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1
Solve for x: x/9 + 7 = 20
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanationx/9 = 20 − (7) = 13, so x = 9 × 13 = 117.
Algebra GMAT GRE Mathematics Practice Set
2
Which is greater: |-40| or |-65|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|-40| = 40 and |-65| = 65, so |-65| is greater.
Arithmetic GMAT GRE Mathematics Practice Set
3
What is (7/8)^3 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(7/8)^3 = 7^3/8^3 = 343/512.
Antonyms GMAT GRE Mathematics Practice Set
4
What is the product of the roots of 3x^2 + 25x + 42 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationBy Vieta's formulas, the product of the roots equals c/a = 42/3 = 14.
Algebra GMAT GRE Mathematics Practice Set
5
What is the reciprocal of 13/15?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationThe reciprocal of 13/15 is 15/13, since (13/15) × (15/13) = 1.
Arithmetic GMAT GRE Mathematics Practice Set
6
What is the simple interest on Rs. 10395 at 2% per annum for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (10395 × 2 × 2) / 100 = Rs. 415.8.
Arithmetic GMAT GRE Mathematics Practice Set
7
Simplify: (2^3)^2
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen raising a power to another power, multiply the exponents: (2^3)^2 = 2^(3×2) = 2^6.
Antonyms GMAT GRE Mathematics Practice Set
8
What is the value of (3 × 2)^3?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(3 × 2)^3 = 3^3 × 2^3 = 27 × 8 = 216.
Antonyms GMAT GRE Mathematics Practice Set
9
Which of the following numbers lies between 27 and 53?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation46 lies strictly between 27 and 53, while the other options fall outside that range.
Arithmetic GMAT GRE Mathematics Practice Set
10
Solve for x: -x − 1 > 2
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by the negative coefficient -1 reverses the inequality sign, giving x < -3.
Algebra GMAT GRE Mathematics Practice Set
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11
What is the axis of symmetry of the parabola y = 6x^2 + 72x − 20?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe axis of symmetry is x = −b/(2a) = −(72)/(2×6) = -6.
Algebra GMAT GRE Mathematics Practice Set
12
What is |10| − |12|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|10| − |12| = 10 − 12 = -2. (Note this is generally different from |10 − 12|.)
Arithmetic GMAT GRE Mathematics Practice Set
13
What are the solutions to 6x^2 + 12x − 288 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationUsing the quadratic formula with a=6, b=12, c=-288, the discriminant is a perfect square, giving x = -8 or x = 6.
Algebra GMAT GRE Mathematics Practice Set
14
For a = -1 and b = -13, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 14 and |a| + |b| = 14. Since a and b have the same sign, the two are equal.
Arithmetic GMAT GRE Mathematics Practice Set
15
What is the value of (7 × 3)^2?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(7 × 3)^2 = 7^2 × 3^2 = 49 × 9 = 441.
Antonyms GMAT GRE Mathematics Practice Set
16
What is the difference between the compound interest and simple interest on Rs. 6875 at 8% per annum for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationFor 2 years, the difference between CI and SI is always P × (R/100)^2 = 6875 × (8/100)^2 = Rs. 44.
Arithmetic GMAT GRE Mathematics Practice Set
17
√7 × √10 is equivalent to which of the following?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationBy the product rule for radicals, √a × √b = √(ab), so √7 × √10 = √70.
Antonyms GMAT GRE Mathematics Practice Set
18
What is the greatest common divisor of 168, 126, and 112?
Arithmetic - Number Properties
Medium
ExplanationThe largest integer dividing all of 168, 126, and 112 evenly is 14.
Arithmetic GMAT GRE Mathematics Practice Set
19
What is the distance between -60 and -100 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationThe distance between two points on a number line is |-60 − (-100)| = 40.
Arithmetic GMAT GRE Mathematics Practice Set
20
What is the product of the roots of 7x^2 + 16x + 7 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationBy Vieta's formulas, the product of the roots equals c/a = 7/7 = 1.
Algebra GMAT GRE Mathematics Practice Set
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21
For a = -9 and b = 27, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 18 and |a| + |b| = 36. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
Arithmetic GMAT GRE Mathematics Practice Set
22
A value is first decreased by 3% and then decreased by 20%. What is the overall net percentage change?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationStarting with 100: after the first change it becomes 97.00, and after the second change it becomes 77.60 — a net change of -22.4% from the original 100.
Arithmetic GMAT GRE Mathematics Practice Set
23
A car travels 14 km in 7 hours at a constant speed. How far will it travel in 9 hours?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationSpeed = 14 km / 7 hr = 2 km/hr. In 9 hours, distance = 2 × 9 = 18 km.
