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1
What is the sum of the first 15 terms of an arithmetic sequence with first term -14 and common difference 9?
Algebra - Functions and Sequences (including word…
Medium
ExplanationThe 15th term is 112. Sum = n(a₁ + aₙ)/2 = 15(-14 + 112)/2 = 735.
Algebra GMAT GRE Mathematics Practice Set
2
What is the length of the solution interval for |x + 33| < 28?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 33| < 28 describes the interval (-61, -5), which has length -5 − (-61) = 56.
Arithmetic GMAT GRE Mathematics Practice Set
3
Solve for x: 2(x + 7) = 40
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by 2: x + 7 = 20, so x = 13.
Algebra GMAT GRE Mathematics Practice Set
4
What is the nature of the roots of 2x^2 + 10x + 7 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe discriminant is b^2 − 4ac = (10)^2 − 4(2)(7) = 44, which is positive, so the equation has two distinct real roots.
Algebra GMAT GRE Mathematics Practice Set
5
If 23 workers can complete a task in 26 days, how many days would 13 workers take to complete the same task (assuming the same work rate per worker)?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationTotal work = 23 × 26 = 598 worker-days. With 13 workers, days = 598/13 = 46.
Arithmetic GMAT GRE Mathematics Practice Set
6
f(x) = -6x + 2 if x < 2, and f(x) = -3x − 10 if x ≥ 2. What is f(1)?
Algebra - Functions and Sequences (including word…
Medium
ExplanationSince 1 < 2, use f(x) = -6x + 2: f(1) = -4.
Algebra GMAT GRE Mathematics Practice Set
7
What is 170.69 + 37.96?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation170.69 + 37.96 = 208.65.
Arithmetic GMAT GRE Mathematics Practice Set
8
For a = 28 and b = -11, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 17 and |a| + |b| = 39. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
Arithmetic GMAT GRE Mathematics Practice Set
9
What is the distance between -71 and 30 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationThe distance between two points on a number line is |-71 − 30| = 101.
Arithmetic GMAT GRE Mathematics Practice Set
10
Between which two consecutive integers does √137 lie?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation11^2 = 121 and 12^2 = 144, and since 121 < 137 < 144, √137 lies between 11 and 12.
Antonyms GMAT GRE Mathematics Practice Set
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11
A geometric sequence has first term 2 and common ratio 3. What is the 7th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationaₙ = a₁ × r^(n−1) = 2 × (3)^6 = 1458.
Algebra GMAT GRE Mathematics Practice Set
12
What is |-17|?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationAbsolute value gives the distance from 0, which is always non-negative, so |-17| = 17.
Arithmetic GMAT GRE Mathematics Practice Set
13
How many trailing zeros are in 74! (74 factorial)?
Arithmetic - Number Properties
Medium
ExplanationTrailing zeros come from factors of 5 in 74!. Counting multiples of 5, 25, 125, ... gives 16 trailing zeros.
Arithmetic GMAT GRE Mathematics Practice Set
14
A delivery service charges a fixed fee of Rs. 5 plus Rs. 9 per item. If a customer has a budget of Rs. 68, what is the maximum number of items they can order?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation5 + 9n ≤ 68, so n ≤ 63/9 ≈ 7.00, meaning at most 7 items.
Algebra GMAT GRE Mathematics Practice Set
15
What is the value of 3x^2 − 19x + 21 when x = 7?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanation3(7)^2 + (-19)(7) + (21) = (147) + (-133) + (21) = 35.
Algebra GMAT GRE Mathematics Practice Set
16
What is the x-intercept of the line 6x + 4y = 18?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSet y = 0: 6x = 18, so x = 18/6 = 3.
Algebra GMAT GRE Mathematics Practice Set
17
What is the greatest common divisor of 88, 96, and 40?
Arithmetic - Number Properties
Medium
ExplanationThe largest integer dividing all of 88, 96, and 40 evenly is 8.
Arithmetic GMAT GRE Mathematics Practice Set
18
Simplify: 2^13 ÷ 2^9
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 2^13 ÷ 2^9 = 2^(13-9) = 2^4.
Antonyms GMAT GRE Mathematics Practice Set
19
What is the y-intercept of y = 8x^2 − 15x − 11?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe y-intercept occurs at x = 0: y = 8(0)^2 + (-15)(0) − 11 = -11.
Algebra GMAT GRE Mathematics Practice Set
20
A shopkeeper buys an item for Rs. 390 and sells it for Rs. 585. What is the profit percentage?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationProfit % = ((SP − CP) / CP) × 100 = ((585 − 390) / 390) × 100 = 50%.
