NBT Quantitative Literacy: Charts, Tables and Graphs 4

Question 1

A company's annual budget of R5,200,000 is allocated as follows: Salaries 42%, Rent 18%, Supplies 15%, Marketing 13%, R&D 12%. The board approves increasing R&D to 18% by reducing only the Salaries allocation, keeping all other categories unchanged. What is the new rand value allocated to Salaries?

Accepted Answer

R1,872,000

Answer

R&D increases by 6 percentage points (from 12% to 18%), funded entirely from Salaries. New Salary percentage = 42% − 6% = 36%. New Salary value = 36% × R5,200,000 = R1,872,000. Option A (R2,184,000) is the original salary figure (42%). Option C (R1,560,000) incorrectly subtracts 12 points instead of 6. Option D (R2,028,000) uses 39%, halving the required reduction.

Question 2

A line graph tracks a city reservoir's water level (% of capacity) over 8 weeks: Week 1=82%, Week 2=79%, Week 3=73%, Week 4=68%, Week 5=71%, Week 6=65%, Week 7=60%, Week 8=58%. Which statement is mathematically supported by the data?

Accepted Answer

The reservoir shows a general decline with one temporary recovery; the average weekly change is approximately −3.4 percentage points

Answer

Net change = 58% − 82% = −24 percentage points over 7 intervals. Average = −24 ÷ 7 ≈ −3.43, which rounds to −3.4. The rate was NOT constant — Week 4→5 rose by 3 points (+3pp), so Option A is wrong. Option B is false because of that same Week 4→5 recovery. Option C states the average incorrectly as −3.0. The steepest drops were Week 2→3 and Week 5→6 (both −6pp), tied — not solely Week 5→6.

Question 3

A frequency density histogram shows the distribution of scores for 200 students. The class intervals and their frequency densities are: 0–20 (density=1.5), 20–50 (density=2.0), 50–60 (density=5.0), 60–80 (density=2.5), 80–100 (density=0.5). What percentage of students scored 50 or above?

Accepted Answer

55%

Answer

Frequency = density × class width. Frequencies: 0–20: 1.5×20=30; 20–50: 2.0×30=60; 50–60: 5.0×10=50; 60–80: 2.5×20=50; 80–100: 0.5×20=10. Total = 200. Students scoring 50+: 50+50+10 = 110. Percentage = 110/200 × 100 = 55%. Option B (69.6%) is the classic error of treating frequency density as frequency and computing a density ratio: (5.0+2.5+0.5)÷(1.5+2.0+5.0+2.5+0.5) ≈ 69.6%. Option C (30%) counts only the 60–80 and 80–100 bars.

Question 4

A survey on transport preferences produced the following two-way table:

| Age Group | Bus | Car | Train | Total |
|-----------|-----|-----|-------|-------|
| Under 30  |  45 |  30 |   25  |  100  |
| 30–50     |  20 |  55 |   25  |  100  |
| Over 50   |  35 |  40 |   25  |  100  |
| Total     | 100 | 125 |   75  |  300  |

A randomly selected respondent is known to be a Car user. What is the probability that this person is aged 30–50?

Accepted Answer

55/125 = 44%

Answer

This is a conditional probability question: P(aged 30–50 | Car user). We restrict our sample space to Car users only (column total = 125). Of those 125 Car users, 55 are aged 30–50. So P = 55/125 = 44%. Option A (55/300) incorrectly uses the grand total. Option B (55/100) incorrectly uses the row total for the 30–50 age group. Option D (125/300) gives the overall probability of being a Car user, which is not what was asked.

Question 5

A stacked bar chart shows the percentage breakdown of sales across three product categories (A, B, C) for three regional stores. Region 1 (total sales R800,000): A=40%, B=35%, C=25%. Region 2 (total sales R1,200,000): A=25%, B=45%, C=30%. Region 3 (total sales R600,000): A=30%, B=30%, C=40%. What were the total combined rand sales of Category B across all three regions?

Accepted Answer

R1,000,000

Answer

Calculate Category B for each region separately using its own total: Region 1: 35% × R800,000 = R280,000. Region 2: 45% × R1,200,000 = R540,000. Region 3: 30% × R600,000 = R180,000. Total = R280,000 + R540,000 + R180,000 = R1,000,000. Option B (R953,000) is the trap of averaging the B percentages (35+45+30)/3 = 36.67% and applying that to total combined sales (R2,600,000). Option A uses Category A's percentage for Region 2 by mistake. Option D applies the highest B% (45%) to all regions.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT Quantitative Literacy: Charts, Tables and Graphs 4