Civil Services Prep

Prelims 2022 · CSAT / Logical Reasoning · Question 19

Consider the Question and two Statements given below: 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?

  1. Statement-1 alone is sufficient to answer the Question
  2. Statement-2 alone is sufficient to answer the Question
  3. Both Statement-1 and Statement-2 are sufficient to answer the Question
  4. Both Statement-1 and Statement-2 are not sufficient to answer the Question

Answer

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

  • Statement-1: x/3 is not an integer. This does not tell whether x itself is an integer; e.g., x = 1 (integer) and x = 1/2 (not integer) both satisfy it. Verdict: Not sufficient.
  • Statement-2: 3x is an integer. This also does not tell whether x is an integer; e.g., x = 1 (integer) and x = 1/3 (not integer) both satisfy it. Verdict: Not sufficient.
  • Using both together: Both can hold for x = 1 (integer) and also for x = 1/3 (not integer), since 3x = 1 is an integer and x/3 = 1/9 is not an integer. So the question still cannot be answered definitively. Verdict: Both together not sufficient.
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