Arithmetic GMAT GRE Mathematics Practice Set
24
What is 5/6 of 342?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation5/6 of 342 = (5 × 342) / 6 = 285.
Arithmetic GMAT GRE Mathematics Practice Set
25
If f(x) = x − 13 and g(x) = f(x + 12) − 13, what is g(-7)?
Algebra - Functions and Sequences (including word…
Medium
Explanationg(-7) = f(5) − 13 = -8 − 13 = -21.
Algebra GMAT GRE Mathematics Practice Set
26
What single discount is equivalent to two successive discounts of 12.5% and 30%?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationEquivalent discount = 100 − (100−12.5)(100−30)/100 = 38.75%.
Arithmetic GMAT GRE Mathematics Practice Set
27
Which is greater: |66| or |-21|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|66| = 66 and |-21| = 21, so |66| is greater.
Arithmetic GMAT GRE Mathematics Practice Set
28
If f(x) = -2x + 5, what is f(3) − f(-10)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(3) = -1 and f(-10) = 25, so f(3) − f(-10) = -26.
Algebra GMAT GRE Mathematics Practice Set
29
If f(x) = 6x − 5 and g(x) = f(x + 12) + 12, what is g(-2)?
Algebra - Functions and Sequences (including word…
Medium
Explanationg(-2) = f(10) + 12 = 55 + 12 = 67.
Algebra GMAT GRE Mathematics Practice Set
30
What is |-4 × -6|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|-4 × -6| = |-4| × |-6| = 4 × 6 = 24.
Arithmetic GMAT GRE Mathematics Practice Set
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31
A rectangle has length (x + 5) and width (x + 12). If the area of the rectangle is 120 square units, what is the value of x (where x is a positive number)?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanation(x + 5)(x + 12) = 120. Testing x = 3: (8)(15) = 120, which checks out (the other algebraic root is negative and not valid here).
Algebra GMAT GRE Mathematics Practice Set
32
Factor: 30x^2 − 30x
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe GCF of 30 and -30 (besides x) is 10, and factoring it out (along with one x) gives 10x(3x − 3).
Algebra GMAT GRE Mathematics Practice Set
33
If f(x) = 7x − 1 and g(x) = f(x + 10) − 8, what is g(9)?
Algebra - Functions and Sequences (including word…
Medium
Explanationg(9) = f(19) − 8 = 132 − 8 = 124.
Algebra GMAT GRE Mathematics Practice Set
34
What is the simple interest on Rs. 1962 at 9% per annum for 7 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (1962 × 9 × 7) / 100 = Rs. 1236.06.
Arithmetic GMAT GRE Mathematics Practice Set
35
An arithmetic sequence has first term -33 and common difference 15. What is the 15th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationaₙ = a₁ + (n−1)d = -33 + (15−1)(15) = 177.
Algebra GMAT GRE Mathematics Practice Set
36
Rs. 10170 is invested at 16% simple interest per annum for 6 years. What is the total amount after 6 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = Principal + Interest = 10170 + 9763.2 = Rs. 19933.2.
Arithmetic GMAT GRE Mathematics Practice Set
37
Complete the square: x^2 − 20x + 113 = (x + h)^2 + k. What are the values of h and k?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanationx^2 − 20x + 113 = (x − 10)^2 + 13, since -20 = 2×-10 and 113 − 100 = 13.
Algebra GMAT GRE Mathematics Practice Set
38
What are the solutions to |x − 7| = 5?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 7| = 5 means x is 5 away from 7, so x = 7 + 5 = 12 or x = 7 − 5 = 2.
Arithmetic GMAT GRE Mathematics Practice Set
39
If |x| = |-10|, what are the possible values of x?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x| = |-10| = 10 means x is 10 units from 0, so x = 10 or x = -10.
Arithmetic GMAT GRE Mathematics Practice Set
40
What is the solution set of |x − 27| < 25?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 27| < 25 means x is within 25 of 27, giving 2 < x < 52.
Arithmetic GMAT GRE Mathematics Practice Set
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41
If f(x) = -6x − 4 and g(x) = f(x − 11) − 4, what is g(9)?
Algebra - Functions and Sequences (including word…
Medium
Explanationg(9) = f(-2) − 4 = 8 − 4 = 4.
Algebra GMAT GRE Mathematics Practice Set
42
For a = 11 and b = 4, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 15 and |a| + |b| = 15. Since a and b have the same sign, the two are equal.
