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In the expression a $ b, the $ symbol represents one of the [#permalink]
19 Mar 2013, 09:40
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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]
19 Mar 2013, 09:56
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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]
19 Mar 2013, 14:17
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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]
19 Mar 2013, 15:21
2
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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]
23 Jul 2013, 17:42
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]
02 Nov 2014, 05:00
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Re: In the expression a $ b, the $ symbol represents one of the [#permalink]
25 Dec 2015, 15:52
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