BASIC-MATHEMATICS-SOLVINGS2-FORM1

Objectives: BASIC-MATHEMATICS-SOLVINGS-FORM1

Even, Odd, and Prime Numbers - Questions & Answers

Even, Odd, and Prime Numbers: Questions & Competent Solutions

1. Identify whether the following numbers are even, odd, or prime: 2, 7, 12, 19, 21.

Answer:

  • 2 β†’ Even and Prime (only even prime number)
  • 7 β†’ Odd and Prime
  • 12 β†’ Even (not prime)
  • 19 β†’ Odd and Prime
  • 21 β†’ Odd (not prime; divisible by 3 and 7)

2. Find all even prime numbers between 1 and 50.

Answer:

  • Method 1: Only 2 is an even prime number (since all other even numbers are divisible by 2 and thus not prime).
  • Method 2: Check even numbers 2,4,6,...50 and test primality. Only 2 qualifies.

3. Are all odd numbers prime? Explain using examples.

Answer:

  • No, not all odd numbers are prime.
  • Example 1: 9 is odd but not prime (divisible by 3).
  • Example 2: 15 is odd but not prime (divisible by 3 and 5).
  • Only odd numbers without divisors other than 1 and itself are prime.

4. List the first 10 prime numbers and highlight which are odd and even.

Answer:

  • First 10 primes: 2(even), 3(odd), 5(odd), 7(odd), 11(odd), 13(odd), 17(odd), 19(odd), 23(odd), 29(odd)
  • Only 2 is even; the rest are odd primes.

5. Explain why 1 is neither prime nor composite.

Answer:

  • Definition of prime: has exactly two distinct positive divisors (1 and itself).
  • 1 has only one divisor (1 itself), so it fails the prime definition.
  • It’s also not composite since composite numbers have more than two divisors.

6. Show how to test if 37 is prime.

Answer:

  • Method 1: Check divisibility by prime numbers less than √37 (~6.08). Test 2, 3, 5.
  • 37 not divisible by 2 (odd), 3 (3Γ—12=36 remainder 1), 5 (ends with 7 not 0 or 5) β†’ prime.
  • Method 2: Use prime sieve or primality test algorithms.

7. Write all even numbers between 30 and 50 and identify which are prime.

Answer:

  • Even numbers: 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50
  • Prime among them: None (only 2 is even prime and it’s not in range)

8. If a number is divisible by 2 and 3, is it prime? Explain with examples.

Answer:

  • No, because it has at least 3 divisors (1, 2 or 3, and itself), thus composite.
  • Example: 6 is divisible by 2 and 3 β†’ not prime.

9. Classify these numbers as even, odd, prime, or composite: 4, 5, 6, 17, 20, 23, 25, 28.

Answer:

  • 4: even, composite
  • 5: odd, prime
  • 6: even, composite
  • 17: odd, prime
  • 20: even, composite
  • 23: odd, prime
  • 25: odd, composite
  • 28: even, composite

10. How many prime numbers are there between 10 and 30?

Answer: Primes are 11, 13, 17, 19, 23, 29 β†’ 6 primes total.

11. Given the numbers: 15, 18, 23, 27, 31. Identify all prime numbers.

Answer: 23 and 31 are prime. Others are composite.

12. Find the sum of the first 5 prime numbers.

Answer:

  • First 5 primes: 2, 3, 5, 7, 11
  • Sum = 2 + 3 + 5 + 7 + 11 = 28
  • Alternate method: Use formula for prime summation (not simple for small primes, so add directly)

13. Write the first 10 even numbers and find their average.

Answer:

  • First 10 even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
  • Sum = 2+4+6+8+10+12+14+16+18+20 = 110
  • Average = 110 Γ· 10 = 11
  • Alternate method: Average of first n even numbers = n + 1 (here 10+1=11)

14. Between 50 and 70, find all odd prime numbers.

Answer:

  • Odd primes: 53, 59, 61, 67
  • Check primality of odd numbers in this range.

15. Scenario: A bus can only stop at prime-numbered stops. List the stops from 1 to 30 where it will stop.

Answer:

  • Prime stops: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
  • Explanation: Bus skips composite stops

16. Prove that the sum of two even numbers is always even using examples.

Answer:

  • Example 1: 4 + 6 = 10 (even)
  • Example 2: 12 + 20 = 32 (even)
  • General: Even = 2k, so sum = 2k + 2m = 2(k+m) which is even

17. Write a JavaScript program snippet that highlights prime numbers between 1 and 30 on a number line.

Answer: See the interactive number line below.