Arithmetic GMAT GRE Mathematics Practice Set
43
What are the solutions to |x| + 7 = 35?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x| + 7 = 35 means |x| = 28, so x = 28 or x = -28.
Arithmetic GMAT GRE Mathematics Practice Set
44
Does the parabola y = 3x^2 + 16x − 2 open upward or downward?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSince a = 3 is positive, the parabola opens upward.
Algebra GMAT GRE Mathematics Practice Set
45
Rs. 15472 is invested at 16% simple interest per annum for 5 years. What is the total amount after 5 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = Principal + Interest = 15472 + 12377.6 = Rs. 27849.6.
Arithmetic GMAT GRE Mathematics Practice Set
46
A cinema sells adult tickets for Rs. 29 and child tickets for Rs. 21. If 60 tickets were sold for a total of Rs. 1628, how many adult tickets were sold?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 60 and 29a + 21c = 1628. Solving gives a = 46, c = 14.
Algebra GMAT GRE Mathematics Practice Set
47
Simplify √423 to its simplest radical form.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation423 = 3^2 × 47, so √423 = 3√47.
Antonyms GMAT GRE Mathematics Practice Set
48
What is the sum of the first 7 terms of a geometric sequence with first term 3 and common ratio -3?
Algebra - Functions and Sequences (including word…
Medium
ExplanationSum = a₁(rⁿ − 1)/(r − 1) = 3((-3)^7 − 1)/(-3 − 1) = 1641.
Algebra GMAT GRE Mathematics Practice Set
49
What is the simple interest on Rs. 3090 at 7% per annum for 6 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (3090 × 7 × 6) / 100 = Rs. 1297.8.
Arithmetic GMAT GRE Mathematics Practice Set
50
Does the fraction 28/274 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
ExplanationIn lowest terms, 28/274 = 14/137. 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).
Arithmetic GMAT GRE Mathematics Practice Set
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51
Does the fraction 27/499 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
ExplanationIn lowest terms, 27/499 = 27/499. 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).
Arithmetic GMAT GRE Mathematics Practice Set
52
What are the solutions to |x + 21| = 29?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 21| = 29 means x is 29 away from -21, so x = -21 + 29 = 8 or x = -21 − 29 = -50.
Arithmetic GMAT GRE Mathematics Practice Set
53
How many digits does 3^50 have?
Arithmetic - Number Properties
Medium
ExplanationThe number of digits of 3^50 is floor(50 × log10(3)) + 1 = 24.
Arithmetic GMAT GRE Mathematics Practice Set
54
An interest rate rises from 35% to 45%. By how many percentage points did it increase?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationA percentage-point increase is a simple subtraction: 45% − 35% = 10 percentage points.
Arithmetic GMAT GRE Mathematics Practice Set
55
What is the smallest positive number that must be added to 5122 so that the sum is exactly divisible by 36?
Arithmetic - Number Properties
Medium
Explanation5122 divided by 36 leaves remainder 10, so adding 36 − 10 = 26 makes it exactly divisible by 36.
Arithmetic GMAT GRE Mathematics Practice Set
56
If 9:14 = 63:x, what is the value of x?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationSince 63/9 = 7, x = 14 × 7 = 98.
Arithmetic GMAT GRE Mathematics Practice Set
57
What is 1/3 + 7/15?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 1/3 + 7/15 = 4/5.
Arithmetic GMAT GRE Mathematics Practice Set
58
What is (6.2 × 10^7) ÷ (3.4 × 10^4) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationDivide the mantissas (6.2 ÷ 3.4 ≈ 1.82) and subtract the exponents (7 − 4 = 3), adjusting the mantissa as needed: 1.82 × 10^3.
Antonyms GMAT GRE Mathematics Practice Set
59
Which of the following numbers lies between -40 and -14?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation-26 lies strictly between -40 and -14, while the other options fall outside that range.
Arithmetic GMAT GRE Mathematics Practice Set
60
Simplify √364 to its simplest radical form.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation364 = 2^2 × 91, so √364 = 2√91.
Antonyms GMAT GRE Mathematics Practice Set
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61
For a = -27 and b = -16, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 43 and |a| + |b| = 43. Since a and b have the same sign, the two are equal.
Arithmetic GMAT GRE Mathematics Practice Set
62
How many solutions does |x + 19| = −15 have?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationAn absolute value can never equal a negative number, so |x + 19| = −15 has no solution.
Arithmetic GMAT GRE Mathematics Practice Set
63
How many integers satisfy |x − 17| < 13?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 17| < 13 means 4 < x < 30. The integers strictly between 4 and 30 number 25.
