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

If x, y and z are integers, each greater than 1, then is x a prime…

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

Answer

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

Statement I: xy^2 = 116 = 2^2×29. Since y>1 is an integer, y^2 must be a square factor of 116. The only such value is 4, so y=2 and x=116/4=29, which is prime. Sufficient.
Statement II: xz = 261 = 3^2×29. Then x could be 3 or 29 (prime), or 9 or 87 (composite). Not sufficient.
Hence only one statement alone is sufficient.

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

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