NBT Mathematics: Number Sense and Calculations 4

Question 1

A town's population decreased by 15% in 2024, then increased by 15% in 2025. Compared to its population at the start of 2024, what is the net percentage change at the end of 2025?

Accepted Answer

A decrease of 2.25%

Answer

Multiplying the two factors: 0.85 × 1.15 = 0.9775. This means the population is 97.75% of the original — a net decrease of 2.25%. Percentage changes applied successively multiply, they do not add or cancel. A 15% decrease followed by a 15% increase always yields a net loss because the increase is applied to a smaller base.

Question 2

Three siblings share an inheritance. The eldest receives 2/5 of the total, the middle child receives 1/3, and the youngest receives the remainder. If the youngest's share is R26,000, what is the total inheritance?

Accepted Answer

R97,500

Answer

The eldest and middle child together receive 2/5 + 1/3 = 6/15 + 5/15 = 11/15 of the total. The youngest therefore receives 1 − 11/15 = 4/15. Setting 4/15 × T = R26,000 gives T = R26,000 × 15/4 = R97,500.

Question 3

Evaluate: (6.4 × 10⁵) ÷ (3.2 × 10⁻²)

Accepted Answer

2 × 10⁷

Answer

Divide the coefficients: 6.4 ÷ 3.2 = 2. Subtract the exponents: 5 − (−2) = 5 + 2 = 7. The result is 2 × 10⁷. The common error is treating 5 − (−2) as 5 − 2 = 3, yielding the wrong power of 10.

Question 4

A positive number added to its reciprocal equals 10/3. What is the number? (Both solutions are valid.)

Accepted Answer

3 or 1/3

Answer

Setting x + 1/x = 10/3 and multiplying both sides by 3x gives 3x² − 10x + 3 = 0. Factoring: (3x − 1)(x − 3) = 0, so x = 3 or x = 1/3. Note that if x = 3, its reciprocal is 1/3, and 3 + 1/3 = 10/3 ✓. Both values satisfy the equation and are reciprocals of each other.

Question 5

The sequence 2, 6, 12, 20, 30, 42, … follows the rule that the nth term equals n(n + 1). What is the 10th term of this sequence?

Accepted Answer

110

Answer

Applying the rule with n = 10: 10 × (10 + 1) = 10 × 11 = 110. Verification: the differences between consecutive terms are 4, 6, 8, 10, 12, …, increasing by 2 each time (second differences are constant at 2), confirming a quadratic formula. The 10th term is 110.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT Mathematics: Number Sense and Calculations 4