Explanationx^2 − 2x − 99 = (x + 9)(x - 11), with roots -9 and 11. Since the parabola opens upward, the expression is negative between the roots, giving -9 < x < 11.
AlgebraGMATGREMathematicsPractice Set
8
What is the length of the solution interval for |x + 34| < 7?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 34| < 7 describes the interval (-41, -27), which has length -27 − (-41) = 14.
ArithmeticGMATGREMathematicsPractice Set
9
Are 32 and 36 relatively prime (i.e., is their greatest common divisor 1)?
Arithmetic - Number Properties
Medium
ExplanationGCD(32, 36) = 4, so they are not relatively prime, since they share the common factor 4.
ArithmeticGMATGREMathematicsPractice Set
10
What is the slope of the line through (0, -17) and (3, -27)?
Algebra - Linear equations (1 and 2 variables) an…
ExplanationA trinomial x^2 + bx + c is a perfect square exactly when c = (b/2)^2. Here (b/2)^2 = (-9)^2 = 81, which matches c, so it is a perfect square trinomial.
Explanation|x − 2| < 18 means -16 < x < 20. The integers strictly between -16 and 20 number 35.
ArithmeticGMATGREMathematicsPractice Set
58
Does the fraction 6/394 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
ExplanationIn lowest terms, 6/394 = 3/197. A fraction terminates only if its denominator (in lowest terms) has no prime factors other than 2 and 5. Here that is not the case, so it repeats (does not terminate).
ArithmeticGMATGREMathematicsPractice Set
59
Are 14 and 69 relatively prime (i.e., is their greatest common divisor 1)?
Arithmetic - Number Properties
Medium
ExplanationGCD(14, 69) = 1, so they are relatively prime.
ArithmeticGMATGREMathematicsPractice Set
60
Simplify: 8^9 ÷ 8^4
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 8^9 ÷ 8^4 = 8^(9-4) = 8^5.
AntonymsGMATGREMathematicsPractice Set
— Sponsored —
61
What is the highest power of 3 that divides 55! (55 factorial) exactly?
Arithmetic - Number Properties
Medium
ExplanationUsing Legendre's formula, the exponent of 3 in 55! is floor(55/3) + floor(55/9) + ... = 26.
ArithmeticGMATGREMathematicsPractice Set
62
In an arithmetic sequence, the 3rd term is 31 and the 18th term is 16. What is the 25th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (16 − 31)/(18−3) = -1. Then the 25th term = 31 + (25−3)(-1) = 9.
Explanation75% of 35% of 1992 = (75/100) × (35/100) × 1992 = 522.9.
ArithmeticGMATGREMathematicsPractice Set
64
A cinema sells adult tickets for Rs. 10 and child tickets for Rs. 6. If 52 tickets were sold for a total of Rs. 364, how many adult tickets were sold?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 52 and 10a + 6c = 364. Solving gives a = 13, c = 39.
AlgebraGMATGREMathematicsPractice Set
65
A sum of Rs. 121 is divided between two people in the ratio 3:8. What is the smaller share?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationTotal parts = 3 + 8 = 11. Each part = Rs. 121 / 11 = Rs. 11. So the shares are Rs. 33 and Rs. 88; the smaller share is Rs. 33.
ArithmeticGMATGREMathematicsPractice Set
66
What is (6.9 × 10^4) × (6.2 × 10^6) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (6.9 × 6.2 = 42.78) and add the exponents (4 + 6 = 11), adjusting so the mantissa stays between 1 and 10: 4.28 × 10^11.
AntonymsGMATGREMathematicsPractice Set
67
What is 12/5 × 9/2?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationMultiply numerators and denominators: (12×9)/(5×2) = 54/5.
ArithmeticGMATGREMathematicsPractice Set
68
An employee's salary starts at Rs. 72610 and increases by Rs. 2200 each year. What will the salary be after 14 years?
Algebra - Functions and Sequences (including word…
Medium
ExplanationSalary after 14 years = 72610 + 14 × 2200 = Rs. 103410.
AlgebraGMATGREMathematicsPractice Set
69
Which is greater: 4^5 or 6^3?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation4^5 = 1024 and 6^3 = 216, so 4^5 is greater.
AntonymsGMATGREMathematicsPractice Set
70
Which is greater: 6/13 or 14/15?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation6/13 = 0.4615 and 14/15 = 0.9333, so 14/15 is greater.
ArithmeticGMATGREMathematicsPractice Set
— Sponsored —
71
Is 34442 divisible by 11?
Arithmetic - Number Properties
Medium
ExplanationUsing the alternating digit-sum rule for 11, the result is 1, which is not a multiple of 11, so the answer is No.
ArithmeticGMATGREMathematicsPractice Set
72
A line has slope -3/5 and passes through (-25, -27). What is its y-intercept?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationUsing y = mx + b: -27 = (-3/5)(-25) + b, so b = -27 − 15 = -42.
AlgebraGMATGREMathematicsPractice Set
73
What is 17/20 expressed as a decimal?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation17 ÷ 20 = 0.85.
ArithmeticGMATGREMathematicsPractice Set
74
What is the least common multiple (LCM) of 12 and 22?
Arithmetic - Number Properties
Medium
ExplanationLCM(12, 22) = 132, the smallest number divisible by both 12 and 22.
ArithmeticGMATGREMathematicsPractice Set
75
If f(x) = -3x − 9 and g(x) = 6x + 7, what is g(f(-3))?
Algebra - Functions and Sequences (including word…
ExplanationStarting with 100: after the first change it becomes 82.00, and after the second change it becomes 111.52 — a net change of +11.52% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
80
What are the solutions to |9x + 54| = 45?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation9x + 54 = 45 or 9x + 54 = −45, which solve to x = -1 and x = -11.
ArithmeticGMATGREMathematicsPractice Set
— Sponsored —
81
A trader buys an item for Rs. 1440 and wants to make a profit of 25%. At what price should the item be sold?
ExplanationA trinomial x^2 + bx + c is a perfect square exactly when c = (b/2)^2. Here (b/2)^2 = (2)^2 = 4, which does not match c = 11, so it is not a perfect square trinomial.
Explanationx^2 − 29x + 138 = (x - 6)(x - 23), with roots 6 and 23. Since the parabola opens upward, the expression is negative between the roots, giving 6 < x < 23.
AlgebraGMATGREMathematicsPractice Set
86
Solve for x: x/10 − 24 = -38
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanationx/10 = -38 − (-24) = -14, so x = 10 × -14 = -140.
AlgebraGMATGREMathematicsPractice Set
87
Solve the system for x: 4x + 7y = 5, 9x − 3y = 105
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system by elimination or substitution gives x = 10 (and y = -5).
AlgebraGMATGREMathematicsPractice Set
88
What are the solutions to |x − 13| = 15?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 13| = 15 means x is 15 away from 13, so x = 13 + 15 = 28 or x = 13 − 15 = -2.
ArithmeticGMATGREMathematicsPractice Set
89
If f(x) = 12x − 18, what is f⁻¹(6)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf⁻¹(6) is the x-value such that f(x) = 6: 12x − 18 = 6, so x = 2.
AlgebraGMATGREMathematicsPractice Set
90
What is the simple interest on Rs. 9853 at 13% per annum for 6 years?