Arithmetic GMAT GRE Mathematics Practice Set
64
What is the value of (5 × 6)^2?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(5 × 6)^2 = 5^2 × 6^2 = 25 × 36 = 900.
Antonyms GMAT GRE Mathematics Practice Set
65
If 8 pens cost Rs. 184, how much would 27 pens cost?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationCost per pen = Rs. 184/8 = Rs. 23. So 27 pens cost 27 × Rs. 23 = Rs. 621.
Arithmetic GMAT GRE Mathematics Practice Set
66
20^2 − 11^2 is exactly divisible by which of the following?
Arithmetic - Number Properties
Medium
Explanation20^2 − 11^2 = (20 − 11)(20 + 11) = 9 × 31, so it is always divisible by 9 (and by 31).
Arithmetic GMAT GRE Mathematics Practice Set
67
Rs. 16632 is invested at 10% simple interest per annum for 1 year. What is the total amount after 1 year?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = Principal + Interest = 16632 + 1663.2 = Rs. 18295.2.
Arithmetic GMAT GRE Mathematics Practice Set
68
What is the highest power of 3 that divides 54! (54 factorial) exactly?
Arithmetic - Number Properties
Medium
ExplanationUsing Legendre's formula, the exponent of 3 in 54! is floor(54/3) + floor(54/9) + ... = 26.
Arithmetic GMAT GRE Mathematics Practice Set
69
What is |-1| − |-14|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|-1| − |-14| = 1 − 14 = -13. (Note this is generally different from |-1 − (-14)|.)
Arithmetic GMAT GRE Mathematics Practice Set
70
If f(x) = 7x − 8 and g(x) = -8x − 9, what is g(f(9))?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(9) = 55, so g(f(9)) = g(55) = -8(55) − 9 = -449.
Algebra GMAT GRE Mathematics Practice Set
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71
What is the smallest number that must be subtracted from 8527 so that the result is exactly divisible by 7?
Arithmetic - Number Properties
Medium
Explanation8527 divided by 7 leaves remainder 1, so subtracting 1 makes it exactly divisible by 7.
Arithmetic GMAT GRE Mathematics Practice Set
72
Which is greater: 6^5 or 5^6?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation6^5 = 7776 and 5^6 = 15625, so 5^6 is greater.
Antonyms GMAT GRE Mathematics Practice Set
73
What is the solution set of |x − 26| > 23?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 26| > 23 means x is farther than 23 from 26, giving x < 3 or x > 49.
Arithmetic GMAT GRE Mathematics Practice Set
74
A shopkeeper buys an item for Rs. 975 and sells it for Rs. 585. What is the loss percentage?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationLoss % = ((CP − SP) / CP) × 100 = ((975 − 585) / 975) × 100 = 40%.
Arithmetic GMAT GRE Mathematics Practice Set
75
What is (4.7 × 10^8) ÷ (2.2 × 10^5) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationDivide the mantissas (4.7 ÷ 2.2 ≈ 2.14) and subtract the exponents (8 − 5 = 3), adjusting the mantissa as needed: 2.14 × 10^3.
Antonyms GMAT GRE Mathematics Practice Set
76
What is the greatest common divisor of 130, 110, and 80?
Arithmetic - Number Properties
Medium
ExplanationThe largest integer dividing all of 130, 110, and 80 evenly is 10.
Arithmetic GMAT GRE Mathematics Practice Set
77
What is 625^(2/4) equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation625^(2/4) means take the 4-th root of 625 (which is 5), then raise it to the 2 power: 5^2 = 25.
Antonyms GMAT GRE Mathematics Practice Set
78
What is the value of -2x^2 − 2x − 11 when x = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanation-2(0)^2 + (-2)(0) + (-11) = (0) + (0) + (-11) = -11.
Algebra GMAT GRE Mathematics Practice Set
79
Which is greater: 3^2 or 3^4?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation3^2 = 9 and 3^4 = 81, so 3^4 is greater.
Antonyms GMAT GRE Mathematics Practice Set
80
Solve for x: 14/17 = 336/x
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationCross-multiplying: 14 × x = 17 × 336, so x = 5712/14 = 408.
Arithmetic GMAT GRE Mathematics Practice Set
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81
What is 3.1 × 5.7?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation3.1 × 5.7 = 17.67.
Arithmetic GMAT GRE Mathematics Practice Set
82
A sum of Rs. 217 is divided between two people in the ratio 3:4. What is the smaller share?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationTotal parts = 3 + 4 = 7. Each part = Rs. 217 / 7 = Rs. 31. So the shares are Rs. 93 and Rs. 124; the smaller share is Rs. 93.
