Which of the following statements must be true?
I)The product of first 100 prime numbers is even
II)The sum of first 100 prime numbers is odd.
III)The sum of first five non-negative even numbers is divisible by both 4 and 5
Choose the correct choice from the following options
A) I only  B) II only  C) I and II only  D) I and III only  E) I, II and III
First look at some Odd &amp; Even Rules:-   Multiplication   E x E = E   O x O = O   E x O = E = O x O   Addition   E + E = E   E + O = O = O + E   O + O = E   Now coming to the statements:-   I. The product of first 100 prime numbers is even   First 100 prime nos. includes 2 which is the ONLY even no. Hence, any no. multiplied by even no will give an Even No.   II. The sum of first 100 prime numbers is odd   We can figure this out through Cyclicity Rule. Ignore the First TWO Prime Nos. and let us start with 5, which is Odd.   O + O = E (Sum of two primes)   E + O = O (Even is carried over and added to 3rd prime)   O + O = E (Carry over and 4th prime)   E + O = O (5th prime)   O + O = E (6th prime)   Through Cyclicity, we can find out that the sum of any Even No of ODDS will always be EVEN. Since 98th no is Even, the answer will also be EVEN. Now, include the first two prime nos. i.e. 2 &amp; 3.   E + 2(E) + 3(O) = O   Hence, the statement is TRUE.   III. The sum of first five non-negative even numbers is divisible by both 4 and 5   First five non negative even nos. = 0, 2, 4, 6 and 8   Sum = 20. Divisible by both 4 AND 5   Answer : I, II and III
<result>E</result>
Which of the following statements must be true?
I)The product of first 100 prime numbers is even
II)The sum of first 100 prime numbers is odd.
III)The sum of first five non-negative even numbers is divisible by both 4 and 5