PI Cognitive Numerical Assessment 2 — Questions and Answers

Question 1: A company's quarterly profits were: Q1: $45,000, Q2: $52,000, Q3: $48,000, Q4: $55,000. What was the average quarterly profit?

$48,000
$49,000
$50,000 (Correct answer)
$51,000

Correct answer: $50,000

Average = (45,000 + 52,000 + 48,000 + 55,000) / 4 = 200,000 / 4 = $50,000.

The arithmetic mean is the sum of all values divided by the count. Sum = $45,000 + $52,000 + $48,000 + $55,000 = $200,000. Count = 4 quarters. Average = $200,000 ÷ 4 = $50,000. On the PI assessment, quick mental math helps: the values cluster around $50K, so the average should be near $50K. Deviations: -5K, +2K, -2K, +5K sum to zero, confirming $50K.

Question 2: If a product costs $80 and is marked up by 25%, what is the selling price?

$95
$100 (Correct answer)
$105
$110

Correct answer: $100

Markup = 25% of $80 = $20. Selling price = $80 + $20 = $100.

Markup pricing adds a percentage of the cost to the cost itself. Cost = $80. Markup = 25% × $80 = 0.25 × $80 = $20. Selling price = cost + markup = $80 + $20 = $100. Alternatively: selling price = cost × (1 + markup rate) = $80 × 1.25 = $100.

Question 3: A data set contains the values: 12, 15, 18, 15, 20, 15, 22. What is the mode?

12
15 (Correct answer)
18
20

Correct answer: 15

The mode is the most frequently occurring value. 15 appears 3 times, more than any other value.

The mode is the value that appears most frequently in a data set. Frequency count: 12 appears 1 time, 15 appears 3 times, 18 appears 1 time, 20 appears 1 time, 22 appears 1 time. Since 15 has the highest frequency (3 occurrences), the mode is 15. This is a basic statistical measure commonly tested on the PI Cognitive Assessment.

Question 4: A car depreciates 15% per year. If it was purchased for $30,000, what is its value after 2 years?

$21,000
$21,675 (Correct answer)
$22,500
$25,500

Correct answer: $21,675

After year 1: $30,000 × 0.85 = $25,500. After year 2: $25,500 × 0.85 = $21,675.

Depreciation is compound, meaning each year's reduction is based on the current value, not the original. Year 1: $30,000 × (1 - 0.15) = $30,000 × 0.85 = $25,500. Year 2: $25,500 × 0.85 = $21,675. Note: simple depreciation would give $30,000 - (2 × $4,500) = $21,000, but compound depreciation gives $21,675. The compound method is standard.

Question 5: If 5 machines produce 200 widgets in 8 hours, how many widgets will 8 machines produce in 5 hours?

150
200 (Correct answer)
250
320

Correct answer: 200

Rate per machine per hour = 200/(5×8) = 5 widgets. 8 machines × 5 hours × 5 widgets = 200.

Find the unit rate: 5 machines × 8 hours = 40 machine-hours produce 200 widgets. Rate = 200/40 = 5 widgets per machine-hour. With 8 machines for 5 hours: 8 × 5 = 40 machine-hours. Production = 40 × 5 = 200 widgets. Interestingly, the answer equals the original production because the machine-hours are the same (40 in both cases).

Question 6: The ratio of boys to girls in a class is 3:5. If there are 40 students total, how many more girls are there than boys?

5
10 (Correct answer)
15
20

Correct answer: 10

Total parts = 3+5 = 8. Boys = (3/8)×40 = 15. Girls = (5/8)×40 = 25. Difference = 25-15 = 10.

In a 3:5 ratio with 40 total students: total parts = 3 + 5 = 8. Each part = 40 ÷ 8 = 5 students. Boys = 3 × 5 = 15. Girls = 5 × 5 = 25. Difference = 25 - 15 = 10 more girls than boys. Verification: 15 + 25 = 40 ✓ and 15:25 = 3:5 ✓.

PI Cognitive Numerical Assessment 2

A company's quarterly profits were: Q1: $45,000, Q2: $52,000, Q3: $48,000, Q4: $55,000.
What was the average quarterly profit?