Arithmetic GMAT GRE Mathematics Practice Set
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21
What is 2.7 × 10^8 written as an ordinary number?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation2.7 × 10^8 means moving the decimal point 8 places to the right, giving 270,000,000.
Antonyms GMAT GRE Mathematics Practice Set
22
Which equation has roots 15 and 4?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSum of roots = 19, product of roots = 60, giving x^2 − (19)x + (60) = 0, i.e. x^2 − 19x + 60 = 0.
Algebra GMAT GRE Mathematics Practice Set
23
What is the least common multiple (LCM) of 13 and 11?
Arithmetic - Number Properties
Medium
ExplanationLCM(13, 11) = 143, the smallest number divisible by both 13 and 11.
Arithmetic GMAT GRE Mathematics Practice Set
24
What single discount is equivalent to two successive discounts of 32% and 24%?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationEquivalent discount = 100 − (100−32)(100−24)/100 = 48.32%.
Arithmetic GMAT GRE Mathematics Practice Set
25
What is the y-intercept of y = -x^2 − 3x + 2?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe y-intercept occurs at x = 0: y = -1(0)^2 + (-3)(0) + 2 = 2.
Algebra GMAT GRE Mathematics Practice Set
26
What is the axis of symmetry of the parabola y = -5x^2 − 40x − 24?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe axis of symmetry is x = −b/(2a) = −(-40)/(2×-5) = -4.
Algebra GMAT GRE Mathematics Practice Set
27
What is the solution set of |x − 35| > 9?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 35| > 9 means x is farther than 9 from 35, giving x < 26 or x > 44.
Arithmetic GMAT GRE Mathematics Practice Set
28
Factor: 18x^2 + 36x
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe GCF of 18 and 36 (besides x) is 6, and factoring it out (along with one x) gives 6x(3x + 6).
Algebra GMAT GRE Mathematics Practice Set
29
A cinema sells adult tickets for Rs. 20 and child tickets for Rs. 11. If 53 tickets were sold for a total of Rs. 799, how many adult tickets were sold?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 53 and 20a + 11c = 799. Solving gives a = 24, c = 29.
Algebra GMAT GRE Mathematics Practice Set
30
What is the y-intercept of y = x^2 − 8x + 41?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe y-intercept occurs at x = 0: y = 1(0)^2 + (-8)(0) + 41 = 41.
Algebra GMAT GRE Mathematics Practice Set
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31
Which is greater: 2.8 × 10^8 or 4.3 × 10^9?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 4.3 × 10^9 is greater.
Antonyms GMAT GRE Mathematics Practice Set
32
What is the solution set of |x + 36| > 14?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 36| > 14 means x is farther than 14 from -36, giving x < -50 or x > -22.
Arithmetic GMAT GRE Mathematics Practice Set
33
A shopkeeper marks up an item costing Rs. 1931 by 48%. What is the markup amount (in Rs.)?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationMarkup amount = CP × 48/100 = 1931 × 0.4800 = Rs. 926.88.
Arithmetic GMAT GRE Mathematics Practice Set
34
Two buses leave a station together. One returns to the station every 26 minutes and the other every 38 minutes. After how many minutes will both buses be at the station together again?
Arithmetic - Number Properties
Medium
ExplanationBoth buses will be at the station together again after LCM(26, 38) = 494 minutes.
Arithmetic GMAT GRE Mathematics Practice Set
35
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
36
Which is greater: 6^6 or 6^4?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation6^6 = 46656 and 6^4 = 1296, so 6^6 is greater.
Antonyms GMAT GRE Mathematics Practice Set
37
What is 7^-3 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationA negative exponent means take the reciprocal: 7^-3 = 1/7^3 = 1/343.
Antonyms GMAT GRE Mathematics Practice Set
38
What is 82.69 + 8.44?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation82.69 + 8.44 = 91.13.
Arithmetic GMAT GRE Mathematics Practice Set
39
A line has slope -8/7 and another line has slope 7/9. Are the lines parallel, perpendicular, or neither?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationTwo lines are parallel if their slopes are equal, and perpendicular if their slopes multiply to −1. Here, -8/7 and 7/9 are neither.
Algebra GMAT GRE Mathematics Practice Set
40
What is the greatest common divisor of 16, 8, and 44?
Arithmetic - Number Properties
Medium
ExplanationThe largest integer dividing all of 16, 8, and 44 evenly is 4.
Arithmetic GMAT GRE Mathematics Practice Set
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41
Solve for x: 15x + 6 > 231
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation15x > 231 − (6) = 225, so x > 15.
