Number Line & Ordering — Practice Set

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

Right on the number line is greater; for negatives, closer to zero wins - and whenever a variable is unpinned, test x < -1, -1 < x < 0, 0 < x < 1 and x > 1 before you 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-NLO-001 · MCQ · 40s

Which of the following lists -3, 1, -7, 0, 4 from least to greatest?

(A) -3, -7, 0, 1, 4
(B) -7, -3, 0, 1, 4
(C) 4, 1, 0, -3, -7
(D) -7, -3, 1, 0, 4
(E) 0, -3, -7, 1, 4

Q2 · ARI-NLO-005 · Numeric Entry · 40s

What is the distance between -6 and 2 on the number line? Enter your answer as a number.

Numeric entry — write the number.

Q3 · ARI-NLO-006 · MCQ · 50s

Which of the following numbers lies strictly between -1/2 and 1/4 on the number line?

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

Q4 · ARI-NLO-007 · QC · 45s

Column A: The distance from -5 to 3 on the number line Column B: The distance from 2 to -6 on the number line

Q5 · ARI-NLO-010 · Numeric Entry · 45s

Point A is at -8 on the number line and point B is at 4. What is the coordinate of the midpoint of AB? Enter your answer as a number.

Numeric entry — write the number.

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Level 2 · Medium — 8 questions · ~10 min

two or three steps, one planted trap each

Q6 · ARI-NLO-011 · MCQ · 85s

Which of the following lists -3/4, 0.7, -0.8, sqrt(0.5), -5/8 from least to greatest?

(A) -0.8, -3/4, -5/8, 0.7, sqrt(0.5)
(B) sqrt(0.5), 0.7, -5/8, -3/4, -0.8
(C) -0.8, -3/4, -5/8, sqrt(0.5), 0.7
(D) -3/4, -0.8, -5/8, 0.7, sqrt(0.5)
(E) -0.8, -5/8, -3/4, 0.7, sqrt(0.5)

Q7 · ARI-NLO-012 · QC · 65s

x is a negative number.

Column A: x Column B: x^2

Q8 · ARI-NLO-019 · MCQ · 75s

Which of the following lists all integers n such that |n - 3| < 4?

(A) 0, 1, 2, 3, 4, 5, 6
(B) -1, 0, 1, 2, 3, 4, 5, 6
(C) 0, 1, 2, 3, 4, 5
(D) -1, 0, 1, 2, 3, 4, 5, 6, 7
(E) -1, 0, 1, 2, 3, 4, 5

Q9 · ARI-NLO-020 · Select all that apply · 80s

Which of the following pairs (a, b) satisfy BOTH a < b and |a| > |b|? Select all that apply.

(A) a = -5, b = 3
(B) a = 2, b = 7
(C) a = -4, b = -1
(D) a = -3, b = -5
(E) a = -6, b = -2

Q10 · ARI-NLO-021 · MCQ · 65s

On a number line, A = -6 and B = 2. Point C is positioned so that B is the midpoint of AC. What is the coordinate of C?

(A) -14
(B) -2
(C) 8
(D) 10
(E) 12

Q11 · ARI-NLO-022 · Numeric Entry · 70s

If -3 <= x <= 5 and -2 <= y <= 4, what is the maximum possible value of x - y? Enter your answer as a number.

Numeric entry — write the number.

Q12 · ARI-NLO-023 · QC · 65s

0 < x < 1

Column A: x^2 Column B: x^3

Q13 · ARI-NLO-026 · Select all that apply · 80s

On the number line, which of the following points are strictly closer to -2 than to 4? Select all that apply.

(A) -5
(B) -1
(C) 0
(D) 1
(E) 3

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Level 3 · Hard — 12 questions · ~19 min

where 162+ is won or lost

Q14 · ARI-NLO-027 · QC · 85s

x < y < 0

Column A: x^2 - y^2 Column B: 0

Q15 · ARI-NLO-028 · MCQ · 100s

a < 0 < b and |a| < b. Which of the following must be true?

