Can you explain the answer of this question below:
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
  • A:
    I only
  • B:
    II only
  • C:
    I and II only
  • D:
    I and III only
  • E:
    I, II and III
The answer is e.

GMAT Question

I didn't remember the sum of first 100 prime nos.

So the first 100 prime nos would start from 2,3,5,7,11....97
There are a total of 25 Prime Nos between 1-100.
2 is the only Even No. Rest all 24 are Odd.

We have a property that Odd nos added even no of Times will give an even result.
By that logic, 24 Odd Nos added 24 Times will give an Even Result, No? Hence 2 + Even Result will be an even no.

I'm sure I'm making a mistake somewhere because the sum is actually Odd. It'll be helpful if someone can point out my silly mistake in this statement.

And in Statement 3 I have considered 2+4+6+8+10 as the first five non negative even numbers. Sum is 30 i.e. not divisible by 4. :/ Didn't consider 0 coz it's neither positive nor negative.

James Hill
May 16, 2019
I. The product of first 100 prime numbers is even is true because by definition multiplying an even number by an odd equals an odd number (even * odd = even). The pattern continues indefinitely as there are only odd prime numbers after the integer two.
II. The sum of first 100 prime numbers is odd is true because the last numbers to add are odd and even. By rule this is odd.
III. The sum of first five non-negative even numbers is divisible by both 4 and 5 I was confused on because there is obviously only one even prime number, 2. So I figured the sequence they were referring to is (2, 4, 6, 8, 10), which the sum is 30. I may have misinterpreted this by ruling it false due to 4 having a remainder.

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