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Manager  Joined: 16 Feb 2012
Posts: 171
Concentration: Finance, Economics
For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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Question Stats: 62% (01:56) correct 38% (01:53) wrong based on 565 sessions

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For any numbers a and b, a#b=a + b - ab. If a#b=0, which of the following CANNOT be a value of b?

A. 2
B. 1
C. 0
D. -1
E. -3/2

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Originally posted by Stiv on 05 Jul 2012, 02:33.
Last edited by Bunuel on 11 Apr 2013, 05:05, edited 2 times in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 55709
Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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Stiv wrote:
For any numbers a and b, ab= a + b - ab. If ab=0, which of the following CANNOT be a value of b?

A. 2
B. 1
C. 0
D. -1
E. -3/2

Some function (#) is defined for all numbers $$a$$ and $$b$$ as $$a#b= a + b - ab$$.

Now, since given that $$a#b=0$$, then $$a + b - ab=0$$ --> $$a=\frac{b}{b-1}$$ --> if $$b=1$$ then the given expression is undefined so $$b$$ cannot equal to 1.

Or: $$a + b - ab=0$$ --> $$(a-1)(1-b)+1=0$$ --> $$(a-1)(1-b)=-1$$. If $$b=1$$, then $$(a-1)(1-b)=0$$ not -1, so $$b$$ cannot equal to 1.

Hope it's clear.
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GMAT 1: 620 Q46 V30 GMAT 2: 720 Q50 V38 Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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Can someone pls edit the question.? i was wondering where i was going wrong thinking. question was ab=a+b-ab => 2ab=a+b. and then saw bunuel's reply then understood what the question was! Manager  Status: Prevent and prepare. Not repent and repair!!
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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asax wrote:
Can someone pls edit the question.? i was wondering where i was going wrong thinking. question was ab=a+b-ab => 2ab=a+b. and then saw bunuel's reply then understood what the question was! Even I got it wrong... _________________
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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asax wrote:
Can someone pls edit the question.? i was wondering where i was going wrong thinking. question was ab=a+b-ab => 2ab=a+b. and then saw bunuel's reply then understood what the question was! Yes indeed, very annoying..
Math Expert V
Joined: 02 Sep 2009
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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notsureifseriousor wrote:
asax wrote:
Can someone pls edit the question.? i was wondering where i was going wrong thinking. question was ab=a+b-ab => 2ab=a+b. and then saw bunuel's reply then understood what the question was! Yes indeed, very annoying..

Done: edited the question.
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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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Stiv wrote:
For any numbers a and b, a#b=a + b - ab. If a#b=0, which of the following CANNOT be a value of b?

A. 2
B. 1
C. 0
D. -1
E. -3/2

------------------------------------------
for me the fastest way must be the use of answer choices to find the value of a if a will be an integer after putting the value of of b as given in the answer choices then the answer will be correct with no cumbersome calculations & its fast too ....!!
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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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2
Can I do it this way?

I will just plug the number in to see if we can solve for a.

a#b=a+b-ab and a#b=0

=> a+b-ab=0

A. b=2 -> a=2
B. b=1 -> a+1-a=0 -> 1=0???
C. b=0 -> a=0
D. b=-1 -> a=1/2
E. b=-3/2 -> a= 3/5

So it's clear that b cannot be 1!
Math Expert V
Joined: 02 Sep 2009
Posts: 55709
Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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linhnd1492 wrote:
Can I do it this way?

I will just plug the number in to see if we can solve for a.

a#b=a+b-ab and a#b=0

=> a+b-ab=0

A. b=2 -> a=2
B. b=1 -> a+1-a=0 -> 1=0???
C. b=0 -> a=0
D. b=-1 -> a=1/2
E. b=-3/2 -> a= 3/5

So it's clear that b cannot be 1!

Yes, it's a valid approach.

Check other function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions

Hope it helps.
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Use answer choices to see whether a valid value for a can be determined.
B shows that 1=0 which is never true, so that is the answer.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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Hi All,

This is an example of a Symbolism question (and you'll likely see 1 on Test Day). The idea is that you'll be given a "made up" math symbol, told what it "means" mathematically and then asked to solve some minor equation.

Here, we're told to substitute values in for A and B so that the equation….

A + B - AB = 0

We're asked which of the following answers CANNOT be the value of B? So 4 of the answers are POSSIBLE and one is IMPOSSIBLE. There are a couple of ways to approach this prompt. You could work mathematically or you can TEST THE ANSWERS. I'm going to use the answers to my advantage and find the 4 that are possible solutions and the one the creates an impossible situation:

If B = 2, then we'd have...
A + 2 - 2A = 0
2 = A
So B COULD be 2

If B = 1, then we'd have…
A + 1 - A = 0
1 = 0???????
B CANNOT equal 1

At this point, we could stop. I'll show you why the other answers are possible though:

If B = 0, then we'd have…
A + 0 - 0 = 0
0 = A
So B COULD be 0

If B = -1, then we'd have…
A -1 -(-1)(A) = 0
2A = 1
1/2 = A
So B COULD be -1

If B = -2/3, then we'd have…
A - 2/3 -(-2/3)(A) = 0
A + 2A/3 = 2/3
5A/3 = 2/3
A = 6/15
So B COULD be -2/3

