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1
Is the sequence 15, 7, 10, 0, ... arithmetic, geometric, or neither?
Algebra - Functions and Sequences (including word…
Medium
ExplanationThere is no constant common difference or common ratio between terms, so this sequence is neither arithmetic nor geometric.
Algebra GMAT GRE Mathematics Practice Set
2
A shop offers successive discounts of 25% and 2% on an item marked at Rs. 4200. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationFinal price = 4200 × (1 − 25/100) × (1 − 2/100) = Rs. 3087.
Arithmetic GMAT GRE Mathematics Practice Set
3
A sequence is defined by a₁ = -17 and aₙ = aₙ₋₁ − 8 for n > 1. What is a11?
Algebra - Functions and Sequences (including word…
Medium
ExplanationEach term adds -8 to the previous one, so a11 = a₁ + (11−1)(-8) = -97.
Algebra GMAT GRE Mathematics Practice Set
4
What is the value of 8x^2 − 5x when x = -3?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanation8(-3)^2 + (-5)(-3) + (0) = (72) + (15) + (0) = 87.
Algebra GMAT GRE Mathematics Practice Set
5
In an arithmetic sequence, the 4th term is -51 and the 10th term is -93. What is the 17th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (-93 − (-51))/(10−4) = -7. Then the 17th term = -51 + (17−4)(-7) = -142.
Algebra GMAT GRE Mathematics Practice Set
6
How many digits does 5^32 have?
Arithmetic - Number Properties
Medium
ExplanationThe number of digits of 5^32 is floor(32 × log10(5)) + 1 = 23.
Arithmetic GMAT GRE Mathematics Practice Set
7
What is 4/5 × 1/3?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationMultiply numerators and denominators: (4×1)/(5×3) = 4/15.
Arithmetic GMAT GRE Mathematics Practice Set
8
Express 5,300 in scientific notation.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 5,300 = 5.3 × 10^3.
Antonyms GMAT GRE Mathematics Practice Set
9
What is the ratio of 340 to 20, expressed in lowest terms?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation340:20 reduces by dividing both terms by their GCD (20), giving 17:1.
Arithmetic GMAT GRE Mathematics Practice Set
10
How many multiples of 3 are there between 165 and 234, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe multiples of 3 in this range run from 165 to 234, giving 24 multiples.
Arithmetic GMAT GRE Mathematics Practice Set
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11
What is the compound interest on Rs. 12500 at 16% per annum, compounded annually, for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = P(1 + R/100)^2 = 12500 × (1 + 16/100)^2 = Rs. 16820, so CI = Rs. 16820 − Rs. 12500 = Rs. 4320.
Arithmetic GMAT GRE Mathematics Practice Set
12
Does the parabola y = -2x^2 + 7x − 19 open upward or downward?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSince a = -2 is negative, the parabola opens downward.
Algebra GMAT GRE Mathematics Practice Set
13
For the function f(x) = 1/(x − (-68)), which value of x must be excluded from the domain?
Algebra - Functions and Sequences (including word…
Medium
ExplanationThe denominator x − (-68) cannot equal 0, so x = -68 must be excluded from the domain.
Algebra GMAT GRE Mathematics Practice Set
14
Which equation has roots 8 and -10?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSum of roots = -2, product of roots = -80, giving x^2 − (-2)x + (-80) = 0, i.e. x^2 + 2x − 80 = 0.
Algebra GMAT GRE Mathematics Practice Set
15
A shopkeeper marks up an item costing Rs. 83 by 44%. What is the markup amount (in Rs.)?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationMarkup amount = CP × 44/100 = 83 × 0.4400 = Rs. 36.52.
Arithmetic GMAT GRE Mathematics Practice Set
16
The digits of 5636 sum to 20. Based on this, is 5636 divisible by 3?
Arithmetic - Number Properties
Medium
ExplanationA number is divisible by 3 if and only if its digit sum is divisible by 3. Here the digit sum is 20, which is not divisible by 3.
Arithmetic GMAT GRE Mathematics Practice Set
17
What is (3.3 × 10^4) ÷ (2.6 × 10^3) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationDivide the mantissas (3.3 ÷ 2.6 ≈ 1.27) and subtract the exponents (4 − 3 = 1), adjusting the mantissa as needed: 1.27 × 10^1.
Antonyms GMAT GRE Mathematics Practice Set
18
What is the vertex of the parabola y = 3x^2 + 22?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe vertex x-coordinate is −b/(2a) = −(0)/(2×3) = 0. Substituting gives y = 22, so the vertex is (0, 22).
