Rates & Unit Conversions — Practice Set

Bank code: ARI-RAE · Section: Arithmetic · 30 questions — Easy 5 · Medium 8 · Hard 12 · Extreme 5

A rate is a ratio with units attached: add rates, never times, and average speed is total distance over total time - always.

Every question below is live in the question bank under the ID shown — the sheet and the portal are the same questions. Attempt a level with the clock running, then check Part C.

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Part A — Questions

Quantitative Comparison — the four choices are always the same, so they are not reprinted: (A) Column A is greater · (B) Column B is greater · (C) The two quantities are equal · (D) The relationship cannot be determined from the information given

Level 1 · Easy — 5 questions · ~4 min

warm-up — these must be automatic

Q1 · ARI-RAE-004 · MCQ · 40s

1 mile is approximately 1.6 kilometres. Approximately how many kilometres are in 5 miles?

(A) 3.125 km
(B) 6.6 km
(C) 7.5 km
(D) 8 km
(E) 16 km

Q2 · ARI-RAE-011 · MCQ · 45s

Convert a speed of 72 kilometres per hour to metres per second.

(A) 0.02 m/s
(B) 1.2 m/s
(C) 20 m/s
(D) 259.2 m/s
(E) 72,000 m/s

Q3 · ARI-RAE-012 · Numeric Entry · 40s

A machine produces 120 units in 8 hours. Working at the same constant rate, how many units does it produce in 3 hours? Enter your answer as a number.

Numeric entry — write the number.

Q4 · ARI-RAE-013 · Select all that apply · 55s

Which of the following are equal to a speed of 30 metres per second? Select all that apply.

(A) 108 km/h
(B) 1,800 m/min
(C) 0.3 km/s
(D) 3,000 cm/s
(E) 1,800 km/h

Q5 · ARI-RAE-018 · MCQ · 50s

A car travels 60 km in 45 minutes. What is its average speed in kilometres per hour?

(A) 45 km/h
(B) 60 km/h
(C) 80 km/h
(D) 133.3 km/h
(E) 2,700 km/h

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · ARI-RAE-039 · MCQ · 75s

A tap leaks at a constant 5 millilitres per minute. How many litres does it waste in one week? (1 litre = 1,000 millilitres)

(A) 2.1 L
(B) 5.04 L
(C) 50.4 L
(D) 504 L
(E) 50,400 L

Q7 · ARI-RAE-042 · Numeric Entry · 65s

A runner's pace is 5 minutes per kilometre. What is her speed in kilometres per hour? Enter your answer as a number.

Numeric entry — write the number.

Q8 · ARI-RAE-071 · MCQ · 70s

A pump moves water at a constant 250 litres per minute. How many cubic metres of water does it move in 2 hours? (1 cubic metre = 1,000 litres)

(A) 0.25 m^3
(B) 15 m^3
(C) 30 m^3
(D) 500 m^3
(E) 30,000 m^3

Q9 · ARI-RAE-025 · MCQ · 70s

Working at the same constant rate, 8 workers can build a wall in 15 days. How many days would 12 workers take to build the same wall?

(A) 7.5 days
(B) 10 days
(C) 11 days
(D) 22.5 days
(E) 180 days

Q10 · ARI-RAE-022 · QC · 75s

A car travels 100 km at a constant 50 km/h, then immediately travels a further 100 km at a constant 100 km/h.

Column A: The car's average speed over the full 200 km Column B: 75 km/h

Q11 · ARI-RAE-029 · Select all that apply · 85s

A car travels at 80 km/h for part of a journey and at 60 km/h for the rest, spending equal amounts of TIME at each speed. Which of the following must be true? Select all that apply.

(A) The average speed for the journey is 70 km/h
(B) The average speed equals 2(80)(60)/(80 + 60)
(C) The car covers more distance at 80 km/h than at 60 km/h
(D) If T is the total time, the total distance is 70T
(E) The average speed is less than 70 km/h because the harmonic mean applies

Q12 · ARI-RAE-023 · MCQ · 75s

Pipe A alone fills an empty tank in 6 hours. Pipe B alone drains a full tank in 9 hours. Starting with the tank empty and both pipes open, how long does the tank take to fill?

(A) 3.6 hours
(B) 7.5 hours
(C) 15 hours
(D) 18 hours
(E) 54 hours

Q13 · ARI-RAE-028 · Numeric Entry · 65s

A tank has two inlet pipes that deliver 5 litres per minute and 3 litres per minute, and one outlet pipe that removes 2 litres per minute. The tank holds 360 litres and starts empty. With all three pipes open, how many minutes does it take to fill? Enter your answer as a number.

Numeric entry — write the number.

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Level 3 · Hard — 12 questions · ~19 min

where 162+ is won or lost

Q14 · ARI-RAE-038 · Numeric Entry · 95s

A cyclist rides from home to work at a constant 20 km/h and returns home along the same route at a constant v km/h. Her average speed for the whole round trip is 24 km/h. What is v, in km/h? Enter your answer as a number.

Numeric entry — write the number.

Q15 · ARI-RAE-046 · MCQ · 85s

A person drives from X to Y at a constant speed v and returns along the same route at a constant speed 3v, where v > 0. What fraction of the total travel time was spent driving from X to Y?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4

Q16 · ARI-RAE-048 · MCQ · 90s

A train covers the first third of its route at 40 km/h, the second third at 60 km/h, and the final third at 120 km/h. What is its average speed for the whole route?