Algebra GMAT GRE Mathematics Practice Set
42
What are the solutions to 2x^2 − 16x − 96 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationUsing the quadratic formula with a=2, b=-16, c=-96, the discriminant is a perfect square, giving x = -4 or x = 12.
Algebra GMAT GRE Mathematics Practice Set
43
By selling an item for Rs. 784, a trader makes a profit of 12%. What was the cost price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationCost price = SP / (1 + 12/100) = 784 / 1.1200 = Rs. 700.
Arithmetic GMAT GRE Mathematics Practice Set
44
Which is greater: 6^2 or 3^5?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation6^2 = 36 and 3^5 = 243, so 3^5 is greater.
Antonyms GMAT GRE Mathematics Practice Set
45
A value is first increased by 30% and then increased by 45%. What is the overall net percentage change?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationStarting with 100: after the first change it becomes 130.00, and after the second change it becomes 188.50 — a net change of +88.5% from the original 100.
Arithmetic GMAT GRE Mathematics Practice Set
46
What is the simple interest on Rs. 14040 at 15% per annum for 1 year?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (14040 × 15 × 1) / 100 = Rs. 2106.
Arithmetic GMAT GRE Mathematics Practice Set
47
A shop offers successive discounts of 50% and 24% on an item marked at Rs. 1000. What is the final selling price?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationFinal price = 1000 × (1 − 50/100) × (1 − 24/100) = Rs. 380.
Arithmetic GMAT GRE Mathematics Practice Set
48
What is the discriminant of 7x^2 − 12x + 24 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationDiscriminant = b^2 − 4ac = (-12)^2 − 4(7)(24) = 144 − 672 = -528.
Algebra GMAT GRE Mathematics Practice Set
49
Simplify 7/84 to its lowest terms.
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation7 and 84 share a common factor of 7; dividing both by it gives 1/12.
Arithmetic GMAT GRE Mathematics Practice Set
50
A sum of Rs. 324 is divided between two people in the ratio 1:8. What is the larger share?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationTotal parts = 1 + 8 = 9. Each part = Rs. 324 / 9 = Rs. 36. So the shares are Rs. 36 and Rs. 288; the larger share is Rs. 288.
Arithmetic GMAT GRE Mathematics Practice Set
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51
What is the reciprocal of 2/11?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationThe reciprocal of 2/11 is 11/2, since (2/11) × (11/2) = 1.
Arithmetic GMAT GRE Mathematics Practice Set
52
What is the value of -6x + 22 when x = 7?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation-6(7) + 22 = -42 + 22 = -20.
Algebra GMAT GRE Mathematics Practice Set
53
What is the compound interest on Rs. 10625 at 12% per annum, compounded annually, for 2 years?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationAmount = P(1 + R/100)^2 = 10625 × (1 + 12/100)^2 = Rs. 13328, so CI = Rs. 13328 − Rs. 10625 = Rs. 2703.
Arithmetic GMAT GRE Mathematics Practice Set
54
What is the axis of symmetry of the parabola y = 6x^2 − 168x + 1?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationThe axis of symmetry is x = −b/(2a) = −(-168)/(2×6) = 14.
Algebra GMAT GRE Mathematics Practice Set
55
What is the least common multiple (LCM) of 18 and 11?
Arithmetic - Number Properties
Medium
ExplanationLCM(18, 11) = 198, the smallest number divisible by both 18 and 11.
Arithmetic GMAT GRE Mathematics Practice Set
56
What is the minimum value of y = 4x^2 + 112x + 3?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationSince a = 4 is positive, the parabola opens upward and has a minimum at its vertex, where y = -781.
Algebra GMAT GRE Mathematics Practice Set
57
Are 45 and 72 relatively prime (i.e., is their greatest common divisor 1)?
Arithmetic - Number Properties
Medium
ExplanationGCD(45, 72) = 9, so they are not relatively prime, since they share the common factor 9.
Arithmetic GMAT GRE Mathematics Practice Set
58
What is the discriminant of 6x^2 + 23x − 3 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationDiscriminant = b^2 − 4ac = (23)^2 − 4(6)(-3) = 529 − -72 = 601.
Algebra GMAT GRE Mathematics Practice Set
59
f(x) = -2x − 15 if x < -6, and f(x) = 8x − 11 if x ≥ -6. What is f(-15)?
Algebra - Functions and Sequences (including word…
Medium
ExplanationSince -15 < -6, use f(x) = -2x − 15: f(-15) = 15.
