Bunuel wrote:
The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defined in the table. What is the value of x*y ?
(1) (x*y) + y = 1
(2) (x*y) + x = 1
Kudos for a correct solution.Attachment:
2015-07-28_0114.png
Tricky question.
I got C (incorrect, 3 minutes) but I will still go ahead and post my explanation to see where I went wrong.
Per statement 1, (x*y)+y=1 ---> treat (x*y) as 'z' for now ---> z+y=1
Based on the table, a+b = 1 for 3 cases:
a=0,b=1 ---> z=0,y=1 --->
x*y=0 and y =1 --->
x=0 and y =1 ...(1)
a=1,b=0 ---> z=1,y=0 ---> x*y=1 and y =0 ---> Not possible per the table.
a=1,b=1 ---> z=1,y=1 --->
x*y=1 and y =1 --->
x=1 and y =1 ...(2)
Thus 2 possible combinations of x,y possible ---->2 values of x*y possible ----> Statement 1 is not sufficient.
Per statement 2, (x*y)+x=1 ---> treat (x*y) as 'z' for now ---> z+x=1
Based on the table, a+b = 1 for 3 cases:
a=0,b=1 ---> z=0,x=1 --->
x*y=0 and x =1 --->
x=1 and y =0 ...(3)
a=1,b=0 ---> z=1,x=0 ---> x*y=1 and x =0 ---> Not possible per the table.
a=1,b=1 ---> z=1,x=1 --->
x*y=1 and x =1 --->
x=1 and y =1 ...(4)
Thus 2 possible combinations of x,y possible ----> 2 values of x*y possible -----> Statement 2 is not sufficient.
Combining 1 and 2 , we get that x=1 and y =1 ---> x*y = 1. We get 1 unique value of x*y and C is thus the correct answer (IMO!)