Algebra GMAT GRE Mathematics Practice Set
19
What is the vertex of the parabola y = -2x^2 + 32x + 3?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe vertex x-coordinate is −b/(2a) = −(32)/(2×-2) = 8. Substituting gives y = 131, so the vertex is (8, 131).
Algebra GMAT GRE Mathematics Practice Set
20
What is (6/11)^3 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(6/11)^3 = 6^3/11^3 = 216/1331.
Antonyms GMAT GRE Mathematics Practice Set
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21
Solve the system for x: -6x + 2y = 50, -2x + 4y = 40
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system by elimination or substitution gives x = -6 (and y = 7).
Algebra GMAT GRE Mathematics Practice Set
22
Solve for x: -11x + 19 < -212
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by the negative coefficient -11 reverses the inequality sign, giving x > 21.
Algebra GMAT GRE Mathematics Practice Set
23
Simplify √90 to its simplest radical form.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation90 = 3^2 × 10, so √90 = 3√10.
Antonyms GMAT GRE Mathematics Practice Set
24
Simplify: 5^3 × 5^3
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 5^3 × 5^3 = 5^(3+3) = 5^6.
Antonyms GMAT GRE Mathematics Practice Set
25
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
26
What is 3/10 of 250?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation3/10 of 250 = (3 × 250) / 10 = 75.
Arithmetic GMAT GRE Mathematics Practice Set
27
What is (3.3 × 10^8) ÷ (1.7 × 10^4) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationDivide the mantissas (3.3 ÷ 1.7 ≈ 1.94) and subtract the exponents (8 − 4 = 4), adjusting the mantissa as needed: 1.94 × 10^4.
Antonyms GMAT GRE Mathematics Practice Set
28
What are the solutions to x^2 − 196 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanationx^2 − 196 = (x + 14)(x - 14), so x = -14 or x = 14.
Algebra GMAT GRE Mathematics Practice Set
29
The ratio of boys to girls in a class is 13:11. If there are 416 boys, how many girls are there?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationSince boys:girls = 13:11 and there are 416 boys, each 'part' = 416/13 = 32, so girls = 11 × 32 = 352.
Arithmetic GMAT GRE Mathematics Practice Set
30
What is the smallest number that must be subtracted from 1016 so that the result is exactly divisible by 20?
Arithmetic - Number Properties
Medium
Explanation1016 divided by 20 leaves remainder 16, so subtracting 16 makes it exactly divisible by 20.
Arithmetic GMAT GRE Mathematics Practice Set
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31
What is the difference between the compound interest and simple interest on Rs. 3750 at 4% 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 = 3750 × (4/100)^2 = Rs. 6.
Arithmetic GMAT GRE Mathematics Practice Set
32
Simplify: 5^6 × 5^3
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 5^6 × 5^3 = 5^(6+3) = 5^9.
Antonyms GMAT GRE Mathematics Practice Set
33
Is 449 a prime number?
Arithmetic - Number Properties
Medium
Explanation449 is not divisible by any integer other than 1 and itself, so it is prime.
Arithmetic GMAT GRE Mathematics Practice Set
34
What is (5.3 × 10^5) × (1.3 × 10^5) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (5.3 × 1.3 = 6.89) and add the exponents (5 + 5 = 10), adjusting so the mantissa stays between 1 and 10: 6.89 × 10^10.
Antonyms GMAT GRE Mathematics Practice Set
35
What is 13/6 − 3/2?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 13/6 − 3/2 = 2/3.
Arithmetic GMAT GRE Mathematics Practice Set
36
In an arithmetic sequence, the 14th term is -176 and the 15th term is -189. What is the common difference?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-189 − (-176))/(15−14) = -13.
Algebra GMAT GRE Mathematics Practice Set
37
Is x^2 − 18x + 83 a perfect square trinomial?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationA trinomial x^2 + bx + c is a perfect square exactly when c = (b/2)^2. Here (b/2)^2 = (-9)^2 = 81, which does not match c = 83, so it is not a perfect square trinomial.
Algebra GMAT GRE Mathematics Practice Set
38
Among 75, 39, 77, and 36, which is closest to 0 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationThe number closest to 0 has the smallest absolute value. |36| = 36, which is the smallest among the options.
Arithmetic GMAT GRE Mathematics Practice Set
39
After a discount of 20%, an item sells for Rs. 1028. What was the marked price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationMarked price = SP / (1 − 20/100) = 1028 / 0.8000 = Rs. 1285.
Arithmetic GMAT GRE Mathematics Practice Set
40
What is |20| − |-35|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|20| − |-35| = 20 − 35 = -15. (Note this is generally different from |20 − (-35)|.)
