Set Theory
Intersection of defined sets; divisors of sum
MJMT_Full_Test_09
Grade 12
Question:
Let $A=\{n\in\mathbb{N}: n^2\leq n+15000\}$, $B=\{5k+4: k\in\mathbb{N}\}$, $C=\{3k: k\in\mathbb{N}\}$. If sum of elements of $A\cap(B-C)=N$, number of proper divisors of $N$ is
Step-by-Step Solution
Key Concept: $A$: $n\leq 122$ (solve $n^2-n-15000\leq0$). $B-C$: elements $5k+4$ NOT divisible by 3. $A\cap(B-C)$ are $n\leq122$ of form $5k+4$ and not multiples of 3.
Number of divisors of $N=18$.
Correct Answer: 3