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

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

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New post 27 Jul 2015, 14:21
1
8
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (02:13) correct 54% (02:08) wrong based on 108 sessions

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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 27 Jul 2015, 16:53
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Bunuel wrote:
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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!)
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 28 Jul 2015, 03:53
2
Bunuel wrote:
Image
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


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
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 02 Aug 2015, 05:58
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?
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 02 Aug 2015, 12:23
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.
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 02 Aug 2015, 12:35
visram04 wrote:
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.


You are missing the case when x=y=1. This will satisfy statement 1 as well.
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 03 Aug 2015, 02:28
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.
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 03 Aug 2015, 05:08
visram04 wrote:
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.


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.
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 04 Aug 2015, 11:03
I am getting the answer as E, how is the answer B ?
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 17 Aug 2015, 08:23
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 17 Aug 2015, 08:25
Bunuel wrote:
Bunuel wrote:
Image
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


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


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!
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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New post 17 Aug 2015, 08:36
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.
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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin  [#permalink]

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Re: The operators ‘*’ and ‘+’ operate only on the numbers 0 and 1 as defin   [#permalink] 26 Mar 2019, 23:47
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