Prime and Composite Numbers
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SSAT Middle Level: Quantitative › Prime and Composite Numbers
Prime numbers have exactly two factors; composite numbers have more than two. For examples, 2, 3, 5, 7 are prime; 4 and 6 are composite. How many prime numbers are there between 10 and 20?
3
4
5
6
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, listing primes like 11, 13, 17, and 19 between 10 and 20. Choice B is correct because it accurately reflects the count of primes in the range, showing understanding of prime identification. Choice A is incorrect because it demonstrates a common misconception, such as undercounting the primes in the interval. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
A prime has exactly two factors; a composite has more than two. Small examples: 2, 3, 5, 7 are prime; 4, 6 are composite. Select the prime numbers from the list: 22, 23, 24, 25.
22, 23, and 25
22 and 23
23 and 25
Only 23
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, checking that only 23 has exactly two divisors in the list. Choice A is correct because it accurately reflects the prime in the list, showing understanding of prime identification. Choice B is incorrect because it demonstrates a common misconception, such as including a composite like 22 as prime. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
Prime numbers have exactly two factors; composite numbers have more than two. Examples: 2, 3, 5, 7 are prime; 4 and 6 are composite. Select all the numbers that are prime from this list: 31, 33, 35, 37.
33 and 35
31, 35, and 37
31, 33, and 37
31 and 37
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, checking that 31 and 37 have only two divisors each. Choice A is correct because it accurately reflects the numbers’ properties, showing understanding of prime identification. Choice B is incorrect because it demonstrates a common misconception, such as identifying composites as primes. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
A prime has exactly two factors; a composite has more than two. In the small set 2–7, 2, 3, 5, 7 are prime and 4, 6 are composite. Which of the following numbers is composite?
17
19
21
23
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, recognizing that 21 has more than two divisors like 1, 3, 7, and 21. Choice C is correct because it accurately reflects the number’s properties, showing understanding of composite number identification. Choice A is incorrect because it demonstrates a common misconception, such as assuming 17 is composite when it is prime. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
Prime numbers have exactly two factors; composite numbers have more than two. Examples: 2, 3, 5, 7 are prime; 4 and 6 are composite. How many prime numbers are there between 30 and 40?
1
2
3
4
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, listing primes like 31 and 37 between 30 and 40. Choice B is correct because it accurately reflects the count of primes in the range, showing understanding of prime identification. Choice A is incorrect because it demonstrates a common misconception, such as undercounting the primes in the interval. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
Prime numbers have exactly two factors, 1 and itself; composite numbers have more than two. Using 2, 3, 4, 5, 6, and 7 as examples, decide: Is 29 prime or composite?
29 is prime because it has two factors.
29 is prime because it is not even.
29 is composite because it has four factors.
29 is composite because it is odd.
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, checking if 29 is prime because its only divisors are 1 and 29. Choice B is correct because it accurately reflects the number’s properties, showing understanding of prime number identification. Choice A is incorrect because it demonstrates a common misconception, such as assuming all odd numbers are composite, but oddness does not determine compositeness. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
A prime has exactly two factors; a composite has more than two. In 2–7, 2, 3, 5, 7 are prime while 4 and 6 are composite. Is 49 prime or composite?
49 is composite because it is near 50.
49 is composite because $7\times7=49$.
49 is prime because it is odd.
49 is prime because it ends in nine.
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, noting that 49 equals 7 times 7. Choice B is correct because it accurately reflects the number’s properties, showing understanding of composite identification. Choice A is incorrect because it demonstrates a common misconception, such as assuming all odd numbers are prime. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
A prime has exactly two factors; a composite has more than two. Small examples: 2, 3, 5, 7 are prime; 4 and 6 are composite. Identify the composite numbers in the following set: 18, 19, 20, 21.
18, 20, and 21
Only 19
19 and 21
18 and 19
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, noting that 18, 20, and 21 have more than two divisors while 19 does not. Choice A is correct because it accurately reflects the composites in the set, showing understanding of composite identification. Choice D is incorrect because it demonstrates a common misconception, such as assuming only the prime is composite. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
A prime has exactly two factors; a composite has more than two. In 2–7, 2, 3, 5, 7 are prime while 4 and 6 are composite. Is 39 prime or composite?
39 is prime because it is odd.
39 is composite because it is near 40.
39 is prime because it is not divisible by 2.
39 is composite because $3\times13=39$.
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, noting that 39 equals 3 times 13. Choice B is correct because it accurately reflects the number’s properties, showing understanding of composite identification. Choice A is incorrect because it demonstrates a common misconception, such as assuming all odd numbers are prime. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.
A prime has exactly two factors; a composite has more than two. Small examples: 2, 3, 5, 7 are prime; 4, 6 are composite. Identify the composite numbers in the following set: 14, 15, 16, 17.
Only 17
14 and 17
15 and 17
14, 15, and 16
Explanation
This question tests middle-level SSAT skills: determining whether a number is prime or composite, focusing on number properties and integers. Prime numbers have only two distinct positive divisors: 1 and the number itself, while composite numbers have more than two. In this question, students must use the definitions and identify factors, for example, noting that 14, 15, and 16 have more than two divisors while 17 does not. Choice A is correct because it accurately reflects the numbers’ properties, showing understanding of composite identification. Choice D is incorrect because it demonstrates a common misconception, such as assuming only one number is composite when there are more. To help students: Encourage practice with factorization and using divisibility rules. Teach them to verify by checking divisibility by known smaller primes (2, 3, 5, 7) and practice spotting common mistakes like assuming number patterns.