NBT NBT Mathematics: Number Sense and Calculations 5 — Questions and Answers
Question 1: What is the greatest common factor (GCF) of 84 and 126?
- 14
- 21
- 42 (Correct answer)
- 63
Correct answer: 42
84 = 2² × 3 × 7 and 126 = 2 × 3² × 7, so GCF = 2 × 3 × 7 = 42.
Question 2: Express 4.5 × 10⁻³ in standard notation.
- 0.00045
- 0.0045 (Correct answer)
- 45000
- 4500
Correct answer: 0.0045
Moving the decimal 3 places left gives 0.0045.
Question 3: If p is a prime number greater than 2, which statement is always true?
- p is divisible by 4
- p is odd (Correct answer)
- p + 1 is prime
- p² is prime
Correct answer: p is odd
All prime numbers greater than 2 are odd, since any even number greater than 2 is divisible by 2.
Question 4: A recipe uses 2⅓ cups of flour. If you want to make 1½ times the recipe, how many cups of flour do you need?
- 3 cups
- 3¼ cups
- 3½ cups (Correct answer)
- 3⅔ cups
Correct answer: 3½ cups
2⅓ × 1½ = (7/3) × (3/2) = 21/6 = 7/2 = 3½ cups.
Question 5: Which of the following has the greatest value?
- 2/3
- 0.67 (Correct answer)
- 67%
- 0.6̄
Correct answer: 0.67
0.67 is slightly greater than 2/3 ≈ 0.6667; 67% = 0.67 = 0.67 exactly, and 0.6̄ = 2/3, so 0.67 and 67% are equal and greatest.
Question 6: The product of two consecutive even integers is 168. What is the smaller integer?
- 10
- 12 (Correct answer)
- 14
- 16
Correct answer: 12
12 × 14 = 168, so the smaller consecutive even integer is 12.
Question 7: What is 15% of 15% of 400?
- 6
- 8
- 9 (Correct answer)
- 12
Correct answer: 9
15% of 400 = 60, then 15% of 60 = 9.
NBT NBT Mathematics: Number Sense and Calculations 5
What is the greatest common factor (GCF) of 84 and 126?