December 15, 2018 December 15, 2018 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 31 Aug 2009
Posts: 52

If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
11 Sep 2009, 00:57
Question Stats:
42% (02:36) correct 58% (02:36) wrong based on 845 sessions
HideShow timer Statistics
If a and b are integers, and a > b, is a · b < a – b? (1) a < 0 (2) ab >= 0
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
11 Sep 2009, 01:46
Bunuel wrote: thailandvc wrote: If a and b are integers, and a > b, is a · b < a – b?
(1) a < 0
(2) ab >= 0
anybody have a solution for this (under 2 minute). testing value takes way too long here. E Given: \(a>b\) Question: is \(a*b<ab\)? (1) \(a<0\). If \(a=3\) and \(b=0\), then \(a*b=0>ab=3\) and the answer is NO but if \(a=3\) and \(b=1\), then \(a*b=3<ab=2\) and the answer is YES. Two different answers. Not sufficient. (2) \(ab\geq{0}\) Above example works here as well: \(a=3\) and \(b=0\) > \(a*b=0>ab=3\) > answer NO; \(a=3\) and \(b=1\) > \(a*b=3<ab=2\) > answer YES. Two different answers. Not sufficient. (1)+(2) Again the same example satisfies the stem and both statements and gives two different answers to the question whether \(a*b<ab\). Hence not sufficient. Answer E.
_________________
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
Joined: 16 Apr 2010
Posts: 200

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
05 Jul 2010, 18:36
Hi Kandi, Equate those four conditions as greater or equal to zero and less or equal to zero 1  a<0 we have two conditions  a<b<0 a=5, b=3  a<0<b a=5, b=3 So 1 alone is not sufficient 2  ab>=0 We also have two conditions  a>b>0 a=5, b=3  a<b<0 a=5, b=3 So again 2 alone is not sufficient Taking 1 and 2, we have:  a<b<0 a=5, b=3 So taking 1 and 2, we can answer the questions. Hope it is clearer now. regards, Jack



Director
Joined: 21 Dec 2009
Posts: 519
Concentration: Entrepreneurship, Finance

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
28 Jul 2010, 10:11
utfan2424 wrote: Is this really a 700+ question? I got the question from MHGMAT; maybe it is a 700+ category question under stressed condition, especially given the test conditions required to establish a precise position.
_________________
KUDOS me if you feel my contribution has helped you.



Senior Manager
Joined: 25 Feb 2010
Posts: 352

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
28 Jul 2010, 13:19
utfan2424 wrote: Is this really a 700+ question? Doesn't seems like to be 700 + Its a tricky question and lots of people will choose C.
_________________
GGG (Gym / GMAT / Girl)  Be Serious
Its your duty to post OA afterwards; some one must be waiting for that...



Intern
Joined: 22 Jun 2010
Posts: 33

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
28 Jul 2010, 15:50
Bunuel wrote: Bunuel wrote: thailandvc wrote: If a and b are integers, and a > b, is a · b < a – b?
(1) a < 0
(2) ab >= 0
anybody have a solution for this (under 2 minute). testing value takes way too long here. E Given: \(a>b\) Question: is \(a*b<ab\)? (1) \(a<0\). If \(a=3\) and \(b=0\), then \(a*b=0>ab=3\) and the answer is NO but if \(a=3\) and \(b=1\), then \(a*b=3<ab=2\) and the answer is YES. Two different answers. Not sufficient. (2) \(ab\geq{0}\) Above example works here as well: \(a=3\) and \(b=0\) > \(a*b=0>ab=3\) > answer NO; \(a=3\) and \(b=1\) > \(a*b=3<ab=2\) > answer YES. Two different answers. Not sufficient. (1)+(2) Again the same example satisfies the stem and both statements and gives two different answers to the question whether \(a*b<ab\). Hence not sufficient. Answer E. Please tell me if my reasonning is bad a > b, is a · b < a – b? (1) a < 0 ==> a · b<0 since nothing about b we can not conclude ==> not sufficient (2) ab >= 0 ==> a&b neg or a and b neg but no information abt a relatif to b 1 +2 a<0 ==> b <0 not suff Nevetheless if ab was neg then the ans would be C is tit correct?



