Question Details

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?

Options

Statement-1 alone is sufficient to answer the Question

Statement-2 alone is sufficient to answer the Question

Both Statement-I and Statement-2 are sufficient to answer the Question

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

Show Answer

Correct Answer :

Option D

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

Solution :

The correct option is: Both Statement-I and Statement-2 are not sufficient to answer the Question.

To determine if the given statements are sufficient to answer whether $x$ is an integer, let us analyze each statement individually and then together.

Analysis of Statement-1:
Statement-1 tells us that $\frac{x}{3}$ is not an integer.
Let us test two different values for $x$ that satisfy this condition:
Case 1: Let $x = 1$ . Here, $\frac{x}{3} = \frac{1}{3}$ , which is not an integer. In this case, $x$ is an integer.
Case 2: Let $x = 1.5$ . Here, $\frac{x}{3} = \frac{1.5}{3} = 0.5$ , which is not an integer. In this case, $x$ is not an integer.
Since we can get both "yes" and "no" as answers to the question, Statement-1 alone is not sufficient.

Analysis of Statement-2:
Statement-2 tells us that $3 x$ is an integer.
Let us test two different values for $x$ that satisfy this condition:
Case 1: Let $x = 1$ . Here, $3 x = 3$ , which is an integer. In this case, $x$ is an integer.
Case 2: Let $x = \frac{1}{3}$ . Here, $3 x = 3 (\frac{1}{3}) = 1$ , which is an integer. In this case, $x$ is not an integer.
Since we can get both "yes" and "no" as answers to the question, Statement-2 alone is not sufficient.

Analysis of both Statements together:
Now, let us combine both statements. We need a value of $x$ where $\frac{x}{3}$ is not an integer AND $3 x$ is an integer:
Case 1: Let $x = 1$ . Here, $\frac{x}{3} = \frac{1}{3}$ (not an integer) and $3 x = 3$ (an integer). Both statements are satisfied, and $x$ is an integer.
Case 2: Let $x = \frac{1}{3}$ . Here, $\frac{x}{3} = \frac{1}{9}$ (not an integer) and $3 x = 1$ (an integer). Both statements are satisfied, but $x$ is not an integer.
Since we can still get both "yes" and "no" as answers even when using both statements, the statements together are not sufficient to answer the question.