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In the expression a $ b, the $ symbol represents one of the
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Updated on: 19 Mar 2013, 10:05
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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, nonidentical 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, 09:40.
Last edited by Bunuel on 19 Mar 2013, 10:05, edited 1 time in total.
OA added.




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Re: In the expression a $ b, the $ symbol represents one of the
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19 Mar 2013, 09:56
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, nonidentical 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 \(ab=\frac{a}{b}\) > \(abb^2=a\) > \(a=\frac{b^2}{b1}\) > b cannot be 1, because in this case \(b1=0\) and we cannot divide by zero. Answer: D. Hope it's clear.
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Re: In the expression a $ b, the $ symbol represents one of the
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19 Mar 2013, 10:05
"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



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Re: In the expression a $ b, the $ symbol represents one of the
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19 Mar 2013, 14:17
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=ab abb^2=a After this step, how do I know whether I try to simplify a or b?



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Re: In the expression a $ b, the $ symbol represents one of the
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19 Mar 2013, 15:21
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=ab abb^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: \(b(ab)=a\) \(b=\frac{a}{(ab)}\) and you go nowhere.



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Re: In the expression a $ b, the $ symbol represents one of the
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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=ab abb^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 = aa > 1 = 0?? Makes no sense



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In the expression a $ b, the $ symbol represents one of the
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21 Aug 2017, 20:42
Need some help let b=2 a=1/2 a/b=1/2/2=1/4 ab=1/2(2)=5/2 hence b cannot be 2?



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Re: In the expression a $ b, the $ symbol represents one of the
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21 Aug 2017, 21:06
gps5441 wrote: Need some help let b=2 a=1/2 a/b=1/2/2=1/4 ab=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.
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Re: In the expression a $ b, the $ symbol represents one of the
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