Absolute Values

I tried solving these sums by taking numbers but I felt the process is too time consuming
I am not able to select smart nos in these scenarios


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I also have similar doubt. Choosing numbers in these questions take too much time, with an additional risk that I might have missed any corner case. How to solve this in a more deterministic behaviour?

Same here. I am waiting for a reply regarding this

Could someone pls help me out regarding this

You can solve them a bit, but quickest way will be choosing numbers,

For example :
17,

|x| < 1 which means x<1 and x>-1
y> 0
lets take y =1 and x= 0
|x|+y = 1; xy = 0

lets take x = 0.1, y =1
1.1 ; 0.1

lets take x = -0.1, y=1
0.9 ; -0.1

So, Answer is A

In case of questions like 19, you have quantity B = -9; so you can put value of x = -9 or x<- 9 or x>-9 to find the answer more quickly.

Also, if you use logic - you can find answer more quickly

example
17,

As you can see modulus of x which is |x| will be positive number so |x| + y will result in positive number. On the other side , xy is without modulus which will make the product negative and hence answer is Option A

For the 3rd case u took x = -0
but 0 is not negative right

sorry, it was a typo
I fixed it

Np