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In the expression a $ b, the $ symbol represents one of the [#permalink]

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19 Mar 2013, 10:40

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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

Re: In the expression a $ b, the $ symbol represents one of the [#permalink]

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19 Mar 2013, 10:56

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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

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.

Re: In the expression a $ b, the $ symbol represents one of the [#permalink]

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19 Mar 2013, 15:17

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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?

Re: In the expression a $ b, the $ symbol represents one of the [#permalink]

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19 Mar 2013, 16:21

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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. _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: In the expression a $ b, the $ symbol represents one of the [#permalink]

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23 Jul 2013, 18:42

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

Re: In the expression a $ b, the $ symbol represents one of the [#permalink]

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02 Nov 2014, 06:00

Hello from the GMAT Club BumpBot!

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Re: In the expression a $ b, the $ symbol represents one of the [#permalink]

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25 Dec 2015, 16:52

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).

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