Question

Consider the following statements about set:
A. $35 \in \{x : x \text{ has exactly four positive factors}\}$}
B. $128 \in \{y : \text{the sum of all positive factors of } y \text{ is } 4y\}$}
C. $3 \notin \{x : x^4 - 5x^3 + 2x^2 - 112x + 6 = 0\}$}
D. $28 \in \{y : \text{the sum of all positive factors of } y \text{ is } 2y\}$} Choose the correct answer from the options given below:

• A. A, B, C only
• B. A, B only
• C. A, C, D only
• D. A, B, C, D

Hint:

A number is "Perfect" if the sum of its divisors equals $2n$. For $n=2^p-1(2^p-1)$, if $2^p-1$ is prime, then $n$ is perfect. For $p=3$, $n=4(7)=28$.

Answer 1

The Correct Option is C