PI - Cognitive Assessment Numerical Word Problems 2 — Questions and Answers

Question 1: A store offers a 20% discount on a $150 item. An additional 10% loyalty discount is applied to the reduced price. What is the final price?

$105.00
$108.00 (Correct answer)
$112.50
$120.00

Correct answer: $108.00

First discount: $150 × 0.80 = $120. Second discount: $120 × 0.90 = $108.00.

Successive percentage discounts must be applied one at a time to the resulting price, not added together. First: $150 × (1 - 0.20) = $150 × 0.80 = $120. Then: $120 × (1 - 0.10) = $120 × 0.90 = $108. Note that a 20% + 10% discount is NOT the same as a 30% discount ($150 × 0.70 = $105). The combined discount is actually 28% ($150 - $108 = $42, and $42/$150 = 0.28).

Question 2: A train travels 240 miles in 4 hours. A car leaves at the same time and travels at 45 mph. After 4 hours, how much farther has the train traveled than the car?

40 miles
50 miles
60 miles (Correct answer)
80 miles

Correct answer: 60 miles

Train speed: 240÷4 = 60 mph. Car distance: 45×4 = 180 miles. Difference: 240-180 = 60 miles.

Train: distance = 240 miles (given), speed = 240÷4 = 60 mph. Car: speed = 45 mph, distance = 45×4 = 180 miles. The difference in distance traveled: 240 - 180 = 60 miles. The train has traveled 60 miles farther than the car after 4 hours.

Question 3: If 8 workers can complete a project in 15 days, how many days would it take 12 workers to complete the same project, assuming equal productivity?

8 days
10 days (Correct answer)
12 days
20 days

Correct answer: 10 days

Total work = 8 × 15 = 120 worker-days. With 12 workers: 120 ÷ 12 = 10 days.

This is an inverse proportion problem. Total work required = workers × days = 8 × 15 = 120 worker-days. This total doesn't change regardless of how many workers you assign. With 12 workers: days = 120 ÷ 12 = 10 days. More workers means proportionally fewer days for the same total work.

Question 4: A rectangle has a perimeter of 36 cm. If the length is twice the width, what is the area?

54 cm²
72 cm² (Correct answer)
81 cm²
108 cm²

Correct answer: 72 cm²

Let width = w. Length = 2w. Perimeter: 2(2w + w) = 36, so 6w = 36, w = 6. Length = 12. Area = 12 × 6 = 72 cm².

Let width = w and length = 2w. Perimeter = 2(length + width) = 2(2w + w) = 2(3w) = 6w. Setting 6w = 36 gives w = 6 cm. Therefore length = 2 × 6 = 12 cm. Area = length × width = 12 × 6 = 72 cm². Always verify: perimeter check = 2(12 + 6) = 2(18) = 36 cm ✓.

Question 5: A company's revenue increased from $400,000 to $520,000. What was the percentage increase?

20%
25%
30% (Correct answer)
35%

Correct answer: 30%

Increase = $520,000 - $400,000 = $120,000. Percentage = ($120,000 / $400,000) × 100 = 30%.

Percentage increase = (New - Original) / Original × 100. Increase = $520,000 - $400,000 = $120,000. Percentage = ($120,000 / $400,000) × 100 = 0.30 × 100 = 30%. A common mistake is dividing by the new value instead of the original, which would give approximately 23% — always divide by the starting value.

Question 6: A tank is filled by Pipe A in 6 hours and by Pipe B in 4 hours. If both pipes are open simultaneously, how long does it take to fill the tank?

2 hours
2.4 hours (Correct answer)
3 hours
5 hours

Correct answer: 2.4 hours

Rate A = 1/6 per hour, Rate B = 1/4 per hour. Combined: 1/6 + 1/4 = 5/12. Time = 12/5 = 2.4 hours.

Work rate problems require adding individual rates. Pipe A fills 1/6 of the tank per hour. Pipe B fills 1/4 per hour. Combined rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 of the tank per hour. Time to fill = 1 ÷ (5/12) = 12/5 = 2.4 hours (or 2 hours and 24 minutes). This is always less than the faster pipe alone.

PI - Cognitive Assessment Numerical Word Problems 2

A store offers a 20% discount on a $150 item.
An additional 10% loyalty discount is applied to the reduced price.
What is the final price?