I. a + b > 0

II. ab < 0

III. a/b > -1

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Q16 · ARI-NLO-029 · Numeric Entry · 90s

On the number line A = -5 and B = 7. Point C lies on segment AB with AC : CB = 1 : 3. What is the coordinate of C? Enter your answer as a number.

Numeric entry — write the number.

Q17 · ARI-NLO-030 · MCQ · 100s

Real numbers x, y, z satisfy z < x < y < 0. Which of the following must be true?

(A) z^2 < x^2
(B) xyz > 0
(C) xy < xz
(D) y/z > 1
(E) y - x > y - z

Q18 · ARI-NLO-031 · QC · 105s

-1 < x < 0

Column A: x + 1/x Column B: -2

Q19 · ARI-NLO-032 · Select all that apply · 95s

m and n are integers with -5 <= m <= 2 and 1 <= n <= 4. Which of the following could be the value of mn? Select all that apply.

(A) -20
(B) -6
(C) 0
(D) 6
(E) 9

Q20 · ARI-NLO-033 · Numeric Entry · 85s

Points P and Q lie on a number line at coordinates p and q, with p < q. The distance from P to Q is 10 and the midpoint of PQ is at 3. What is the value of p? Enter your answer as a number.

Numeric entry — write the number.

Q21 · ARI-NLO-034 · MCQ · 95s

0 < a < b < 1. Which of the following must be greater than 1?

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

Q22 · ARI-NLO-035 · QC · 85s

a, b and c are real numbers with a < b < c.

Column A: (a + c)/2 Column B: b

Q23 · ARI-NLO-036 · Numeric Entry · 105s

On the number line, point X is three times as far from -2 as it is from 6. What is the sum of all possible coordinates of X? Enter your answer as a number.

Numeric entry — write the number.

Q24 · ARI-NLO-040 · MCQ · 100s

On the number line, point P is at sqrt(2) and point Q is at sqrt(50). The midpoint of PQ lies between which two consecutive integers?

(A) 1 and 2
(B) 3 and 4
(C) 4 and 5
(D) 5 and 6
(E) 7 and 8

Q25 · ARI-NLO-041 · Select all that apply · 110s

x is a non-zero real number with 1/x < x. Which of the following must be true? Select all that apply.

(A) x > -1
(B) x > 1
(C) x^2 > x
(D) x^2 < 1
(E) 1/x < 1

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Level 4 · Extreme — 5 questions · ~10 min

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

Q26 · ARI-NLO-037 · MCQ · 125s

a and b are real numbers with a < 0 < b. Consider the seven values a, b, a + b, a - b, ab, a/b, b/a. Which of the following must be true?

I. The seven values include both a positive and a negative value.

II. The median of the seven values is positive.

III. a/b and b/a have opposite signs.

(A) I only
(B) I and III only
(C) I and II only
(D) II and III only
(E) None of I, II and III must be true.

Q27 · ARI-NLO-038 · QC · 115s

x and y are non-zero real numbers with xy < 0 and x + y > 0.

Column A: |x + y| Column B: |x| + |y|

Q28 · ARI-NLO-039 · Select all that apply · 125s

Let f(x) = |x - 3| + |x + 2|. For which of the following values of x does f(x) attain its minimum value? Select all that apply.

(A) x = -5
(B) x = -2
(C) x = 0
(D) x = 3
(E) x = 6

Q29 · ARI-NLO-042 · QC · 125s

x is a real number satisfying x^3 < x < x^2.

Column A: x Column B: -1

Q30 · ARI-NLO-043 · Numeric Entry · 125s

-4 <= a <= 3 and -1 <= b <= 5. What is the greatest possible value of (a - b)^2 - (a + b)^2? Enter your answer as a number.

Numeric entry — write the number.

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