The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin

Question

https://gmatclub.com/forum/download/file.php?id=27395 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 . 2015-07-28_0114.png

ENGRTOMBA2018 · Answer

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!)

VenoMfTw · Answer

IMO: C

St 1:
(x*y) + y = 1 (This is in the form a + b = 1 , where a = x*y & b=y)
 a + b = 1 (so from the fig it is possible for following cases)
 0 + 1 = 1=>(x*y = 0 & y = 1 =>  {x =0 & y= 0}  or  {x=0 & y= 1}  or  {x=1 & y= 0}  Since y must be "1" we can strike out other 2 possibilities)
 1 + 0 = 1=>(x*y = 1 & y = 0 => {x=1 & y= 1}  Since y must be "0" we can strike out the possibilities where y not equal to "0"
 1 + 1 = 1=>(x*y = 1 & y = 1 => {x=1 & y= 1} 
Thus for this set we end up two possibilities i.e in bold 
 {x=1 & y= 1}  &  {x=0 & y= 1}  
   x*y = 1 & x*y = 0 (2 different answers) 
Thus not sufficient

St 2:
(x*y) + x = 1 (This is in the form a + b = 1 , where a = x*y & b=x)
 Instead of solving all the cases if we observe we can understand that we will get the same solution set expect that the values of x and y will be interchanged. since y in st:1 is replaced by x in st:2 
 {x=1 & y= 1}  &  {x=1 & y= 0}  
   x*y = 1 & x*y = 0 (2 different answers) 
Thus not sufficient

Combined: common solution set is  {x=1 & y= 1} 
Suff

Hope it is clear

ENGRTOMBA2018 · Answer

Bunuel , can you please provide the OE.

I think most of us are missing some important information or misinterpreting the information provided.

GMATinsight , what is your take on this question?

visram04 · Answer

I think the answer is D.

Based on the 2 equations separately, Value for x and y is either x=1;y=0. Alternatively x=0;y=1.

In any case, xy=0. So both statements are sufficient.

ENGRTOMBA2018 · Answer

You are missing the case when x=y=1. This will satisfy statement 1 as well.

visram04 · Answer

Oh Yes right. I din't notice 1+1 is 1.

Then answer should be E, as x and y can be 0 or 1 or both 1. So xy could be 0 or 1.

ENGRTOMBA2018 · Answer

Not really. If you look at my solution above,

Statement 1, gives : x = 0 , y=1 or x=y=1

Statement 2 gives: x=1, y =0 or x=y=1.

Thus combining we get, x =y=1 (sufficient!) and C should thus be the answer.

sherly123 · Answer

I am getting the answer as E, how is the answer B ?

Bunuel · Answer

The answer should be C. It was a typo in the book.

ENGRTOMBA2018 · Answer

Thanks  Bunuel , although I did spend quite a bit of time on finding out why wasnt I getting the OA in the first place. Good question though!

longranger25 · Answer

This is simple. a*b is the 'and' function, a+b is the 'or' function. 'And' means both of them should be 1 for the value to be 1. 'Or' means either or both should be 1 for the result to be 1.

St.1: (x*y)+y = 1
=>x.y + y =1
=> y.(x+1)=1 (because x+1 = 1)
=>y.1 = 1
=> y=1

Similarly, from statement 2, x = 1

Combining the 2 statements, x.y = 1

Had the question been the value of x+y, the answer would have been D.

bumpbot · Answer

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The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin

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