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For any numbers a and b, a#b=a + b - ab. If a#b=0, which of

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For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] New post 05 Jul 2012, 01:33
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Apr 2013, 04:05, edited 2 times in total.
Edited the question.
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of [#permalink] New post 05 Jul 2012, 01:51
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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.

Answer: B.

Hope it's clear.
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of [#permalink] New post 05 Jul 2012, 23:55
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! :|
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of [#permalink] New post 25 Jul 2012, 00:40
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... :cry:
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of [#permalink] New post 11 Apr 2013, 03:59
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..
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Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of [#permalink] New post 11 Apr 2013, 04:06
Expert's post
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] New post 11 Apr 2013, 04:15
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] New post 16 Jul 2014, 20:40
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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] New post 17 Jul 2014, 06:27
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!
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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of [#permalink] New post 17 Jul 2014, 06:37
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of   [#permalink] 17 Jul 2014, 06:37
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