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In the expression a $b, the$ symbol represents one of the

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Joined: 09 Feb 2013
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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

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

[Reveal] Spoiler:
I would like to have some discussion before posting the correct answer
[Reveal] Spoiler: OA

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Last edited by Bunuel on 19 Mar 2013, 11:05, edited 1 time in total.
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Posts: 44352
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

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

[Reveal] Spoiler:
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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19 Mar 2013, 11:05
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"Given that it is not true that a $b = b$ a for all possible values of a and b"