(A) 20 km/h
(B) 60 km/h
(C) 68.6 km/h
(D) 73.3 km/h
(E) 80 km/h

Q17 · ARI-RAE-047 · Numeric Entry · 105s

A and B together finish a job in 8 days. B and C together finish the same job in 12 days. A and C together finish it in 16 days. How many days does A take working alone? Enter your answer as a number.

Numeric entry — write the number.

Q18 · ARI-RAE-073 · Numeric Entry · 105s

A faucet drips at a constant 4 drops per second, and 15 drops make 1 millilitre. How many litres of water does the faucet waste in 24 hours? (1 litre = 1,000 millilitres) Enter your answer as a number.

Numeric entry — write the number.

Q19 · ARI-RAE-072 · MCQ · 105s

A car travels 12.5 km on each litre of fuel, and fuel costs $1.60 per litre. A tune-up costing $60 would raise the car's fuel efficiency to 20 km per litre, with no change in the price of fuel. Over how many kilometres of driving after the tune-up does the fuel saved first equal the $60 cost of the tune-up?

(A) 125 km
(B) 468.75 km
(C) 750 km
(D) 1,250 km
(E) 2,000 km

Q20 · ARI-RAE-074 · Select all that apply · 105s

Five identical machines, each working 6 hours a day and each working at the same constant rate, together produce 1,200 units in 4 days. Which of the following must be true? Select all that apply.

(A) Each machine produces 10 units per hour
(B) Four of these machines, each working 5 hours a day, would produce 1,200 units in exactly 6 days
(C) Producing 1,200 units always requires 120 machine-hours of these machines
(D) Doubling the number of machines while halving the hours each machine works per day halves the number of days needed
(E) Three of these machines, each working 8 hours a day, would produce 1,200 units in 4 days

Q21 · ARI-RAE-056 · MCQ · 80s

A car's speed is increased by 20% and, on a later trip, its travel time is 20% less than before. Compared with the original trip, what is the change in the distance covered?

(A) No change
(B) 4% decrease
(C) 4% increase
(D) 20% decrease
(E) 40% increase

Q22 · ARI-RAE-057 · Select all that apply · 110s

A pool has two inlet pipes - A fills it in 6 hours and B fills it in 12 hours - and one drain C that empties a full pool in 8 hours. The pool starts exactly half full and all three are opened at once. Which of the following are true? Select all that apply.

(A) The net fill rate is 1/8 of the pool per hour
(B) The pool fills completely in 4 hours
(C) If C is kept closed, the pool fills from half full in 3 hours
(D) With all three open the pool fills in less than 6 hours
(E) Pipe B alone would fill the remaining half in 6 hours

Q23 · ARI-RAE-049 · QC · 95s

A alone can finish a certain job in a days and B alone can finish the same job in b days, where 0 < a < b.

Column A: The number of days A and B take to finish the job working together Column B: b/2

Q24 · ARI-RAE-058 · QC · 100s

Two routes between the same pair of towns have the same length D. On Route 1 a car travels the first half of the DISTANCE at 60 km/h and the second half of the distance at 40 km/h. On Route 2 a car travels the first half of its TRAVEL TIME at 60 km/h and the second half of its travel time at 40 km/h.

Column A: Average speed on Route 1 Column B: Average speed on Route 2

Q25 · ARI-RAE-062 · QC · 85s

Working alone, A and B each complete the same job at constant rates, and their rates in jobs per day are in the ratio 3 : 2.

Column A: (the number of days A takes alone) / (the number of days B takes alone) Column B: 2/3

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Level 4 · Extreme — 5 questions · ~10 min

165+ — expect to need the insight, not the grind

Q26 · ARI-RAE-064 · MCQ · 110s

Pipe A alone fills an empty tank in a hours and pipe B alone empties a full tank in b hours, where 0 < a < b. Both are opened at once on an empty tank. For a value of t small enough that the tank is not yet full, what fraction of the tank is filled after t hours?

(A) t(a + b)/(ab)
(B) t(a - b)/(ab)
(C) t(b - a)/(ab)
(D) t/(a + b)
(E) (b - a)/(ab)

Q27 · ARI-RAE-065 · QC · 120s

n workers, all working at the same constant rate, complete a job in d days. Had there been k additional workers of the same kind from the start, the same job would have been completed in d - x days. Here n, d, k and x are positive and 0 < x < d.

Column A: k Column B: nx/(d - x)

Q28 · ARI-RAE-068 · Select all that apply · 120s

Pipe A alone fills a tank in a hours and pipe B alone fills the same tank in b hours, where 0 < a <= b. With both pipes open the tank fills in T hours. Which of the following must be true? Select all that apply.

(A) T = a + b
(B) T < a
(C) a/2 <= T < a
(D) T = ab/(a + b)
(E) T = (a + b)/2

Q29 · ARI-RAE-070 · Numeric Entry · 125s

A works 50% faster than B, and both work at constant rates. Working together they complete a job in 10 days. Instead, A works alone for the first 4 days and then B finishes the remainder alone. How many days does the job take in total? Enter your answer as a number.

Numeric entry — write the number.

Q30 · ARI-RAE-075 · QC · 125s

A delivery van covers the first 50% of a route at a constant 20 km/h, the next 30% of the route at a constant 40 km/h, and the final 20% of the route at a constant 60 km/h.

Column A: The van's average speed for the whole route Column B: 30 km/h

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