Estimation & Approximation — Practice Set

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

Read the answer choices before you calculate: if they are far apart, round - and always know which way your rounding pushed the answer.

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-EST-003 · Numeric Entry · 45s

Round 0.003862 to 2 significant figures. Enter your answer as a number.

Numeric entry — write the number.

Q2 · ARI-EST-006 · MCQ · 55s

A store sells 197 items per day. Which of the following is closest to the number of items it sells in 48 days?

(A) 7,880
(B) 9,000
(C) 9,500
(D) 10,000
(E) 11,820

Q3 · ARI-EST-008 · Numeric Entry · 50s

What is 4,892 divided by 49, rounded to the nearest whole number? Enter your answer as a number.

Numeric entry — write the number.

Q4 · ARI-EST-009 · MCQ · 45s

Which of the following fractions is closest in value to 0.33?

(A) 1/4
(B) 1/3
(C) 3/8
(D) 2/5
(E) 1/2

Q5 · ARI-EST-010 · Select all that apply · 60s

Which of the following values, when rounded to the nearest tenth, equal 3.5? Select all that apply.

(A) 3.45
(B) 3.449
(C) 3.54
(D) 3.55
(E) 3.501

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · ARI-EST-012 · QC · 70s

Column A: 299 x 301 Column B: 90,000

Q7 · ARI-EST-013 · MCQ · 75s

What is the value of sqrt(26), rounded to the nearest tenth?

(A) 5.0
(B) 5.1
(C) 5.2
(D) 5.3
(E) 5.5

Q8 · ARI-EST-017 · Select all that apply · 80s

Which of the following fractions are within 0.05 of 0.7? Select all that apply.

(A) 5/7
(B) 7/10
(C) 2/3
(D) 3/4
(E) 7/9

Q9 · ARI-EST-018 · QC · 75s

Column A: (0.48 x 210)/99 Column B: 1

Q10 · ARI-EST-020 · Numeric Entry · 65s

A car travels 247 miles on 9.8 gallons of fuel. What is its fuel efficiency, rounded to the nearest whole number of miles per gallon? Enter your answer as a number.

Numeric entry — write the number.

Q11 · ARI-EST-022 · MCQ · 65s

Which of the following is closest to 7,823 x 0.00512?

(A) 0.4
(B) 4
(C) 40
(D) 400
(E) 4,000

Q12 · ARI-EST-024 · MCQ · 75s

One city has a population of approximately 4.83 x 10^5. A neighboring city's population is approximately 3 times as large. Which of the following is closest to the combined population of the two cities?

(A) 1.6 x 10^5
(B) 6.4 x 10^5
(C) 1.4 x 10^6
(D) 1.9 x 10^6
(E) 2.4 x 10^6

Q13 · ARI-EST-025 · Numeric Entry · 75s

What is the value of (3.14 x 48 + 3.14 x 32)/(6.28 x 25)? 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-EST-027 · MCQ · 105s

A factory produced 4,873 units in January and 5,127 units in February. If production continues to increase by the same percent each month, in which month will monthly production first exceed 6,100 units?

(A) April
(B) May
(C) June
(D) July
(E) September

Q15 · ARI-EST-028 · QC · 95s

Column A: sqrt(2) + sqrt(3) Column B: sqrt(5) + 1

Q16 · ARI-EST-029 · MCQ · 100s

A transit system carried 4,847,000 riders over 206 days. A planner wants a quick estimate of the average number of riders per day and needs an estimate that is certainly not below the true average. Which of the following calculations is guaranteed, without any further computation, to give a result greater than 4,847,000/206?

(A) 4,800,000/210
(B) 4,800,000/200
(C) 4,900,000/210
(D) 4,900,000/200
(E) 4,840,000/206

Q17 · ARI-EST-030 · Numeric Entry · 95s

What is the greatest integer n for which sqrt(n) < 41.5? Enter your answer as a number.

Numeric entry — write the number.

Q18 · ARI-EST-031 · QC · 95s

Column A: The sum of all integers from 1 to 100, divided by 99 Column B: 51

Q19 · ARI-EST-032 · Select all that apply · 90s

The length of a rectangle is greater than 19 and less than 20. Its width is greater than 11 and less than 12. Which of the following could be the area of the rectangle? Select all that apply.

(A) 205
(B) 210
(C) 228
(D) 239
(E) 245

Q20 · ARI-EST-034 · Numeric Entry · 105s

What is the value of 1,000,000/999 - 1,000,000/1,001, rounded to the nearest integer? Enter your answer as a number.

Numeric entry — write the number.

Q21 · ARI-EST-035 · QC · 100s

Column A: 1/1.98 + 1/2.02 Column B: 1

Q22 · ARI-EST-036 · MCQ · 90s

To approximate 17/51, a student rounds the numerator to 20 and the denominator to 50, obtaining 20/50 = 0.4. What is the percent error of this approximation, relative to the true value of 17/51?

(A) 7%
(B) 15%
(C) 17%
(D) 20%
(E) 120%

Q23 · ARI-EST-037 · MCQ · 100s

Which of the following is the tightest upper bound for sqrt(47) among the choices given? (An upper bound is a value greater than sqrt(47); the tightest is the smallest such value.)

(A) 6.8
(B) 6.85
(C) 6.86
(D) 6.9
(E) 7

Q24 · ARI-EST-041 · MCQ · 95s

A rectangular hall measures 39.6 feet by 24.8 feet. A contractor estimates its area by rounding each dimension up to the nearest whole foot and multiplying. By approximately what percent does the contractor's estimate exceed the true area?

(A) 0.8%
(B) 1.0%
(C) 1.8%
(D) 2.1%
(E) 3.6%

Q25 · ARI-EST-042 · MCQ · 90s

Which of the following is closest to sqrt(0.0037)?

(A) 0.0019
(B) 0.0061
(C) 0.019
(D) 0.061
(E) 0.19

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Level 4 · Extreme — 5 questions · ~10 min

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

Q26 · ARI-EST-038 · QC · 115s

Column A: 1/51 + 1/52 + 1/53 + ... + 1/100 Column B: 1/2

Q27 · ARI-EST-039 · Numeric Entry · 120s

A ball is dropped from a height of 100 meters. After each bounce it rises to exactly 2/3 of the height from which it last fell. After how many bounces does the ball first rise to a height of less than 1 meter? Enter your answer as a number.

Numeric entry — write the number.

Q28 · ARI-EST-040 · Select all that apply · 125s

A cube has a volume of 2,000 cubic centimeters. Which of the following must be true? Select all that apply.

(A) The edge length is greater than 12 cm
(B) The edge length is greater than 12.5 cm
(C) The edge length is greater than 12.8 cm
(D) The total surface area is greater than 1,000 square centimeters
(E) A cube with twice this edge length would have a volume greater than 15,000 cubic centimeters

Q29 · ARI-EST-043 · MCQ · 115s

Given that 2^10 = 1,024, which of the following is closest to 2^40?

(A) 1.0 x 10^12
(B) 1.02 x 10^12
(C) 1.1 x 10^12
(D) 4.1 x 10^12
(E) 1.0 x 10^16

Q30 · ARI-EST-044 · Select all that apply · 125s

Let Q = 2,987 x 0.0403. Which of the following values are greater than Q? Select all that apply.

(A) 3,000 x 0.04
(B) 3,000 x 0.041
(C) 2,900 x 0.042
(D) 3,000 x 0.0403
(E) 2,987 x 0.04

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