WorkKeys WorkKeys Applied Mathematics Level 4 and 5 2 — Questions and Answers
Question 1: A driver traveled 156 miles in 2 hours and 36 minutes. What was the average speed in miles per hour?
- 60 mph (Correct answer)
- 65 mph
- 78 mph
- 52 mph
Correct answer: 60 mph
Convert time: 2 hours 36 minutes = 2 + 36/60 = 2.6 hours. Speed = 156 ÷ 2.6 = 60 mph.
Step 1: Convert 36 minutes to hours: 36 ÷ 60 = 0.6 hours. Step 2: Total time = 2 + 0.6 = 2.6 hours. Step 3: Speed = distance ÷ time = 156 ÷ 2.6 = 60 mph. Always convert time to a single unit before calculating speed.
Question 2: A hospital orders medical supplies and receives a 12% discount on an order totaling $2,450. After the discount, a 6% sales tax is applied. What is the final amount owed?
- $2,156.00
- $2,285.36 (Correct answer)
- $2,285.04
- $2,302.12
Correct answer: $2,285.36
Discount = $2,450 × 0.12 = $294. Price after discount = $2,450 − $294 = $2,156. Tax = $2,156 × 0.06 = $129.36. Final = $2,156 + $129.36 = $2,285.36.
Step 1: Discount amount = $2,450 × 0.12 = $294.00. Step 2: Discounted price = $2,450 − $294 = $2,156.00. Step 3: Sales tax = $2,156 × 0.06 = $129.36. Step 4: Final total = $2,156 + $129.36 = $2,285.36. Note: tax is applied AFTER the discount.
Question 3: A factory uses a ratio of 3 parts oil to 8 parts coolant in a machine lubricant mix. If 33 liters of oil are used, how many liters of coolant are needed?
- 88 liters (Correct answer)
- 12.375 liters
- 72 liters
- 99 liters
Correct answer: 88 liters
Ratio = 3:8. If oil = 33 liters, then 33/3 = 11. Coolant = 11 × 8 = 88 liters.
Step 1: The ratio is 3 parts oil : 8 parts coolant. Step 2: Scale factor = 33 ÷ 3 = 11. Step 3: Coolant needed = 11 × 8 = 88 liters. Ratios are scaled by the same multiplier to maintain the correct proportion.
Question 4: A grocery store clerk stacks cans in a triangular pyramid display. The base row has 12 cans, and each row above has one fewer can. How many cans are in the entire 8-row display?
- 96 cans
- 68 cans (Correct answer)
- 72 cans
- 60 cans
Correct answer: 68 cans
Rows have 12, 11, 10, 9, 8, 7, 6, 5 cans. Sum = (12+5) × 8 ÷ 2 = 17 × 4 = 68 cans.
Step 1: Rows from bottom to top: 12, 11, 10, 9, 8, 7, 6, 5. Step 2: Sum = 12+11+10+9+8+7+6+5. Step 3: Pair the first and last: (12+5)=17, (11+6)=17, (10+7)=17, (9+8)=17. That's 4 pairs × 17 = 68 cans. The arithmetic series shortcut saves time on WorkKeys.
Question 5: A construction worker needs to build a fence around a rectangular yard that measures 45 feet by 32 feet. Fencing costs $12.75 per linear foot. What is the total material cost?
- $2,168.25 (Correct answer)
- $1,969.50
- $1,836.00
- $2,346.00
Correct answer: $2,168.25
Perimeter = 2(45 + 32) = 2(77) = 154 feet. Cost = 154 × $12.75 = $1,963.50. Closest is $1,969.50.
Step 1: Perimeter = 2 × (length + width) = 2 × (45 + 32) = 2 × 77 = 154 feet. Step 2: Total cost = 154 × $12.75 = $1,963.50. Fencing is a perimeter problem — you are buying linear footage around the outside of the rectangle.
Question 6: A quality control inspector checks a batch of 450 parts. She finds 27 defective parts. What percentage of the batch is defective?
- 4%
- 5%
- 6% (Correct answer)
- 16.67%
Correct answer: 6%
Percentage = (27 ÷ 450) × 100 = 0.06 × 100 = 6%.
Step 1: Defect rate = 27 ÷ 450 = 0.06. Step 2: Convert to percent: 0.06 × 100 = 6%. Step 3: Verify: 6% of 450 = 0.06 × 450 = 27 ✓. This percentage calculation is fundamental in quality control and manufacturing contexts.
Question 7: A plumber charges $85 for the first hour and $60 for each additional hour. He also charges for materials at cost plus 20% markup. If a job takes 3.5 hours and materials cost $140, what is the total bill?
- $337.00
- $337.50
- $378.00 (Correct answer)
- $403.00
Correct answer: $378.00
Labor: $85 + (2.5 × $60) = $85 + $150 = $235. Materials: $140 × 1.20 = $168. Total = $235 + $168 = $403.
Step 1: Labor for 3.5 hours: first hour = $85, remaining 2.5 hours = 2.5 × $60 = $150. Total labor = $85 + $150 = $235. Step 2: Material charge = $140 × 1.20 = $168. Step 3: Total bill = $235 + $168 = $403.
WorkKeys WorkKeys Applied Mathematics Level 4 and 5 2
A driver traveled 156 miles in 2 hours and 36 minutes.
What was the average speed in miles per hour?