Manager
Joined: 20 Mar 2010
Posts: 78

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
28 Jul 2010, 16:55
Quote: Please tell me if my reasonning is bad
a > b, is a · b < a – b?
(1) a < 0 ==> a · b<0 since nothing about b we can not conclude ==> not sufficient (2) ab >= 0
==> a&b neg or a and b neg but no information abt a relatif to b
1 +2 a<0 ==> b <0 not suff
Nevetheless if ab was neg then the ans would be C is tit correct?
I would say it's still not sufficient. If a<0 and ab<0 then b>0 For a=3 and b=1 ab > a  b For a=3 and b=2 ab < a  b
_________________
___________________________________ Please give me kudos if you like my post



VP
Joined: 15 Jul 2004
Posts: 1263
Schools: Wharton (R2  submitted); HBS (R2  submitted); IIMA (admitted for 1 year PGPX)

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
01 Aug 2010, 08:34
If a and b are integers, and a > b, is a · b < a – b? (1) a < 0 (2) ab >= 0 (1) since a > b => a < b < a now a<0 : if b<0 then a.b < a also a  b > a so clearly a.b< a  b but if b=0 then a.b =0 and a  b = a thus a.b > a  b (0>a)  so here itself we see that for two diff ranges of b , a<0 is insufficient to determine the inequality completely. So 1 is insuff
(2) ab>=0  this means either both a and b are negative (as seen above) OR b = 0 since a cannot be 0 because it is stated that a>b so a must be nonzero OR both a and b are greater than 0. As we have seen in (1) we get two different values for a<0, b<0 AND a<0 b=0 combo. So 2 also is insuff
combining 1 and 2 changes nothing  still the same conditon remains. So insufficient.
It's a damned tough problem. I wish I had the brains of Bunuel to pick up relevant numbers quickly and solve the problem as he has shown in his solution.



Manager
Joined: 14 Jul 2010
Posts: 68

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
01 Aug 2010, 21:50
1. a<0
32<32 yes. 32<3+2 no. Not Suff
2. ab >0   = 32<3+2 yes. + + = 32<32 no. Not Suff
But together; 3 2 <3+2 yes
IMO C.



Manager
Joined: 19 Sep 2010
Posts: 140

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
29 Sep 2010, 02:23
is a  b < a  b canceling a from both sides , the eqn becomes b > b so basically the eqn is asking if b is ve or not . Therefore , we will check for that
1 . a < 0 , does not talk about b 2. ab >= 0 implies a>=0 and b>=0 or a<=0 and b<=0
therefore not sufficient
combining both we get b<=0 which is also not sufficient since b=0 does not satisfy the main question . I hope doing this way you feel faster. Also I think that the condition a > b is irrelevant to the question.



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1033

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
08 Apr 2012, 21:45
I believe that this question has been discussed before too. Please do a search before posting in the forum.
1. a<0 but b can be =0 hence Insufficient.
2 for a=2 2 and b = 11 answer is yes and no. insufficient.
1+2 a= 2 b= 1 LHS < RHS
Hence C it is.



Manager
Joined: 07 Sep 2011
Posts: 67
GMAT 1: 660 Q41 V40 GMAT 2: 720 Q49 V39
WE: Analyst (Mutual Funds and Brokerage)

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
24 Aug 2012, 12:14
I find it much easier to pick numbers to figure out the answer than do it algebraically.
WHAT WE KNOW: a & b are both integers a>b
Question Type: YES OR NO Is a*b<ab?
1) a < 0 meaning a is negative. But b could be anything as long as its absolute value is elss than a. Let's say a=3 B coudl equal 2, 0, or 2.
3*2<3(2)? 6<1? .......YES 3*0<30 0<3?..........NO 3*2<32 6<5...........YES >INSUFFICIENT
2) ab>=0 which means a b be either have the same sign, or one of them is 0. We know that a cannot be 0 because a>b. Therefore only b can be 0.
3*2<3(2).... YES 3*0<30...........NO 3*0<30............NO 3*2<32..............NO >INSUFFICIENT
1&2) Combined, if a is negative, and ab>=0, this means that b is either 0 or also negative. 3*2<3(2).... YES 3*0<30............NO >INSUFFICIENT
Answer is E.