Arithmetic GMAT GRE Mathematics Practice Set
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41
Does the fraction 6/479 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
ExplanationIn lowest terms, 6/479 = 6/479. 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
42
What is the solution set of |x − 21| < 29?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 21| < 29 means x is within 29 of 21, giving -8 < x < 50.
Arithmetic GMAT GRE Mathematics Practice Set
43
In an arithmetic sequence, the 12th term is 1 and the 22nd term is -39. What is the common difference?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-39 − 1)/(22−12) = -4.
Algebra GMAT GRE Mathematics Practice Set
44
What are the solutions to x^2 + 13x + 40 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanationx^2 + 13x + 40 = (x + 8)(x + 5), so x = -8 or x = -5.
Algebra GMAT GRE Mathematics Practice Set
45
What is the midpoint between 55 and 27 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationThe midpoint of 55 and 27 is (55 + 27) / 2 = 82/2 = 41.
Arithmetic GMAT GRE Mathematics Practice Set
46
If f(x) = 3x + 16, what is f(12) + f(-10)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(12) = 52 and f(-10) = -14, so f(12) + f(-10) = 38.
Algebra GMAT GRE Mathematics Practice Set
47
How many integers satisfy |x + 10| < 7?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 10| < 7 means -17 < x < -3. The integers strictly between -17 and -3 number 13.
Arithmetic GMAT GRE Mathematics Practice Set
48
What is the value of 9x^2 + 19x − 13 when x = -5?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanation9(-5)^2 + (19)(-5) + (-13) = (225) + (-95) + (-13) = 117.
Algebra GMAT GRE Mathematics Practice Set
49
A geometric sequence has first term -15 and second term 60. What is the common ratio?
Algebra - Functions and Sequences (including word…
Medium
ExplanationCommon ratio = a₂/a₁ = 60/-15 = -4.
Algebra GMAT GRE Mathematics Practice Set
50
What is the simple interest on Rs. 8137 at 6% per annum for 5 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (8137 × 6 × 5) / 100 = Rs. 2441.1.
Arithmetic GMAT GRE Mathematics Practice Set
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51
What is |12 × -6|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|12 × -6| = |12| × |-6| = 12 × 6 = 72.
Arithmetic GMAT GRE Mathematics Practice Set
52
What is the compound interest on Rs. 10625 at 4% per annum, compounded annually, for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = P(1 + R/100)^2 = 10625 × (1 + 4/100)^2 = Rs. 11492, so CI = Rs. 11492 − Rs. 10625 = Rs. 867.
Arithmetic GMAT GRE Mathematics Practice Set
53
How many distinct prime factors does 348 have?
Arithmetic - Number Properties
Medium
ExplanationThe prime factorization of 348 is 2^2 × 3^1 × 29^1, which includes 3 distinct prime(s).
Arithmetic GMAT GRE Mathematics Practice Set
54
What are the solutions to |x − 32| = 1?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 32| = 1 means x is 1 away from 32, so x = 32 + 1 = 33 or x = 32 − 1 = 31.
Arithmetic GMAT GRE Mathematics Practice Set
55
Solve for x: -9x + 1 < -188
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by the negative coefficient -9 reverses the inequality sign, giving x > 21.
Algebra GMAT GRE Mathematics Practice Set
56
What is (6.0 × 10^2) × (1.5 × 10^6) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (6.0 × 1.5 = 9.0) and add the exponents (2 + 6 = 8), adjusting so the mantissa stays between 1 and 10: 9.0 × 10^8.
Antonyms GMAT GRE Mathematics Practice Set
57
If f(x) = -x^2 − 14x + 12, what is f(-4)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(-4) = -1(-4)^2 + (-14)(-4) + (12) = 52.
Algebra GMAT GRE Mathematics Practice Set
58
A shop offers successive discounts of 45% and 60% on an item marked at Rs. 1650. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationFinal price = 1650 × (1 − 45/100) × (1 − 60/100) = Rs. 363.
Arithmetic GMAT GRE Mathematics Practice Set
59
If f(x) = 11x − 7, what is f(-3)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(-3) = (11)(-3) − 7 = -40.
Algebra GMAT GRE Mathematics Practice Set
60
Which is farther from 10 on the number line: -78 or 77?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationDistance from 10: |-78 − 10| = 88, and |77 − 10| = 67. So -78 is farther.
Arithmetic GMAT GRE Mathematics Practice Set
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61
What are the solutions to x^2 − 3x − 10 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanationx^2 − 3x − 10 = (x + 2)(x - 5), so x = -2 or x = 5.
