Question

What is the number $x$?
Statement I
I. The LCM of $x$ and 18 is 36.
Statement II
II. The HCF of $x$ and 18 is 2.

• A. The question can be answered with the help of statement I alone.
• B. The question can be answered with the help of statement II alone.
• C. Both statement I and statement II are needed to answer the question.
• D. The question cannot be answered even with the help of both the statements.

Hint:

In LCM-HCF problems, use $\text{LCM} \times \text{HCF} = \text{Product of numbers}$ to filter possibilities.

Answer 1

The Correct Option is C

Step 1: From Statement I $\text{LCM}(x, 18) = 36$ means $x$ could be values like $36, 12, 9, 6, 18$ (any divisor of 36 × appropriate factor). Multiple possibilities remain. Step 2: From Statement II $\text{HCF}(x, 18) = 2$ means $x$ is even but not divisible by 3. Possible values: $2, 4, 8, 10, 14, 16, \dots$ Infinite possibilities. Step 3: Combining Statements From I and II together, only $x = 4$ satisfies both conditions. Step 4: Conclusion Both statements are require(d)