Algebra GMAT GRE Mathematics Practice Set
60
What is (4.9 × 10^10) ÷ (2.3 × 10^6) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationDivide the mantissas (4.9 ÷ 2.3 ≈ 2.13) and subtract the exponents (10 − 6 = 4), adjusting the mantissa as needed: 2.13 × 10^4.
Antonyms GMAT GRE Mathematics Practice Set
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61
How many prime numbers are there between 12 and 30, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe primes between 12 and 30 are [13, 17, 19, 23, 29], totaling 5.
Arithmetic GMAT GRE Mathematics Practice Set
62
What is 5/11 + 1/4?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 5/11 + 1/4 = 31/44.
Arithmetic GMAT GRE Mathematics Practice Set
63
What is (3.6 × 10^5) × (9.9 × 10^5) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (3.6 × 9.9 = 35.64) and add the exponents (5 + 5 = 11), adjusting so the mantissa stays between 1 and 10: 3.56 × 10^11.
Antonyms GMAT GRE Mathematics Practice Set
64
What is the slope of the line through (17, 11) and (25, 1)?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSlope = (y2 − y1)/(x2 − x1) = (1 − 11)/(25 − 17) = -10/8 = -5/4.
Algebra GMAT GRE Mathematics Practice Set
65
What are the solutions to 6x^2 + 114x + 528 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationUsing the quadratic formula with a=6, b=114, c=528, the discriminant is a perfect square, giving x = -11 or x = -8.
Algebra GMAT GRE Mathematics Practice Set
66
In an arithmetic sequence, the 15th term is 137 and the 30th term is 317. What is the common difference?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (317 − 137)/(30−15) = 12.
Algebra GMAT GRE Mathematics Practice Set
67
What is the sum to infinity of a geometric sequence with first term 15 and common ratio 3/7?
Algebra - Functions and Sequences (including word…
Medium
ExplanationSum to infinity = a₁/(1 − r) = 15/(1 − 3/7) = 105/4.
Algebra GMAT GRE Mathematics Practice Set
68
What is the smallest positive integer that is divisible by all of 24, 22, and 9?
Arithmetic - Number Properties
Medium
ExplanationThe smallest such number is LCM(24, 22, 9) = 792.
Arithmetic GMAT GRE Mathematics Practice Set
69
For a = -28 and b = -8, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 36 and |a| + |b| = 36. Since a and b have the same sign, the two are equal.
Arithmetic GMAT GRE Mathematics Practice Set
70
If 18:7 = 36:x, what is the value of x?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationSince 36/18 = 2, x = 7 × 2 = 14.
Arithmetic GMAT GRE Mathematics Practice Set
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71
If -8x + 7y = -158 and -4x + 2y = -76, what is x + y?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system gives x = 18 and y = -2, so x + y = 16.
Algebra GMAT GRE Mathematics Practice Set
72
Does the parabola y = -2x^2 + 20x + 14 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
73
Simplify: 8^7 ÷ 8^4
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 8^7 ÷ 8^4 = 8^(7-4) = 8^3.
Antonyms GMAT GRE Mathematics Practice Set
74
What is the length of the solution interval for |x + 1| < 19?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 1| < 19 describes the interval (-20, 18), which has length 18 − (-20) = 38.
Arithmetic GMAT GRE Mathematics Practice Set
75
What is 8/3 − 3/2?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 8/3 − 3/2 = 7/6.
Arithmetic GMAT GRE Mathematics Practice Set
76
An arithmetic sequence has first term 11 and common difference -15. What is the 38th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationaₙ = a₁ + (n−1)d = 11 + (38−1)(-15) = -544.
Algebra GMAT GRE Mathematics Practice Set
77
Which is greater: 7.7 × 10^5 or 4.3 × 10^3?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationComparing exponents first: since the exponents differ, the larger exponent wins — 7.7 × 10^5 is greater.
Antonyms GMAT GRE Mathematics Practice Set
78
An interest rate rises from 13% to 30%. By how many percentage points did it increase?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationA percentage-point increase is a simple subtraction: 30% − 13% = 17 percentage points.
Arithmetic GMAT GRE Mathematics Practice Set
79
What are the solutions to 4x^2 − 16x − 308 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationUsing the quadratic formula with a=4, b=-16, c=-308, the discriminant is a perfect square, giving x = -7 or x = 11.
Algebra GMAT GRE Mathematics Practice Set
80
How many solutions does the equation 7x + 16 = 7x + 16 have?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationBoth sides are identical for every x, so every value of x works — infinitely many solutions.
