ExplanationStarting with 100: after the first change it becomes 64.00, and after the second change it becomes 65.92 — a net change of -34.08% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
2
Which is greater: 7.3 × 10^3 or 9.4 × 10^3?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationComparing exponents first: the exponents are equal, so compare the mantissas — 9.4 × 10^3 is greater.
AntonymsGMATGREMathematicsPractice Set
3
A population of 625 grows by 20% each year. What will the population be after 3 years?
Algebra - Functions and Sequences (including word…
Medium
ExplanationPopulation after 3 years = 625 × (1 + 20/100)^3 = 1080.
AlgebraGMATGREMathematicsPractice Set
4
What is 12/7 × 5/8?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationMultiply numerators and denominators: (12×5)/(7×8) = 15/14.
ArithmeticGMATGREMathematicsPractice Set
5
What is the maximum value of y = -6x^2 + 24x − 16?
ExplanationThe GCF of 44 and -33 (besides x) is 11, and factoring it out (along with one x) gives 11x(4x − 3).
AlgebraGMATGREMathematicsPractice Set
16
A rectangle has length (x + 13) and width (x + 12). If the area of the rectangle is 1190 square units, what is the value of x (where x is a positive number)?
Explanation(x + 13)(x + 12) = 1190. Testing x = 22: (35)(34) = 1190, which checks out (the other algebraic root is negative and not valid here).
AlgebraGMATGREMathematicsPractice Set
17
Solve the system for y: -7x + 6y = 27, -2x − 6y = 0
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSolving the system by elimination or substitution gives y = 1 (and x = -3).
AlgebraGMATGREMathematicsPractice Set
18
In an arithmetic sequence, the 7th term is 100 and the 22nd term is 280. What is the 1st term?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (280 − 100)/(22−7) = 12. Then the 1st term = 100 + (1−7)(12) = 28.
AlgebraGMATGREMathematicsPractice Set
19
How many solutions does the equation 11x + 5 = 11x + 5 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.
AlgebraGMATGREMathematicsPractice Set
20
What is the 4th root of 6561?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation9^4 = 6561, so the 4th root of 6561 is 9.
AntonymsGMATGREMathematicsPractice Set
— Sponsored —
21
What is 50.82 + 43.53?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation50.82 + 43.53 = 94.35.
ArithmeticGMATGREMathematicsPractice Set
22
What is the greatest common divisor (GCD) of 276 and 138?
Arithmetic - Number Properties
Medium
ExplanationThe largest integer dividing both 276 and 138 evenly is 138.
ArithmeticGMATGREMathematicsPractice Set
23
A jar contains only Rs. 5 and Rs. 10 coins. There are 55 coins with a total value of Rs. 485. How many Rs. 10 coins are there?
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 55 and 5x + 10y = 485. Solving gives x = 13, y = 42.
AlgebraGMATGREMathematicsPractice Set
24
Is 235 a prime number?
Arithmetic - Number Properties
Medium
Explanation235 is divisible by at least one number between 2 and 234, so it is not prime.
ArithmeticGMATGREMathematicsPractice Set
25
What is the value of -7x + 27 when x = 7?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation-7(7) + 27 = -49 + 27 = -22.
AlgebraGMATGREMathematicsPractice Set
26
What are the solutions to |x − 35| = 2?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 35| = 2 means x is 2 away from 35, so x = 35 + 2 = 37 or x = 35 − 2 = 33.
ArithmeticGMATGREMathematicsPractice Set
27
Three warning lights flash every 9, 14, and 6 seconds respectively. If they all flash together at the same instant, after how many seconds will they next flash together?
Arithmetic - Number Properties
Medium
ExplanationThey will next flash together after LCM(9, 14, 6) = 126 seconds.
ArithmeticGMATGREMathematicsPractice Set
28
What is the smallest number that must be subtracted from 7093 so that the result is exactly divisible by 22?
Arithmetic - Number Properties
Medium
Explanation7093 divided by 22 leaves remainder 9, so subtracting 9 makes it exactly divisible by 22.
ArithmeticGMATGREMathematicsPractice Set
29
What is the smallest number that must be subtracted from 7811 so that the result is exactly divisible by 29?
Arithmetic - Number Properties
Medium
Explanation7811 divided by 29 leaves remainder 10, so subtracting 10 makes it exactly divisible by 29.
ArithmeticGMATGREMathematicsPractice Set
30
Which is greater: 41.215 or 26.728?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationComparing digit by digit, 41.215 is greater than 26.728.
