Data Sufficiency

The operators '*' and '+' operate only on the numbers 0 and 1 as defined in the table (please see attachment). If x*y=1 which one of the following does (x*y)+x equal?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

OA is D

Source: Nova's GMAT DS Prep course, p.119

its more like Boolean. 1 is for true and 0 is false. if any one (x or y) has 1 then true is returned.

since x*y is 1 that means either x has 1 or y has 1 or both have 1.
hence the sum with x will always yield a 1 (true)

Looking at the table, it resembles the output of a Logic OR and AND gate

So x*y=1 , implies both x and y are 1, so (x*y)+y is ON+ON = ON or 1

Confused between D and E. Could somebody please help in this question.

Eg: x = 1 and y = 1. as (x X Y) = 1 also see the attachment.

Now see the other things...

(x X y) + x = 1 + 1 = 2. This is one solution.

the other solution is given by the other people.

The other solution is: The question says that '*' and '+' are operational only when they both are 0 and 1 otherwise the values given in the table chart will be applied.

So does that mean that the operation (x X Y) + x will not be operational as both the numbers are 1 and 1 and the operational sign is '+'. And so we chose the answer as 1 and not 2.

Then what about the chart where a = 0 and b = 0, the final answer given is also not operational so how come the final answer comes out to be the same as when the sign would be operational.

Tricky and just a few doubts. Help needed...

[email protected] wrote:Confused between D and E. Could somebody please help in this question.

Eg: x = 1 and y = 1. as (x X Y) = 1 also see the attachment.

Now see the other things...

(x X y) + x = 1 + 1 = 2. This is one solution.

the other solution is given by the other people.

The other solution is: The question says that '*' and '+' are operational only when they both are 0 and 1 otherwise the values given in the table chart will be applied.

So does that mean that the operation (x X Y) + x will not be operational as both the numbers are 1 and 1 and the operational sign is '+'. And so we chose the answer as 1 and not 2.

Then what about the chart where a = 0 and b = 0, the final answer given is also not operational so how come the final answer comes out to be the same as when the sign would be operational.

Tricky and just a few doubts. Help needed...

for the operations refer the given chart...

x*y = 1
there is just one possibilty according to the chart when x*y can equal 1, and that is if x=1 and y=1

(x*y)+x
(1*1)+1

acc ording to the chart,
1*1 = 1
1+1 = 1

Hence, (x*y)+x = 1

Option D