18. Find three consecutive odd numbers whose sum is 51.

Answer:

  • Method 1 (Algebra): Let numbers be x, x+2, x+4
  • Sum: x + (x+2) + (x+4) = 51 β†’ 3x + 6 = 51 β†’ 3x = 45 β†’ x = 15
  • Numbers: 15, 17, 19
  • Method 2 (Trial): Check odd triples: (13,15,17)=45, (15,17,19)=51 correct

19. Is zero an even number? Explain with examples.

Answer:

  • Yes, zero is even because it is divisible by 2 with no remainder.
  • Example: 0 Γ· 2 = 0 (exact)
  • Zero fits the definition of even numbers (numbers divisible by 2).

20. Complex Problem: The product of two prime numbers is 221. Find the primes.

Answer:

  • Method 1 (Factorization): Find factors of 221
  • 221 Γ· 13 = 17 (both primes)
  • So, primes are 13 and 17.
  • Method 2 (Trial): Test primes < √221 (~14.9). 11, 13, 17 tested: 13 works perfectly.
Even, Odd, and Prime Numbers - Questions and Answers

Even, Odd, and Prime Numbers
Questions and Answers

Question 1:

List all even numbers between 1 and 20.

Answer:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Question 2:

List all odd numbers between 1 and 20.

Answer:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Question 3:

List all prime numbers between 1 and 50.

Answer:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Question 4:

Explain why 2 is the only even prime number.

Answer:

2 is the only even number that has exactly two distinct positive divisors: 1 and itself. All other even numbers are divisible by 2 and another number, so they have more than two divisors and are therefore not prime.

Question 5:

Determine whether 57 is a prime number or not.

Answer 1:

Check divisibility by 3: 5 + 7 = 12, which is divisible by 3. So 57 is not prime.

Answer 2:

Try dividing 57 by 3: 57 Γ· 3 = 19, so 57 = 3 Γ— 19. Thus, 57 is not prime.

Question 6:

Is 97 a prime number?

Answer:

Yes. 97 is only divisible by 1 and itself. It is not divisible by any prime less than √97 (primes below 10).

Question 7:

Write all prime numbers between 50 and 100.

Answer:

53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Question 8:

Using a number line, show even and odd numbers between 1 and 20.

Blue = Even, Red = Odd

Question 9:

Give three consecutive odd numbers whose sum is 99.

Answer:

Let the numbers be x, x+2, and x+4. Then, x + x+2 + x+4 = 99 β‡’ 3x + 6 = 99 β‡’ 3x = 93 β‡’ x = 31. So the numbers are 31, 33, and 35.

Question 10:

Find two even numbers whose product is 48 and their sum is 14.

Answer:

Try 6 and 8: 6 Γ— 8 = 48, and 6 + 8 = 14.

Question 11:

Which numbers between 1 and 100 are both even and divisible by 5?

Answer:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Question 12:

Can a number be both even and prime? Explain and give an example.

Answer:

Yes. 2 is the only number that is both even and prime.

Question 13:

Write a number that is neither prime nor composite.

Answer:

The number 1. It only has one positive divisor and is neither prime nor composite.

Question 14:

Write the first 10 prime numbers and determine their sum.

Answer:

2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129

Question 15:

Can the sum of two odd numbers be even? Justify with an example.

Answer:

Yes. Example: 3 + 5 = 8

Question 16:

Is zero (0) even or odd?

Answer:

Zero is even because it is divisible by 2.

Question 17 (Competency Based):

Your school is organizing students into two lines: one for even-numbered desks and one for odd-numbered desks. If each desk is numbered from 1 to 50, how many students will be in each line?

Answer:

Even desks: 2, 4, ..., 50 β†’ Total = 25 desks
Odd desks: 1, 3, ..., 49 β†’ Total = 25 desks

Question 18 (Competency Based):

You are creating a security system that only uses prime numbers as secret keys between 10 and 30. List all the possible prime keys.

Answer:

11, 13, 17, 19, 23, 29

Question 19 (Competency Based):

A street has 10 lamp posts. Every even-numbered lamp is painted blue, odd-numbered is painted green, and prime-numbered is painted red. What is the color of lamp number 7?

Answer:

Number 7 is odd and also prime. But priority goes to prime β†’ So color is Red.

Question 20 (Competency Based):

Write a program logic or plan for identifying whether a number is even, odd, or prime. Explain with a number like 19.

Answer:
  • Step 1: If number mod 2 = 0 β†’ Even
  • Step 2: Else β†’ Odd
  • Step 3: For i = 2 to √n, if n mod i = 0 β†’ Not prime
  • Step 4: If no factor found β†’ Prime

For 19: It is odd and no divisor between 2 and √19 β‡’ Prime

Reference Book: N/A

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