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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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Manager
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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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Updated on: 11 Apr 2013, 04:05
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Question Stats:

62% (01:26) correct 38% (01:21) wrong based on 691 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, 01:33.
Last edited by Bunuel on 11 Apr 2013, 04:05, edited 2 times in total.
Edited the question.
##### Most Helpful Expert Reply
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Joined: 02 Sep 2009
Posts: 52344
Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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05 Jul 2012, 01:51
3
3
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]

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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]

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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...
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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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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..
Math Expert
Joined: 02 Sep 2009
Posts: 52344
Re: For any numbers a and b, ab= a + b - ab. If ab=0, which of  [#permalink]

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11 Apr 2013, 04:06
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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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]

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17 Jul 2014, 06:27
1
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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Posts: 52344
Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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17 Jul 2014, 06:37
1
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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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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01 Jan 2016, 18:24
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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Re: For any numbers a and b, a#b=a + b - ab. If a#b=0, which of  [#permalink]

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18 Mar 2018, 16:45
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:

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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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08 Aug 2018, 08:00
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 2257 times ]

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

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30 Oct 2018, 00:35
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
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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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