
Data Sufficiency CAT 2013
Question 4 the day:
March 07, 2003
The question for the day is from the topic of Data Sufficiency

The set S of numbers has the following properties: I) If x is in S, then 1/x is in S.
II) If both x and y are in S, then so is x + y.
Is 3 in S?
(1) 1/3 is in S.
(2) 1 is in S.
(1) 
Mark 1 If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone. 

(2) 
Mark 2 If the question can be answered by using either statement alone. 
(3) 
Mark 3 If the question can be answered by using both statements together, but cannot be answered by using either statement alone. 

(4) 
Mark 4 If the question cannot be answered even by using both the statements together. 
Correct Answer  (2)
Solution:
Consider (1) alone. Since 1/3 is in S, we know from Property I that 1/(1/3) = 3 is in S. Hence, (1) is sufficient.
Consider (2) alone. Since 1 is in S, we know from Property II that 1 + 1 = 2 (Note, nothing in Property II prevents x and y from standing for the same number. In this case both stand for 1.) is in S. Applying Property II again shows that 1 + 2 = 3 is in S. Hence, (2) is also sufficient.



