Question 1 of 32: A hummingbird beats its wings 900 times in 15 seconds. A bumblebee beats its wings 130 times in 10 seconds. Which beats its wings faster per second?
A hummingbird beats its wings 900 times in 15 seconds. A bumblebee beats its wings 130 times in 10 seconds. Which beats its wings faster per second? — Hummingbird (60/sec vs 13/sec).Hummingbird: 900 ÷ 15 = 60 beats/sec. Bumblebee: 130 ÷ 10 = 13 beats/sec. Hummingbird is much faster.
A pump fills a tank at a rate of 2.5 liters per minute. A second pump fills at 90 liters per hour. Which pump is faster? — They are equal.First pump: 2.5 L/min = 150 L/hr. Second pump: 90 L/hr. First pump is faster. Wait — 150 ≠ 90 so they are NOT equal. The first pump is faster.
If the ratio of length to width of a rectangle is 5:2 and the perimeter is 56 cm, what is the length? — 20 cm.Let length = 5k, width = 2k. Perimeter = 2(5k + 2k) = 14k = 56. So k = 4. Length = 5 × 4 = 20 cm.
Mixture A has a juice-to-water ratio of 2:5. Mixture B has a ratio of 3:7. Which mixture is "juicier" (higher proportion of juice)? — Mixture B (3/10 > 2/7).Mixture A: 2/(2+5) = 2/7 ≈ 0.286. Mixture B: 3/(3+7) = 3/10 = 0.30. Mixture B has a higher juice proportion.
A car travels the first 100 miles at 50 mph and the next 100 miles at 100 mph. What is the average speed for the entire 200-mile trip? — 66.7 mph.Time for first 100 miles = 100/50 = 2 hrs. Time for next 100 miles = 100/100 = 1 hr. Total time = 3 hrs. Average speed = 200/3 ≈ 66.7 mph.
The ratio of cats to dogs at a shelter is 4:3. If 8 more cats arrive, the ratio becomes 2:1. How many dogs are there? — 12.Let cats = 4x, dogs = 3x. After 8 more cats: (4x+8)/(3x) = 2/1 → 4x+8 = 6x → 2x = 8 → x = 4. Dogs = 3(4) = 12.
A faucet leaks at 3 drops per second. Each drop is approximately 0.05 mL. How many liters leak in one day? — 12.96 liters.3 drops/sec × 0.05 mL/drop = 0.15 mL/sec. Per day: 0.15 × 60 × 60 × 24 = 0.15 × 86400 = 12,960 mL = 12.96 liters.
After a 20% discount, a pair of shoes costs $64. What was the original price? — $80.Sale price = original × (1 − 0.20) = original × 0.80. Original = 64 ÷ 0.80 = $80.
A product is marked up 25%, then the new price is discounted 25%. Is the final price the same as the original? — No, it is less than original.Let original = $100. After 25% markup: $125. After 25% off $125: 125 × 0.75 = $93.75. The final price is less than the original.
Sales tax is 8%. A customer pays $54 total including tax. What was the price before tax? — $50.Pre-tax price × 1.08 = 54. Pre-tax = 54 ÷ 1.08 = $50.
A bank account earns 5% simple interest per year. How much interest is earned on $400 over 3 years? — $60.Simple interest = Principal × Rate × Time = 400 × 0.05 × 3 = $60.
A school increased enrollment by 15% this year to 460 students. How many students were enrolled last year? — 400.Last year × 1.15 = 460. Last year = 460 ÷ 1.15 = 400 students.
Item A is $45 after a 10% discount. Item B is $48 after a 20% discount. Which item had the higher original price? — Item B ($60 vs $50).Item A: 45 ÷ 0.90 = $50. Item B: 48 ÷ 0.80 = $60. Item B had the higher original price.
A car gets 30 miles per gallon. Convert to feet per ounce. (1 mile = 5,280 ft; 1 gallon = 128 oz) — 1,237.5 ft/oz.30 mi/gal × 5280 ft/mi ÷ 128 oz/gal = 158,400 / 128 = 1,237.5 ft/oz.
Light travels at 3 × 10^8 m/s. How many kilometers per hour is that? (1 km = 1000 m) — 1.08 × 10^9 km/h.3×10^8 m/s × (1 km/1000 m) × (3600 s/hr) = 3×10^8 × 3.6 = 1.08×10^9 km/h.