Arithmetic GMAT GRE Mathematics Practice Set
83
What is the maximum value of y = -5x^2 − 140x − 22?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSince a = -5 is negative, the parabola opens downward and has a maximum at its vertex, where y = 958.
Algebra GMAT GRE Mathematics Practice Set
84
Which equation has roots 7 and -9?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSum of roots = -2, product of roots = -63, giving x^2 − (-2)x + (-63) = 0, i.e. x^2 + 2x − 63 = 0.
Algebra GMAT GRE Mathematics Practice Set
85
If f(x) = x + 8, what is f(-6) − f(7)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(-6) = 2 and f(7) = 15, so f(-6) − f(7) = -13.
Algebra GMAT GRE Mathematics Practice Set
86
In an arithmetic sequence, the 4th term is -31 and the 8th term is -87. What is the common difference?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-87 − (-31))/(8−4) = -14.
Algebra GMAT GRE Mathematics Practice Set
87
What is the smallest positive integer that is divisible by all of 17, 18, and 24?
Arithmetic - Number Properties
Medium
ExplanationThe smallest such number is LCM(17, 18, 24) = 1224.
Arithmetic GMAT GRE Mathematics Practice Set
88
Convert 107/10 to a mixed number.
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation107 ÷ 10 = 10 remainder 7, so 107/10 = 10 7/10.
Arithmetic GMAT GRE Mathematics Practice Set
89
What is (8.2 × 10^10) ÷ (3.7 × 10^6) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationDivide the mantissas (8.2 ÷ 3.7 ≈ 2.22) and subtract the exponents (10 − 6 = 4), adjusting the mantissa as needed: 2.22 × 10^4.
Antonyms GMAT GRE Mathematics Practice Set
90
Which is greater: 7/3 or 8/13?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation7/3 = 2.3333 and 8/13 = 0.6154, so 7/3 is greater.
Arithmetic GMAT GRE Mathematics Practice Set
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91
If an integer n leaves a remainder of 4 when divided by 11, what is the remainder when (n + 17) is divided by 11?
Arithmetic - Number Properties
Medium
Explanation(n + 17) ≡ (4 + 17) = 21 (mod 11), which leaves remainder 10 when divided by 11.
Arithmetic GMAT GRE Mathematics Practice Set
92
Solve for x: x/-7 − 21 = -9
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanationx/-7 = -9 − (-21) = 12, so x = -7 × 12 = -84.
Algebra GMAT GRE Mathematics Practice Set
93
How many multiples of 4 are there between 98 and 347, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe multiples of 4 in this range run from 100 to 344, giving 62 multiples.
Arithmetic GMAT GRE Mathematics Practice Set
94
Solve the system for x: 2x − 3y = 52, 5x + 9y = -167
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system by elimination or substitution gives x = -1 (and y = -18).
Algebra GMAT GRE Mathematics Practice Set
95
What is (3.2 × 10^5) × (6.7 × 10^3) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (3.2 × 6.7 = 21.44) and add the exponents (5 + 3 = 9), adjusting so the mantissa stays between 1 and 10: 2.14 × 10^9.
Antonyms GMAT GRE Mathematics Practice Set
96
Solve the inequality: x^2 − 32x + 220 < 0
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanationx^2 − 32x + 220 = (x - 10)(x - 22), with roots 10 and 22. Since the parabola opens upward, the expression is negative between the roots, giving 10 < x < 22.
Algebra GMAT GRE Mathematics Practice Set
97
A delivery service charges a fixed fee of Rs. 15 plus Rs. 30 per item. If a customer has a budget of Rs. 449, what is the maximum number of items they can order?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation15 + 30n ≤ 449, so n ≤ 434/30 ≈ 14.47, meaning at most 14 items.
Algebra GMAT GRE Mathematics Practice Set
98
What single discount is equivalent to two successive discounts of 12.5% and 36%?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationEquivalent discount = 100 − (100−12.5)(100−36)/100 = 44%.
Arithmetic GMAT GRE Mathematics Practice Set
99
What is the nature of the roots of x^2 + 3x + 9 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe discriminant is b^2 − 4ac = (3)^2 − 4(1)(9) = -27, which is negative, so the equation has no real roots.
Algebra GMAT GRE Mathematics Practice Set
100
What is the highest power of 2 that divides 59! (59 factorial) exactly?
Arithmetic - Number Properties
Medium
ExplanationUsing Legendre's formula, the exponent of 2 in 59! is floor(59/2) + floor(59/4) + ... = 54.
Arithmetic GMAT GRE Mathematics Practice Set
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