
21 Jun 2013, 23:12
navigator123 wrote: fozzzy wrote: If a and b are nonzero integers, and , then which of the following must be true?
\(a>b\)
\(2a>b\)
\(a^2< b^2\)
\(ab> b\)
\(a^3 < b^3\) A & B are non zero integers then, a>b .. Assume a = 10 & b = 20. Not true2a>b.. assume a = 10 and b =40 20>40?? Not true. B^2 > a^2. assume a = 5 and b = 2. 4 > 25?? Not true ab > b assume a = 3 and b =7 21>7?? Not true a^3 < b^3.. assume a = 3 and b = 2 9 < 8?? Not true. I guess question is not correctly worded or i am making a mistake somewhere. Sorry I have updated the question!
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Director
Joined: 03 Aug 2012
Posts: 822
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
25 Jul 2013, 11:55
Bunuel wrote: If a and b are nonzero integers, and a/b > 1, then which of the following must be true?
A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3
If b is positive, then we have that a>b>0. If b is negative, then we have that a<b<0.
A. a > b. Not necessarily true.
B. 2a > b. Not necessarily true.
C. a^2< b^2 > a<b. Not necessarily true.
D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.
E. a^3 < b^3 > a<b. Not necessarily true.
Answer: D.
Hope it's clear. I Aspire to learn even 10% of the approaches you use to solve a math question. Rgds, TGC !!
_________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________



SVP
Joined: 06 Sep 2013
Posts: 1851
Concentration: Finance

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
01 Jan 2014, 07:56
fozzzy wrote: If a and b are nonzero integers, and a/b > 1, then which of the following must be true?
A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3 Yeah very good question a bit complicated, maybe I took the long way home but let's see We get ab/b > 0 One has to scenarios 1) If ab>0, then b>0, therefore a>0. So all in all a>b>0 2) If ab<0, then b<0, therefore a<0. So all in all 0>b>a Let's check out the answer choices A. a > b Not always true, could be scenario 2 B. 2a > b Not true at all C. a^2< b^2 Too many different possibilities D. ab > b This is equal to b(a1)>0 Now we have two scenarios as well If b>0, then a>1. Note that we are told that a.b are integers. Therefore b>0 means that b has to be 1 at least and therefore a>1. If b<0, then a<1. Same as above So it works for both of our scenarios E. a^3 < b^3 This is the same as to say b>a, which is not always true Hence answer is D Hope it helps Kudos rain!!! [/quote]



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 520
Location: India

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
02 Jan 2014, 03:14
fozzzy wrote: If a and b are nonzero integers, and a/b > 1, then which of the following must be true?
A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3 Lets plug in here a = 3, b = 2 A  Eliminated B  Eliminated C  Eliminated D  True E  Eliminated
_________________
For more info on GMAT and MBA, follow us on @AskCrackVerbal



Intern
Joined: 13 Dec 2013
Posts: 38

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
08 Jun 2014, 08:35
If a = 0.5 and b = 0.1
Then a/b = 0.5/0.1 = 5
When I tried to plug in the values into the d) option I got a*b = (0.5)(0.1) = 0.05 which isn't greater than b = 0.1
So option D also wouldn't hold true.
Am I doing something wrong?



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
08 Jun 2014, 10:24



Manager
Joined: 07 Dec 2009
Posts: 99
GMAT Date: 12032014

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
05 Jan 2015, 11:18
I guess the best approach here would be to Plug in values... Try a=3 and b = 2
All get eliminated except for D



Intern
Joined: 22 Jan 2017
Posts: 2

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
19 Jun 2017, 19:48
Bunuel wrote: If a and b are nonzero integers, and a/b > 1, then which of the following must be true?
A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3
If b is positive, then we have that a>b>0. If b is negative, then we have that a<b<0.
A. a > b. Not necessarily true.
B. 2a > b. Not necessarily true.
C. a^2< b^2 > a<b. Not necessarily true.
D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.
E. a^3 < b^3 > a<b. Not necessarily true.
Answer: D.
Hope it's clear. Hi Brunel, I am still confused. I can't see the connection between the question asking : a/b>1 , and the answers below Could you or anyone kindly explaain this Thank you



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
19 Jun 2017, 22:20
whoisjon2 wrote: Bunuel wrote: If a and b are nonzero integers, and a/b > 1, then which of the following must be true?
A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3
If b is positive, then we have that a>b>0. If b is negative, then we have that a<b<0.
A. a > b. Not necessarily true.
B. 2a > b. Not necessarily true.
C. a^2< b^2 > a<b. Not necessarily true.
D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.
E. a^3 < b^3 > a<b. Not necessarily true.
Answer: D.
Hope it's clear. Hi Brunel, I am still confused. I can't see the connection between the question asking : a/b>1 , and the answers below Could you or anyone kindly explaain this Thank you The question does not asks whether a/b > 1. It says that a/b > 1. So, the question is: given that a/b > 1, which of the following options must be true?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2727

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
20 Jun 2017, 19:15
fozzzy wrote: If a and b are nonzero integers, and a/b > 1, then which of the following must be true?
A. a > b B. 2a > b C. a^2< b^2 D. ab > b E. a^3 < b^3 If a/b > 1, then a and b must have the same sign, with a > b. For example, a = 3 and b = 2 OR a = 3 and b = 2. Let’s analyze each given answer choice. A. a > b Let a = 3 and b = 2; we can see that A is not true. B. 2a > b Let a = 3 and b = 2; we can see that B is not true. C. a^2 < b^2 Let a = 3 and b = 2; we can see that C is not true. D. ab > b Let a = 3 and b = 2; we have ab > b. Let a = 3 and b = 2; we have ab > b. We see that D can be true, but let’s also analyze choice E before we conclude that choice D is definitely true. E. a^3 < b^3 Let a = 3 and b = 2; we can see that E is not true. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 26 Dec 2015
Posts: 277
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)

Re: If a and b are nonzero integers, and a/b > 1, then which of
[#permalink]
Show Tags
05 Dec 2017, 12:33
my .02:
* MUST BE TRUE questions tend to be D or E. so even if you're running out of time or trying to burn the Q, you have a 50/50 here.
we're told that: 1) a & b = integers AND ARE NOT 0 (aka NO FRACTIONS) 2) \(\frac{a}{b}\)>1
Let's make sense of (2): for a fraction to be GREATER THAN 1, what needs to be true? a) The numerator must be greater than the denominator b) The numerator AND denominator must share the same sign (i.e. both must be POSITIVE or NEGATIVE)
KEYS TO THE PROBLEM: > if b = positive (let's say b=2), then we can say a=4. that way, 2>1. > if b = negative (let's say b=2), then we can say a=4. that way, 2>1. ** Both of these conditions match the above proofs. ** Very helpful to PICK #s to solve
Let's plug in these sets of #s for A/C A>E. A) a>b > what if a=4, b=2? Incorrect. B) 2a>b > what if a=4, b=2? Incorrect. C) \(a^{2}\)<\(b^{2}\) > what if a=4, b=2? Incorrect. D) ab>b > try: a=4, b=2. then, 8>2. or: a=4, b=2. then, 8>2. Correct. E) \(a^{3}\)<\(b^{3}\) >what if a=4, b=2? then 64<8. Incorrect.




Re: If a and b are nonzero integers, and a/b > 1, then which of &nbs
[#permalink]
05 Dec 2017, 12:33