A snail moves 2.5 cm per second. Convert to meters per hour. — 90 m/hr.2.5 cm/s × (1 m / 100 cm) × (3600 s / 1 hr) = 2.5 × 36 = 90 m/hr.
A pool holds 12,000 liters. It fills at 25 liters per minute. How many hours to fill it? (1 hour = 60 minutes) — 8 hours.12,000 ÷ 25 = 480 minutes. 480 ÷ 60 = 8 hours.
A plane flies 900 km/h. How many meters does it travel in 1 second? — 250 m/s.900 km/h × 1000 m/km ÷ 3600 s/hr = 900,000/3600 = 250 m/s.
Convert 45 miles per hour to feet per second. (1 mile = 5,280 ft, 1 hour = 3,600 s) — 66 ft/s.45 mi/hr × 5280 ft/mi ÷ 3600 s/hr = 237,600/3600 = 66 ft/s.
How many seconds are in 1 week? (1 week = 7 days, 1 day = 24 hours, 1 hour = 60 min, 1 min = 60 sec) — 604,800 seconds.7 × 24 × 60 × 60 = 7 × 86,400 = 604,800 seconds.
In a class, the ratio of students who prefer math to those who prefer reading is 5:3. If 16 students prefer reading, how many prefer math? — 26.7 ≈ 27.Scale factor = 16 ÷ 3. Math = 5 × (16/3) ≈ 26.7. Since this must be a whole number, the ratio likely means: scale factor is not a whole number here. Let scale = 16/3; Math = 80/3 ≈ 26.7 — the question assumes it can be non-whole. Actually: 5 × (16/3) = 26.67, so approximately 27. But this is an odd ratio situation. Best whole-number answer: 26.7.
Three ingredients A, B, C are in ratio 2:3:5. If 40 units of C are used, how many total units of all three ingredients are used? — 80.Scale factor = 40 ÷ 5 = 8. A = 2×8 = 16, B = 3×8 = 24, C = 5×8 = 40. Total = 16 + 24 + 40 = 80.
A recipe uses flour, sugar, and butter in ratio 4:2:1. You have 14 cups of flour. How many cups of butter do you need? — 3.5.Scale factor = 14 ÷ 4 = 3.5. Butter = 1 × 3.5 = 3.5 cups.
In a tape diagram for ratio 3:4, each segment = 6.5. What is the difference between the two quantities? — 6.5.Larger = 4 × 6.5 = 26. Smaller = 3 × 6.5 = 19.5. Difference = 26 − 19.5 = 6.5.
Gold alloy is 14 parts gold to 10 parts other metals. If a ring contains 7g of gold, what is the total mass of the ring? — 12 g.Scale factor = 7 ÷ 14 = 0.5. Other metals = 10 × 0.5 = 5g. Total = 7 + 5 = 12 g.
A map ratio is 1:50,000. Two cities are 6 cm apart on the map. What is the real distance in km? (100 cm = 1 m, 1000 m = 1 km) — 3 km.Real distance = 6 × 50,000 = 300,000 cm = 3,000 m = 3 km.
An item costs $p. After a 30% increase then a 30% decrease, is the final price equal to $p? — No, it is less than $p.After 30% increase: p × 1.30. After 30% decrease: p × 1.30 × 0.70 = p × 0.91. The final price is 91% of original — less than p.
A company's profits decreased by 40% in year 1, then increased by 40% in year 2. By what percent did profits change overall from start to end? — −16%.Let profits = 100. After −40%: 60. After +40% of 60: 60 × 1.40 = 84. Overall change: (84−100)/100 = −16%.
A lab measures a liquid's boiling point as 99.1°C. The true value is 100°C. What is the percent error? — 0.9%.|99.1 − 100| / 100 × 100% = 0.9/100 × 100% = 0.9%.
A car's value depreciates 15% per year. After 2 years, by what overall percent has it decreased from the original price? — 27.75%.After year 1: × 0.85. After year 2: × 0.85 × 0.85 = × 0.7225. Decrease = (1 − 0.7225) × 100% = 27.75%.
A student says: "My grade went from 60 to 80, so I improved by 20 percentage points." The teacher says it was a 33% increase. Who is right? — Both are correct — they measure different things.The student describes an absolute change (20 points). The teacher uses percent change: (80−60)/60 × 100% = 33%. Both are valid but measure different things.
A temperature drops from −5°C to −10°C. What is the percent change? — −100%.(−10 − (−5)) / |−5| × 100% = (−5) / 5 × 100% = −100%. The temperature dropped by 100% relative to the original (absolute) value.