UPSC CDS I 2019 Math Paper

Concept:Check each statement for mathematical truth; identify the one that is false.Explanation:Statement A: All primes greater than $2$ are odd.The difference of two odd numbers is even.Thus the difference is divisible by $2$. True.Statement B: This is Euclid's lemma for prime numbers.If a prime $p$ divides the product $m \times n$, then $p$ must divide at least one of $m$ or $n$.Example: $p = 3$ divides $4 \times 6 = 24$, and $3$ divides $6$. True.Statement C: A number of the form $6n - 1$ is not always prime.For $n = 6$, $6(6)-1 = 35$, which is $5 \times 7$, composite.Thus the statement is false.Statement D: Consider three consecutive primes with a gap of $2$ between neighbours.The only such set is $(3,5,7)$ because any larger set would contain a multiple of $3$.Hence only one set exists. True.Only statement C is not true.Answer:Option C