Algebra GMAT GRE Mathematics Practice Set
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81
If A:B = 12:4 and B:C = 11:12, what is A:B:C?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationScale both ratios so B matches: A:B = 132:44 and B:C = 44:48, giving A:B:C = 132:44:48.
Arithmetic GMAT GRE Mathematics Practice Set
82
If f(x) = -5x + 29, what is f(5)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(5) = (-5)(5) + 29 = 4.
Algebra GMAT GRE Mathematics Practice Set
83
3031 is exactly divisible by which of the following numbers?
Arithmetic - Number Properties
Medium
Explanation3031 ÷ 7 = 433, a whole number, so 7 divides 3031 exactly.
Arithmetic GMAT GRE Mathematics Practice Set
84
What is |-32| − |-20|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|-32| − |-20| = 32 − 20 = 12. (Note this is generally different from |-32 − (-20)|.)
Arithmetic GMAT GRE Mathematics Practice Set
85
A value is first increased by 12% and then increased by 85%. What is the overall net percentage change?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationStarting with 100: after the first change it becomes 112.00, and after the second change it becomes 207.20 — a net change of +107.2% from the original 100.
Arithmetic GMAT GRE Mathematics Practice Set
86
What is the discriminant of 5x^2 − 7x − 10 = 0?
Algebra - Quadratic equations (factoring, roots, …
Medium
ExplanationDiscriminant = b^2 − 4ac = (-7)^2 − 4(5)(-10) = 49 − -200 = 249.
Algebra GMAT GRE Mathematics Practice Set
87
What is the value of 2x^2 + 19x − 6 when x = -7?
Algebra - Quadratic equations (factoring, roots, …
Medium
Explanation2(-7)^2 + (19)(-7) + (-6) = (98) + (-133) + (-6) = -41.
Algebra GMAT GRE Mathematics Practice Set
88
A shopkeeper marks up an item costing Rs. 1589 by 25%. What is the markup amount (in Rs.)?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationMarkup amount = CP × 25/100 = 1589 × 0.2500 = Rs. 397.25.
Arithmetic GMAT GRE Mathematics Practice Set
89
What is 36% of 25% of 1937?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
Explanation36% of 25% of 1937 = (36/100) × (25/100) × 1937 = 174.33.
Arithmetic GMAT GRE Mathematics Practice Set
90
What is (2.5 × 10^5) × (8.9 × 10^3) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (2.5 × 8.9 = 22.25) and add the exponents (5 + 3 = 9), adjusting so the mantissa stays between 1 and 10: 2.23 × 10^9.
Antonyms GMAT GRE Mathematics Practice Set
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91
What is |7 × 9|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|7 × 9| = |7| × |9| = 7 × 9 = 63.
Arithmetic GMAT GRE Mathematics Practice Set
92
What is 6561^(4/4) equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation6561^(4/4) means take the 4-th root of 6561 (which is 9), then raise it to the 4 power: 9^4 = 6561.
Antonyms GMAT GRE Mathematics Practice Set
93
How many prime numbers are there between 51 and 74, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe primes between 51 and 74 are [53, 59, 61, 67, 71, 73], totaling 6.
Arithmetic GMAT GRE Mathematics Practice Set
94
How many solutions does the equation 2x + -12 = 4x + 2 have?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSince the coefficients of x differ, the equation has exactly one solution.
Algebra GMAT GRE Mathematics Practice Set
95
What single discount is equivalent to two successive discounts of 40% and 45%?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationEquivalent discount = 100 − (100−40)(100−45)/100 = 67%.
Arithmetic GMAT GRE Mathematics Practice Set
96
Which is greater: |55| or |47|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|55| = 55 and |47| = 47, so |55| is greater.
Arithmetic GMAT GRE Mathematics Practice Set
97
An interest rate rises from 52% to 65%. What is the percent increase relative to the original rate?
Artithmetic - Percentages (Profit/Loss, Interest,…
Medium
ExplanationRelative percent increase = (((65 − 52) / 52) × 100 = 25%. (Note this differs from the 13-percentage-point change.)
Arithmetic GMAT GRE Mathematics Practice Set
98
What is |8| − |36|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|8| − |36| = 8 − 36 = -28. (Note this is generally different from |8 − 36|.)
Arithmetic GMAT GRE Mathematics Practice Set
99
What is 7/3 × 3/11?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationMultiply numerators and denominators: (7×3)/(3×11) = 7/11.
Arithmetic GMAT GRE Mathematics Practice Set
100
Solve for x: 4(x + 20) = 4
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by 4: x + 20 = 1, so x = -19.
Algebra GMAT GRE Mathematics Practice Set
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