p is a positive integer greater than 100. Is p divisible by 36?

Solution

Step 1: Analyse Question Stem

• p > 100
• p is a positive integer.
• We need to find if p is divisible by 36.

o Or, if \(p = 2^2*3^2*k\) where k is a positive integer.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• According to this statement, p has total 8 positive factors.
• Now, total positive factors of \(36 = 2^2*3^2 = (2+1)(2+1) = 9\)

o Had p been in the form of \(p =2^2*3^2*k\), number of factors p would have been more than or equal to 9.
• Since, total number of positive factors of p < total number of positive factors of 36

o Therefore, p is not divisible by 36.

• p is divisible by 75 but not divisible by 100.

o It means p is in the form of, \(p = 5^2*3*n\), but not in the form of, \(p = 5^2*2^2*m\)
o Where n and m are positive integer.
• Therefore, p cannot be divisible by 36 as \(2^2\) in 36 won’t cancel out.