Algebra GMAT GRE Mathematics Practice Set
62
If f(x) = 6x − 2 and g(x) = -2x − 6, what is g(f(-4))?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(-4) = -26, so g(f(-4)) = g(-26) = -2(-26) − 6 = 46.
Algebra GMAT GRE Mathematics Practice Set
63
An arithmetic sequence has first term -15 and common difference -5. What is the 34th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationaₙ = a₁ + (n−1)d = -15 + (34−1)(-5) = -180.
Algebra GMAT GRE Mathematics Practice Set
64
What is the product of the roots of 4x^2 + 3x − 28 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationBy Vieta's formulas, the product of the roots equals c/a = -28/4 = -7.
Algebra GMAT GRE Mathematics Practice Set
65
How many trailing zeros are in 49! (49 factorial)?
Arithmetic - Number Properties
Medium
ExplanationTrailing zeros come from factors of 5 in 49!. Counting multiples of 5, 25, 125, ... gives 10 trailing zeros.
Arithmetic GMAT GRE Mathematics Practice Set
66
Solve the system for y: 7x + 7y = 0, -6x − 3y = 57
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system by elimination or substitution gives y = 19 (and x = -19).
Algebra GMAT GRE Mathematics Practice Set
67
How many integers satisfy |x + 15| < 12?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 15| < 12 means -27 < x < -3. The integers strictly between -27 and -3 number 23.
Arithmetic GMAT GRE Mathematics Practice Set
68
If f(x) = -2x + 21, what is f(14) − f(-3)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(14) = -7 and f(-3) = 27, so f(14) − f(-3) = -34.
Algebra GMAT GRE Mathematics Practice Set
69
What is 16^(2/2) equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation16^(2/2) means take the 2-th root of 16 (which is 4), then raise it to the 2 power: 4^2 = 16.
Antonyms GMAT GRE Mathematics Practice Set
70
What is the sum of all positive divisors of 108 (including 108 itself)?
Arithmetic - Number Properties
Medium
ExplanationThe divisors of 108 are [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108], which sum to 280.
Arithmetic GMAT GRE Mathematics Practice Set
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71
What is 1/2 + 8/5?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 1/2 + 8/5 = 21/10.
Arithmetic GMAT GRE Mathematics Practice Set
72
How many multiples of 7 are there between 39 and 129, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe multiples of 7 in this range run from 42 to 126, giving 13 multiples.
Arithmetic GMAT GRE Mathematics Practice Set
73
Simplify: 2^15 ÷ 2^11
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 2^15 ÷ 2^11 = 2^(15-11) = 2^4.
Antonyms GMAT GRE Mathematics Practice Set
74
A value is first increased by 6% and then increased by 22%. What is the overall net percentage change?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationStarting with 100: after the first change it becomes 106.00, and after the second change it becomes 129.32 — a net change of +29.32% from the original 100.
Arithmetic GMAT GRE Mathematics Practice Set
75
Solve for x: -13x − 24 < -258
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by the negative coefficient -13 reverses the inequality sign, giving x > 18.
Algebra GMAT GRE Mathematics Practice Set
76
What is the axis of symmetry of the parabola y = -x^2 − 8x − 28?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe axis of symmetry is x = −b/(2a) = −(-8)/(2×-1) = -4.
Algebra GMAT GRE Mathematics Practice Set
77
If an integer n leaves a remainder of 13 when divided by 15, what is the remainder when n^2 is divided by 15?
Arithmetic - Number Properties
Medium
Explanationn = 15q + 13 for some integer q, so n^2 ≡ 13^2 = 169 (mod 15), which leaves remainder 4 when divided by 15.
Arithmetic GMAT GRE Mathematics Practice Set
78
What is 215^0 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
Antonyms GMAT GRE Mathematics Practice Set
79
At 15% simple interest per annum, a sum earns Rs. 6549 in 5 years. What is the principal?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationPrincipal = (SI × 100) / (R × T) = (6549 × 100) / (15 × 5) = Rs. 8732.
Arithmetic GMAT GRE Mathematics Practice Set
80
A shopkeeper marks up an item costing Rs. 208 by 48%. What is the markup amount (in Rs.)?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationMarkup amount = CP × 48/100 = 208 × 0.4800 = Rs. 99.84.
Arithmetic GMAT GRE Mathematics Practice Set
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81
Factor: x^2 − 19x + 70
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanationx^2 − 19x + 70 factors as the product of (x − r) for each root: (x - 14)(x - 5).