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1131
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
24 Aug 2012, 12:53
Nice explanation Chris. But I don't think that picking up numbers is the best strategy. Can you tell how to decide which method , mathematics or picking numbers , to be chosen after seeing the question. Moreover can you tell me my mistake in the post just before your post.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Manager
Joined: 07 Sep 2011
Posts: 67
GMAT 1: 660 Q41 V40 GMAT 2: 720 Q49 V39
WE: Analyst (Mutual Funds and Brokerage)

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
24 Aug 2012, 14:00
siddharthasingh wrote: Nice explanation Chris. But I don't think that picking up numbers is the best strategy. Can you tell how to decide which method , mathematics or picking numbers , to be chosen after seeing the question. Moreover can you tell me my mistake in the post just before your post. Hi siddharthasingh, I think choosing between solving a problem conceptually, algebraically, or by picking numbers is really up to what you are comfortable with. For myself, when it comes to these types of questions with lots of absolute values, equations, and , I know I figure it out quicker either conceptually or by picking numbers. It's basically the best strategy for myself. I basically came to this conclusion after doing lots of practice problems with the help of my error log. Now, keep in mind I probably would not have done ALL those calculations in my post. I'm not aiming to solve the question, I just want to see if I have enough information to solve the question. Once I came up with a "yes" AND a "no" for each statement, I would have stopped. I just wrote it all out to explain. a>b => either i)a>b ii)a<bActually, there is a multitude of possibilities. What this statement means is that a is farther away from 0 than b is. Both positive: a>b both negative: a<b a neg, b pos: a<b where 0a>b0 a pos, b neg: a>b where a0>0b So I personally think it would be easier to view the statement conceptually, knowing that a>b means the distance of a is greater than the distance of b. Now, please keep in mind that the above scenarios are POSSIBILITIES. Only 1 is true. We want to figure out if they're both positive or not. 1) a<0 On combining i and 1, b<a<0. Therefore ab is positive. ab is negative. On combining ii and 1) Two cases are emerging. a0(b) a(b)0We don't know if b<a. we only know that a>b. knowing that a is a NEGATIVE gets rid of a few possiblities above. A<0, and be can be EITHER neg, pos, or both. i) b=pos while a>b (neg)pos<(neg)(pos)....neg<pos... YES ii)b=neg while a>b (neg)neg<(neg)(neg)....neg<neg....YES Keep in mind that in this case ab will be a bigger negative than ab iii)b=0 (neg)0<(neg)0....0<neg.... NO. 1 is insufficient. Not sure if this helped clear anything up....



Manager
Joined: 24 Mar 2010
Posts: 69

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
20 Dec 2012, 09:55
Any nice algebraic solution to this problem. I picked numbers and got to the solution but still took over 3 minutes to do so.
_________________
 Stay Hungry, stay Foolish 



Intern
Joined: 08 Oct 2011
Posts: 36

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
24 Sep 2013, 05:47
Thank you so much for the explanation. I completely ruled out the possibility for a and b to be equivalent to zero. I will keep that in mind for my future questions. Helps a lot! thanks



Intern
Joined: 17 Jun 2013
Posts: 24

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
05 Jan 2014, 20:21
If a & b are integers ,and a > b, is a*b< ab ?
A)a<0
B)\(ab>=0\)
How to solve this algebraically ?



Manager
Joined: 20 Dec 2013
Posts: 123

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
06 Jan 2014, 00:04
gmatgambler wrote: If a & b are integers ,and a > b, is a*b< ab ?
A)a<0
B)\(ab>=0\)
How to solve this algebraically ? Statement I is insufficient 'a' is a negative number. (Negative) (Positive) < Negative  Number Not always 2(3) < 2  3 AND 1(3) > 1  3 Statement II is insufficient A and B have the same signs. (Negative) (Positive) < Negative  Negative (Positive) (Positive) < Positive  Positive Not always the sign will hold as (+3)(9) > 3  9 AND (2)(+3) < 2 +3 Combining is insufficient a is negative and b is also negative (AB>0) Now it comes to (Negative) (Positive) < Negative  Negative Not always: (3)(2) < 3 + 2 AND (0.2) (0.1) > 0.2 + 0.1 Hence the answer is E.
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views
Perfect Scores http://perfectscores.org http://www.youtube.com/perfectscores



Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
06 Jan 2014, 01:52



Manager
Joined: 20 Mar 2015
Posts: 59

Re: If a and b are integers, and a > b, is a b < a
[#permalink]
Show Tags
06 May 2016, 02:09
Raths wrote: is a  b < a  b canceling a from both sides , the eqn becomes b > b so basically the eqn is asking if b is ve or not . Therefore , we will check for that
1 . a < 0 , does not talk about b 2. ab >= 0 implies a>=0 and b>=0 or a<=0 and b<=0
therefore not sufficient
combining both we get b<=0 which is also not sufficient since b=0 does not satisfy the main question . I hope doing this way you feel faster. Also I think that the condition a > b is irrelevant to the question. Can anyone tell me if this is a correct method or not?




Re: If a and b are integers, and a > b, is a b < a &nbs
[#permalink]
06 May 2016, 02:09



Go to page
1 2
Next
[ 26 posts ]