GMAT assassins aren't born, they're made,
Rich
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Manager  S Joined: 02 Aug 2017 Posts: 54 Concentration: Strategy, Nonprofit Schools: ISB '20 GPA: 3.71 Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] Show Tags Stiv wrote: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of the following CANNOT be a value of b? A. 2 B. 1 C. 0 D. -1 E. -3/2 Please find here the simple solution in the picture. Hope it helps. Posted from my mobile device Attachments 1533743971297718472570848051729.jpg [ 2.02 MiB | Viewed 3827 times ] _________________ Everything is in flux, nothing stays still MGMAT1 :590 Q42 V30 (07/07/18) VERITAS :660 Q48 V33 (16/07/18) GMATPREP1 :690 Q46 V36 (22/07/18) GMATPREP2 :740 Q51 V39 (06/08/18) ECONOMIST :740 Q49 V44 (11/08/18) KAPLAN :690 Q49 V36 (17/08/18) PRINCETON :690 Q48 V38 (26/08/18) MGMAT2 :720 Q43 V45 (02/09/18) CEO  D Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2942 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] Show Tags Stiv wrote: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of the following CANNOT be a value of b? A. 2 B. 1 C. 0 D. -1 E. -3/2 Given: a # b = a + b – ab. and a # b = 0 i.e. a + b – ab = 0 (Adding 1 and subtracting 1 simultaneously in the left part of the equation) i.e. a + b - ab -1 +1 = 0 i.e. a(1-b) -1 (1-b) = -1 i.e. (a-1)*(1-b) = -1 i.e. (a-1)*(b-1) = 1 i.e. either a = 0 and b = 0 or a = 2 and b = 2 or (a, b) = (3, 3/2) in any order etc. Point to be Noted: for $$(a-1)*(b-1) = 1$$to be true none of the parts of equation can be zero i.e. (a-1)≠0 as well as (b-1)≠0 i.e. a and b can NOT be 1 Answer: Option B _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Senior Manager  G Joined: 31 May 2017 Posts: 339 Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] Show Tags 1 EMPOWERgmatRichC wrote: Hi All, This is an example of a Symbolism question (and you'll likely see 1 on Test Day). The idea is that you'll be given a "made up" math symbol, told what it "means" mathematically and then asked to solve some minor equation. Here, we're told to substitute values in for A and B so that the equation…. A + B - AB = 0 We're asked which of the following answers CANNOT be the value of B? So 4 of the answers are POSSIBLE and one is IMPOSSIBLE. There are a couple of ways to approach this prompt. You could work mathematically or you can TEST THE ANSWERS. I'm going to use the answers to my advantage and find the 4 that are possible solutions and the one the creates an impossible situation: If B = 2, then we'd have... A + 2 - 2A = 0 2 = A So B COULD be 2 If B = 1, then we'd have… A + 1 - A = 0 1 = 0??????? B CANNOT equal 1 At this point, we could stop. I'll show you why the other answers are possible though: If B = 0, then we'd have… A + 0 - 0 = 0 0 = A So B COULD be 0 If B = -1, then we'd have… A -1 -(-1)(A) = 0 2A = 1 1/2 = A So B COULD be -1 If B = -2/3, then we'd have… A - 2/3 -(-2/3)(A) = 0 A + 2A/3 = 2/3 5A/3 = 2/3 A = 6/15 So B COULD be -2/3 Final Answer: GMAT assassins aren't born, they're made, Rich Rich, Thanks for the TEST the Answers method. I was trying to find answer through solving the function and took time whereas your method was very effective. _________________ Please give kudos if it helps Resources | | | | | EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14353 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] Show Tags Hi akadiyan, Since the GMAT is a big 'critical thinking test', you'll find that almost every question that you'll face can be approached using more than one approach. In that way, the Exam actually 'rewards' strong thinkers - if you know multiple ways to get to the correct answer, and choose the most efficient method for the question that's in front of you, then you can get to the solution with less work and in a shorter amount of time. By extension, it then becomes easier to score at a higher level overall. Many Test Takers focus solely on questions that they get wrong - and that makes a certain amount of sense - but there's some significant potential benefits to reviewing questions that you answered correctly (since there might be faster methods that you could use or other 'efficiencies' that can help you to improve your Scores AND your pacing). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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Stiv wrote:
For any numbers a and b, a#b=a + b - ab. If a#b=0, which of the following CANNOT be a value of b?

A. 2
B. 1
C. 0
D. -1
E. -3/2

We are given that a#b=a + b - ab and that a#b=0. Thus we have

a + b - ab = 0

a + b = ab

Now let’s look at the choices:

A. If b = 2, then

a + 2 = a(2)

2 = a

So b can be 2.

B. If b = 1, then

a + 1 = a(1)

We see that a + 1 (1 more than a) can’t be equal to a itself. So b CANNOT be 1, and that is the number we are looking for.

Alternate Solution:

We are given that a#b=a + b - ab and that a#b=0. Thus we have

a + b - ab = 0

a + b = ab

b = ab - a

b = a(b - 1)

We observe here that b = 1 results in the inconsistent result of 1 = 0. Thus, the only value that b cannot assume is 1.

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