Prelims 2026 · CSAT / Quantitative Aptitude · Question 5
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
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.