CCTST Numeracy & Quantitative Reasoning 2 — Questions and Answers
Question 1: A pie chart shows that 40% of a budget is spent on personnel. If the total budget is $2.5 million, how much is spent on personnel?
- $1,000,000 (Correct answer)
- $250,000
- $1,500,000
- $500,000
Correct answer: $1,000,000
40% of $2,500,000 = 0.40 × $2,500,000 = $1,000,000.
Question 2: A study finds the average (mean) salary increased from $50,000 to $55,000. Which conclusion is best supported?
- The typical worker earned $5,000 more (Correct answer)
- Every worker received a $5,000 raise
- The median salary also rose by 10%
- No worker earned less than $55,000
Correct answer: The typical worker earned $5,000 more
The mean increased by $5,000, meaning on average workers earned more, though individual outcomes may vary.
Question 3: If a dataset has a mean of 80 and a standard deviation of 10, what range captures approximately 68% of values (assuming normal distribution)?
- 70 to 90 (Correct answer)
- 60 to 100
- 75 to 85
- 50 to 110
Correct answer: 70 to 90
In a normal distribution, approximately 68% of data falls within one standard deviation (±10) of the mean (80).
Question 4: A line graph shows unemployment declining from 10% in January to 8% in June. Which is the most precise description?
- Unemployment fell by 2 percentage points, a 20% relative decrease (Correct answer)
- Unemployment fell by 20%
- Unemployment fell by 2%
- Unemployment fell by 2 percentage points only
Correct answer: Unemployment fell by 2 percentage points, a 20% relative decrease
The absolute drop is 2 percentage points, and the relative drop is 2/10 = 20%, making the combined statement most precise.
Question 5: A survey of 1,000 people finds 60% support a policy. The margin of error is ±3%. Which range best represents the true population support?
- 57% to 63% (Correct answer)
- 60% to 63%
- 57% to 60%
- 50% to 70%
Correct answer: 57% to 63%
Margin of error means the true value is likely within 60% ± 3%, giving a range of 57% to 63%.
Question 6: City A has a population of 100,000 with 500 crimes. City B has 500,000 people and 1,500 crimes. Which city has the higher crime rate?
- City A (Correct answer)
- City B
- They are equal
- Cannot be determined
Correct answer: City A
City A: 500/100,000 = 0.5%; City B: 1,500/500,000 = 0.3%, so City A has the higher rate.
Question 7: A table shows that Program X costs $400 per student and Program Y costs $300 per student, but Y has a 70% success rate and X has an 85% success rate. Which metric best compares cost-effectiveness?
- Cost per successful outcome (Correct answer)
- Total program cost
- Success rate alone
- Number of students enrolled
Correct answer: Cost per successful outcome
Dividing cost by the success rate gives cost per successful outcome, which accounts for both price and effectiveness.
CCTST Numeracy & Quantitative Reasoning 2
A pie chart shows that 40% of a budget is spent on personnel.
If the total budget is $2.5 million, how much is spent on personnel?