If $x$, $y$ and $z$ are integers, each greater than $1$, then is $x$ a prime number? Statement I : $xy^2 = 116$ Statement II : $xz = 261$

Question

Accepted Answer

Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement

Explanation: Statement I: $xy^2 = 116 = 2^2 imes 29$. Since $y > 1$ is an integer, $y^2$ must be a perfect square divisor of $116$. The only such divisor is $4$, so $y^2 = 4$ and $y = 2$. Thus $x = 116/4 = 29$, which is prime. Statement I alone is sufficient. Statement II: $xz = 261 = 3^2 imes 29$. Possible values for $x$ are $3, 9, 29, 87$. Since $x = 3$ or $29$ gives prime, while $x = 9$ or $87$ gives composite, we cannot determine definitively. Statement II alone is insufficient. Therefore, the question can be answered using Statement I alone but not Statement II alone, making Option 1 the correct answer.

Detailed Explanation:

Question 1 of 4 Factors & Multiples

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