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Manager  Joined: 09 Feb 2013
Posts: 111
In the expression a $b, the$ symbol represents one of the  [#permalink]

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Question Stats: 51% (02:43) correct 49% (03:01) wrong based on 369 sessions

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In the expression a $b, the$ symbol represents one of the following arithmetic operations on a and b (in the order the variables are shown): addition, subtraction, multiplication, and division. Given that it is not true that a $b = b$ a for all possible values of a and b, a pair of nonzero, non-identical values for a and b is chosen such that a $b produces the same result, no matter which of the operations (under the given constraints) that$ represents. The nonzero value of b that cannot be chosen, no matter the value of a, is

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

I would like to have some discussion before posting the correct answer

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Originally posted by emmak on 19 Mar 2013, 10:40.
Last edited by Bunuel on 19 Mar 2013, 11:05, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 59000
Re: In the expression a $b, the$ symbol represents one of the  [#permalink]

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emmak wrote:
In the expression a $b, the$ symbol represents one of the following arithmetic operations on a and b (in the order the variables are shown): addition, subtraction, multiplication, and division. Given that it is not true that a $b = b$ a for all possible values of a and b, a pair of nonzero, non-identical values for a and b is chosen such that a $b produces the same result, no matter which of the operations (under the given constraints) that$ represents. The nonzero value of b that cannot be chosen, no matter the value of a, is

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

I would like to have some discussion before posting the correct answer

Since it's NOT true that a$b=b$a for all possible values of a and b, then $is neither addition not multiplication (because $$a+b=b+a$$ and $$ab=ba$$ for all possible values of a and b). So, we have that$ is either subtraction or division.

Next, we are told that a$b produces the same result, no matter which of the operations (under the given constraints) that$ represents so no matter whether $is subtraction or division a$b will produce the same result, so $$a-b=\frac{a}{b}$$ --> $$ab-b^2=a$$ --> $$a=\frac{b^2}{b-1}$$ --> b cannot be 1, because in this case $$b-1=0$$ and we cannot divide by zero.

Hope it's clear.
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Re: In the expression a $b, the$ symbol represents one of the  [#permalink]

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DoItRight wrote:
Great explainations. I have 1 question. In the equation, why do you solve for a instead of solving for b? Is there something in the wording that tells you to solve "a=" instead of "b=?"

a/b=a-b
ab-b^2=a After this step, how do I know whether I try to simplify a or b?

I tried to get all "a" and "b" terms on different sides, that's the main point.

However if you try to simplify b you get:

$$b(a-b)=a$$

$$b=\frac{a}{(a-b)}$$

and you go nowhere.
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Re: In the expression a $b, the$ symbol represents one of the  [#permalink]

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1
"Given that it is not true that a $b = b$ a for all possible values of a and b"

so $cannot be + or * because $$a * b = b * a$$ $$a + b = b + a$$ for every a,b we know that $$a/b = a - b$$ $$a = ab - b^2$$ $$a - ab = -b^2$$ $$a(1 - b) = -b^2$$ $$a = -b^2/(1 - b)$$ B cannot be 1 _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] Intern  Joined: 18 Feb 2013 Posts: 29 GMAT 1: 710 Q49 V38 Re: In the expression a$ b, the $symbol represents one of the [#permalink] ### Show Tags 1 Great explainations. I have 1 question. In the equation, why do you solve for a instead of solving for b? Is there something in the wording that tells you to solve "a=" instead of "b=?" a/b=a-b ab-b^2=a After this step, how do I know whether I try to simplify a or b? Intern  Joined: 04 May 2013 Posts: 39 Re: In the expression a$ b, the $symbol represents one of the [#permalink] ### Show Tags DoItRight wrote: Great explainations. I have 1 question. In the equation, why do you solve for a instead of solving for b? Is there something in the wording that tells you to solve "a=" instead of "b=?" a/b=a-b ab-b^2=a After this step, how do I know whether I try to simplify a or b? Simplifying b does not work. i.e. it wont give you any result: You will have: b^2 = ab - a b = a - a/b The value of b cannot be 1 because substituting b = 1 give you: 1 = a-a --> 1 = 0?? Makes no sense Manager  B Joined: 04 May 2014 Posts: 150 Location: India WE: Sales (Mutual Funds and Brokerage) In the expression a$ b, the $symbol represents one of the [#permalink] ### Show Tags Need some help let b=-2 a=1/2 a/b=1/2/-2=1/-4 a-b=1/2-(-2)=5/2 hence b cannot be -2? Math Expert V Joined: 02 Sep 2009 Posts: 59000 Re: In the expression a$ b, the $symbol represents one of the [#permalink] ### Show Tags gps5441 wrote: Need some help let b=-2 a=1/2 a/b=1/2/-2=1/-4 a-b=1/2-(-2)=5/2 hence b cannot be -2? Why should a be 1/2 if b = -2? b = -2 is possible: a - (-2) = a/(-2) --> a = -4/3. _________________ Non-Human User Joined: 09 Sep 2013 Posts: 13581 Re: In the expression a$ b, the $symbol represents one of the [#permalink] ### Show Tags Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: In the expression a$ b, the $symbol represents one of the [#permalink] 15 Oct 2018, 06:49 Display posts from previous: Sort by # In the expression a$ b, the \$ symbol represents one of the  