The following operations are defined for real numbers. A @ B = A if A

Question

The following operations are defined for real numbers.

A 	ext{@}B = A  if A is greater than B else  A	ext{@}B = B  
 A \% B = AB  if A x B is positive else  A \% B = A

Note that all other mathematical symbols have their usual meanings.

\frac{1	ext{@}-1}{(-K)	ext{@}(-K)}\%K , then K =

(A) K^2
(B) 1/K
(C) -1/K
(D) 1 
(E) Cannot be determined

IanStewart · Answer

Bunuel - I think there are a few issues with the way the question has been transcribed, and it's not answerable right now. I'm guessing the "max" function defined in the first sentence is meant to use the "@" symbol, since that shows up later on. There also isn't any relationship given at the end that we could solve for k; we're only given an expression.

TestPrepUnlimited · Answer

I suppose the first part of the question is  A 	ext{@} B= A  if A is greater than B else  A 	ext{@} B = B , essentially this function outputs the bigger of A or B.

Let us tackle one part at a time,  1 @ -1 = 1  since 1 is greater than -1. On the bottom, since -K is not greater than -K the function would output A@B = B which is -K. Hence the left side is  \frac{1}{-K} = -\frac{1}{K} .

Then we simplified the question to what is  -\frac{1}{K}\% K . We do know the two inputs here have opposite signs, therefore we should have A%B = A since AB would be negative with these inputs.

Finally  -\frac{1}{K}\% K = -\frac{1}{K} .

Ans: C

BrushMyQuant · Answer

Given that  A 	ext{@}B = A  if A is greater than B else  A 	ext{@}B= B  and  A \% B = AB  if A x B is positive else  A \% B = A  and we need to find the value of  \frac{1	ext{@}-1}{(-K)	ext{@}(-K)}\%K

Lets start by finding the value of  1	ext{@}-1

To find  1	ext{@}-1  we need to compare what is before and after  	ext{@}  in  1	ext{@}-1  and  A	ext{@}B

=> We need to substitute A with 1 and B with -1 in  A	ext{@}B  to get the value of  1	ext{@}-1 
Since A(1) > B(-1)
=>  1	ext{@}-1  = 1

=> In case of  (-K)	ext{@}(-K)  A = B = -K => A is NOT greater than B
=>  (-K)	ext{@}(-K)  = -K

=>  \frac{1	ext{@}-1}{(-K)	ext{@}(-K)}\%K  =  \frac{1}{-K}\%K

Now,  \frac{-1}{K}  * K = -1

=>  \frac{1}{-K}\%K  =  \frac{-1}{K}

So,  Answer will be C 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

BrushMyQuant · Answer

Bunuel  : I think the question needs to be changed to find the value of  \frac{1	ext{@}-1}{(-K)	ext{@}(-K)}\%K  and NOT find the value of K.

Please check, confirm and update if required.
Thank you.

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The following operations are defined for real numbers. A @ B = A if A

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