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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 III only
- d)I and II only
- e)I, II and III
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements must be true?I. The product of first...
Let's analyze each statement:
**I. The product of the first 100 prime numbers is even.**
- The first 100 prime numbers include 2, which is an even number. Since multiplying any number by an even number results in an even number, the product of the first 100 prime numbers must be even.
- Therefore, Statement I is true.
- The first 100 prime numbers include 2, which is an even number. Since multiplying any number by an even number results in an even number, the product of the first 100 prime numbers must be even.
- Therefore, Statement I is true.
**II. The sum of the first 100 prime numbers is odd.**
- The first prime number is 2 (even), and the remaining 99 prime numbers are all odd. The sum of an even number and an odd number is odd. Since we have one even and 99 odd numbers, the sum will be even + odd (which is odd) + 98 odds (which makes the sum odd).
- Therefore, Statement II is true.
- The first prime number is 2 (even), and the remaining 99 prime numbers are all odd. The sum of an even number and an odd number is odd. Since we have one even and 99 odd numbers, the sum will be even + odd (which is odd) + 98 odds (which makes the sum odd).
- Therefore, Statement II is true.
**III. The sum of the first five non-negative even numbers is divisible by both 4 and 5.**
- The first five non-negative even numbers are 0, 2, 4, 6, and 8. Their sum is \(0 + 2 + 4 + 6 + 8 = 20\).
- 20 is divisible by both 4 and 5.
- Therefore, Statement III is true.
- The first five non-negative even numbers are 0, 2, 4, 6, and 8. Their sum is \(0 + 2 + 4 + 6 + 8 = 20\).
- 20 is divisible by both 4 and 5.
- Therefore, Statement III is true.
Since all three statements are true, the correct answer is:
**5. I, II, and III**
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Community Answer
Which of the following statements must be true?I. The product of first...
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.
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.
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Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer?.
Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer?.
Solutions for Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer?, a detailed solution for Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? has been provided alongside types of Which of the following statements must be true?I. The product of first 100 prime numbers is evenII. 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 5a)I onlyb)II onlyc)I and III onlyd)I and II onlye)I, II and IIICorrect answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
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