ArithmeticGMATGREMathematicsPractice Set
— Sponsored —
31
Among 32, 77, -20, and 40, 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. |-20| = 20, which is the smallest among the options.
ArithmeticGMATGREMathematicsPractice Set
32
If f(x) = 8x + 2, what is f(-6) − f(-9)?
Algebra - Functions and Sequences (including word…
Medium
Explanationf(-6) = -46 and f(-9) = -70, so f(-6) − f(-9) = 24.
AlgebraGMATGREMathematicsPractice Set
33
If f(x) = -5x + 4, for what value of x does f(x) = 59?
Algebra - Functions and Sequences (including word…
Medium
Explanation-5x + 4 = 59, so x = -11.
AlgebraGMATGREMathematicsPractice Set
34
Given 10x + 9y = 18, what is y when x = 72?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation9y = 18 − 10(72) = 18 − 720 = -702, so y = -702/9 = -78.
AlgebraGMATGREMathematicsPractice Set
35
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.
ArithmeticGMATGREMathematicsPractice Set
36
What is |20| − |42|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|20| − |42| = 20 − 42 = -22. (Note this is generally different from |20 − 42|.)
ArithmeticGMATGREMathematicsPractice Set
37
What is the greatest common divisor of 33, 77, and 22?
Arithmetic - Number Properties
Medium
ExplanationThe largest integer dividing all of 33, 77, and 22 evenly is 11.
ArithmeticGMATGREMathematicsPractice Set
38
What is the axis of symmetry of the parabola y = -6x^2 + 72x + 4?
ExplanationStarting with 100: after the first change it becomes 116.00, and after the second change it becomes 95.12 — a net change of -4.88% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
59
What is the length of the solution interval for |x + 21| < 30?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 21| < 30 describes the interval (-51, 9), which has length 9 − (-51) = 60.
ArithmeticGMATGREMathematicsPractice Set
60
After a 70% increase, a quantity became 697. What was the original quantity?
If 40 workers can complete a task in 21 days, how many days would 10 workers take to complete the same task (assuming the same work rate per worker)?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationTotal work = 40 × 21 = 840 worker-days. With 10 workers, days = 840/10 = 84.
ArithmeticGMATGREMathematicsPractice Set
84
A delivery service charges a fixed fee of Rs. 49 plus Rs. 21 per item. If a customer has a budget of Rs. 138, what is the maximum number of items they can order?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation49 + 21n ≤ 138, so n ≤ 89/21 ≈ 4.24, meaning at most 4 items.
AlgebraGMATGREMathematicsPractice Set
85
What is the smallest positive integer that is divisible by all of 17, 11, and 9?
Arithmetic - Number Properties
Medium
ExplanationThe smallest such number is LCM(17, 11, 9) = 1683.
ArithmeticGMATGREMathematicsPractice Set
86
59^2 − 16^2 is exactly divisible by which of the following?
Arithmetic - Number Properties
Medium
Explanation59^2 − 16^2 = (59 − 16)(59 + 16) = 43 × 75, so it is always divisible by 43 (and by 75).
ArithmeticGMATGREMathematicsPractice Set
87
If two positive integers are 30 and 23, what is the product of their LCM and GCD?
Arithmetic - Number Properties
Medium
ExplanationFor any two positive integers, LCM × GCD = product of the numbers = 30 × 23 = 690.
ArithmeticGMATGREMathematicsPractice Set
88
What is 87^0 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationAny nonzero number raised to the power 0 equals 1, by definition.
AntonymsGMATGREMathematicsPractice Set
89
Convert 55/9 to a mixed number.
Arithmetic - Fractions, Decimals, Ratios and Prop…
9569 is exactly divisible by which of the following numbers?
Arithmetic - Number Properties
Medium
Explanation9569 ÷ 7 = 1367, a whole number, so 7 divides 9569 exactly.
ArithmeticGMATGREMathematicsPractice Set
96
If f(x) = -6x + 21, for what value of x does f(x) = 141?
Algebra - Functions and Sequences (including word…
Medium
Explanation-6x + 21 = 141, so x = -20.
AlgebraGMATGREMathematicsPractice Set
97
Two buses leave a station together. One returns to the station every 21 minutes and the other every 40 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(21, 40) = 840 minutes.
ArithmeticGMATGREMathematicsPractice Set
98
Which of the following numbers lies between -24 and 7?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation5 lies strictly between -24 and 7, while the other options fall outside that range.
ArithmeticGMATGREMathematicsPractice Set
99
Simplify: 5^6 ÷ 5^3
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen dividing powers with the same base, subtract the exponents: 5^6 ÷ 5^3 = 5^(6-3) = 5^3.