Question: Is x an integer?
Statement-1: x/3 is not an integer.
Statement-2: 3x is an integer.

Which one of the following is correct in respect of the Question and the Statements?
a.    Statement-1 alone is sufficient to answer the Question
b.   Statement-2 alone is sufficient to answer the Question
c.    Both Statement-1 and Statement-2 are sufficient to answer the Question
d.   Both Statement-1 and Statement-2 are not sufficient to answer the Question
Correct Answer: d.   Both Statement-1 and Statement-2 are not sufficient to answer the Question

Question from UPSC Prelims 2022 CSAT Paper

Explanation :

Is x an integer?

Statement-1: x/3 is not an integer

– This tells us x cannot be evenly divided by 3
– Examples: x could be 2/3 (not an integer) or 4 (integer)
– Statement-1 alone is not sufficient

Statement-2: 3x is an integer

– This means x could be an integer or a fraction multiple of 1/3
– Examples: if 3x = 6, then x = 2 (integer)
if 3x = 2, then x = 2/3 (not integer)
– Statement-2 alone is not sufficient

Combined Analysis:
– Statement-1: x cannot be evenly divided by 3
– Statement-2: 3x is an integer
– Together they tell us x must be a fraction multiple of 1/3
– Still cannot determine if x is definitely an integer

Answer: Both Statement-1 and Statement-2 are not sufficient to answer the Question.