Algebra GMAT GRE Mathematics Practice Set
82
An interest rate rises from 17% to 24%. By how many percentage points did it increase?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationA percentage-point increase is a simple subtraction: 24% − 17% = 7 percentage points.
Arithmetic GMAT GRE Mathematics Practice Set
83
How many distinct prime factors does 266 have?
Arithmetic - Number Properties
Medium
ExplanationThe prime factorization of 266 is 2^1 × 7^1 × 19^1, which includes 3 distinct prime(s).
Arithmetic GMAT GRE Mathematics Practice Set
84
A shop offers successive discounts of 8% and 5% on an item marked at Rs. 1000. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationFinal price = 1000 × (1 − 8/100) × (1 − 5/100) = Rs. 874.
Arithmetic GMAT GRE Mathematics Practice Set
85
A sum of Rs. 1620 earns Rs. 1296 in simple interest over 4 years. What is the annual interest rate?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationRate = (SI × 100) / (P × T) = (1296 × 100) / (1620 × 4) = 20%.
Arithmetic GMAT GRE Mathematics Practice Set
86
If -8x − 4y = -28 and x − 2y = 16, what is x + y?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system gives x = 6 and y = -5, so x + y = 1.
Algebra GMAT GRE Mathematics Practice Set
87
What is the sum to infinity of a geometric sequence with first term -16 and common ratio -2/3?
Algebra - Functions and Sequences (including word…
Medium
ExplanationSum to infinity = a₁/(1 − r) = -16/(1 − (-2)/3) = -48/5.
Algebra GMAT GRE Mathematics Practice Set
88
If f(x) = -5x^2 + x − 19, what is f(-2)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(-2) = -5(-2)^2 + (1)(-2) + (-19) = -41.
Algebra GMAT GRE Mathematics Practice Set
89
Solve the system for x: -6x − 9y = 123, 6x − 8y = -72
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system by elimination or substitution gives x = -16 (and y = -3).
Algebra GMAT GRE Mathematics Practice Set
90
Express 42,000,000 in scientific notation.
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMove the decimal point so only one nonzero digit remains before it: 42,000,000 = 4.2 × 10^7.
Antonyms GMAT GRE Mathematics Practice Set
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91
What is the length of the solution interval for |x − 10| < 23?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 10| < 23 describes the interval (-13, 33), which has length 33 − (-13) = 46.
Arithmetic GMAT GRE Mathematics Practice Set
92
Solve for x: 9/14 = 216/x
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationCross-multiplying: 9 × x = 14 × 216, so x = 3024/9 = 336.
Arithmetic GMAT GRE Mathematics Practice Set
93
What is 5/3 × 8/5?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationMultiply numerators and denominators: (5×8)/(3×5) = 8/3.
Arithmetic GMAT GRE Mathematics Practice Set
94
Which equation has roots -3 and 13?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSum of roots = 10, product of roots = -39, giving x^2 − (10)x + (-39) = 0, i.e. x^2 − 10x − 39 = 0.
Algebra GMAT GRE Mathematics Practice Set
95
Which is greater: 6^6 or 6^5?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation6^6 = 46656 and 6^5 = 7776, so 6^6 is greater.
Antonyms GMAT GRE Mathematics Practice Set
96
Rs. 18516 is invested at 7.5% simple interest per annum for 3 years. What is the total amount after 3 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = Principal + Interest = 18516 + 4166.1 = Rs. 22682.1.
Arithmetic GMAT GRE Mathematics Practice Set
97
A population of 1248 grows by 50% each year. What will the population be after 5 years?
Algebra - Functions and Sequences (including word…
Medium
ExplanationPopulation after 5 years = 1248 × (1 + 50/100)^5 = 9477.
Algebra GMAT GRE Mathematics Practice Set
98
If A:B = 5:11 and B:C = 5:8, what is A:B:C?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationScale both ratios so B matches: A:B = 25:55 and B:C = 55:88, giving A:B:C = 25:55:88.
Arithmetic GMAT GRE Mathematics Practice Set
99
What is the nature of the roots of x^2 + 5x + 6 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe discriminant is b^2 − 4ac = (5)^2 − 4(1)(6) = 1, which is positive, so the equation has two distinct real roots.
Algebra GMAT GRE Mathematics Practice Set
100
What is the average (arithmetic mean) of the 9 consecutive integers from 8 to 16?
Arithmetic - Number Properties
Medium
ExplanationFor consecutive integers, the average equals the middle value, which is 12.
Arithmetic GMAT GRE Mathematics Practice Set
0
0
100
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