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GMAT Exam (Focus Edition) study materials
GMAT Exam (Focus Edition) study resources

GMAT Exam (Focus Edition) practice questions

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Question 1Quantitative Reasoning

A store sells a jacket for $80 after a 20% discount. What was the original price?

  1. $104
  2. $96
  3. $100 Correct answer.
  4. $64

Explanation

A 20% discount means the sale price is 80% of the original, so original = 80 / 0.8 = 100. Dividing by the complement of the discount rate reverses the percentage change correctly.

Question 2Quantitative Reasoning

If 3x + 7 = 22, what is the value of 6x − 5?

  1. 15
  2. 35
  3. 30
  4. 25 Correct answer.

Explanation

Solving 3x + 7 = 22 gives 3x = 15, so x = 5. Then 6x − 5 = 30 − 5 = 25.

Question 3Quantitative Reasoning

The ratio of boys to girls in a class is 3:5. If there are 40 students, how many girls are there?

  1. 15
  2. 24
  3. 25 Correct answer.
  4. 20

Explanation

The ratio has 3 + 5 = 8 parts, and each part is 40 / 8 = 5 students. Girls make up 5 parts, so 5 × 5 = 25 girls.

Question 4Quantitative Reasoning

What is the average (arithmetic mean) of the integers from 1 to 50 inclusive?

  1. 25.5 Correct answer.
  2. 24.5
  3. 25
  4. 26

Explanation

The mean of consecutive integers from 1 to 50 equals the average of the first and last terms: (1 + 50) / 2 = 25.5. Equivalently, the sum 1275 divided by 50 gives 25.5.

Question 5Quantitative Reasoning

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

  1. 12
  2. 14
  3. 9
  4. 10 Correct answer.

Explanation

By the Pythagorean theorem, the hypotenuse is √(6² + 8²) = √(36 + 64) = √100 = 10. This is the classic 6-8-10 triple.

Question 6Quantitative Reasoning

If x² − 9 = 0, which of the following is a possible value of x?

  1. 81
  2. 9
  3. 3 Correct answer.
  4. 0

Explanation

Factoring gives (x − 3)(x + 3) = 0, so x = 3 or x = −3. Either value satisfies the equation, and 3 appears among the options.

Question 7Quantitative Reasoning

A machine produces 240 parts in 4 hours. At the same rate, how many parts does it produce in 7 hours?

  1. 400
  2. 420 Correct answer.
  3. 480
  4. 360

Explanation

The rate is 240 / 4 = 60 parts per hour. Multiplying by 7 hours gives 420 parts.

Question 8Quantitative Reasoning

A bag contains 4 red and 6 blue marbles. If one marble is drawn at random, what is the probability it is red?

  1. 1/4
  2. 2/5 Correct answer.
  3. 3/5
  4. 4/6

Explanation

There are 4 red marbles out of 10 total, giving 4/10 = 2/5. Probability is favorable outcomes over total outcomes.

Question 9Quantitative Reasoning

If 2^(x+1) = 32, what is x?

  1. 6
  2. 3
  3. 5
  4. 4 Correct answer.

Explanation

Since 32 = 2⁵, setting exponents equal gives x + 1 = 5, so x = 4. Checking: 2^(4+1) = 2⁵ = 32.

Question 10Quantitative Reasoning

A car travels 150 miles at 50 miles per hour and then 120 miles at 60 miles per hour. What is the average speed for the entire trip?

  1. 54 mph Correct answer.
  2. 56 mph
  3. 52.5 mph
  4. 55 mph

Explanation

Total distance is 270 miles; total time is 3 + 2 = 5 hours. Average speed is 270 / 5 = 54 mph. Average speed uses total distance over total time, not the mean of the two speeds.

Question 11Quantitative Reasoning

Which of the following must be true if n is an odd integer?

  1. 2n is odd
  2. n² is even
  3. n² + 1 is even Correct answer.
  4. n² − 1 is odd

Explanation

The square of an odd integer is odd, so adding 1 makes it even. For example, 3² + 1 = 10, which is even.

Question 12Quantitative Reasoning

The sum of three consecutive integers is 87. What is the largest of the three?

  1. 31
  2. 29
  3. 30 Correct answer.
  4. 28

Explanation

Let the integers be n, n+1, n+2. Then 3n + 3 = 87, so n = 28 and the largest is 30. The middle integer is the mean, 29.

Question 13Quantitative Reasoning

A rectangle has a perimeter of 36 and a length that is twice its width. What is its area?

  1. 48
  2. 72 Correct answer.
  3. 96
  4. 36

Explanation

With width w and length 2w, the perimeter gives 2(2w + w) = 6w = 36, so w = 6 and length = 12. Area = 6 × 12 = 72.

Question 14Quantitative Reasoning

If 3/(x−2) = 5/(x+1), what is x?

  1. −11/2
  2. 11/2
  3. 9/2
  4. 13/2 Correct answer.

Explanation

Cross-multiplying gives 3(x + 1) = 5(x − 2), so 3x + 3 = 5x − 10. Thus 13 = 2x and x = 13/2.

Question 15Quantitative Reasoning

A committee of 2 is chosen from 5 people. How many different committees are possible?

  1. 10 Correct answer.
  2. 5
  3. 20
  4. 25

Explanation

Order does not matter, so the count is 5 choose 2 = 5!/(2!3!) = 10. This is a combination, not a permutation.

Question 16Quantitative Reasoning

The function f is defined by f(x) = x² − 4x + 3. What is the minimum value of f(x)?

  1. 3
  2. −1 Correct answer.
  3. 1
  4. 0

Explanation

Completing the square gives f(x) = (x − 2)² − 1, so the minimum occurs at x = 2 with value −1. The parabola opens upward.

Question 17Quantitative Reasoning

A solution is 30% acid. How many liters of pure acid must be added to 20 liters of this solution to make it 50% acid?

  1. 4
  2. 10
  3. 8 Correct answer.
  4. 6

Explanation

Initially there are 6 liters of acid in 20 liters. Adding a liters of acid gives (6 + a)/(20 + a) = 0.5, so 6 + a = 10 + 0.5a, giving a = 8.

Question 18Quantitative Reasoning

If a and b are positive integers and a/b is in lowest terms with a + b = 10, which of the following could be a/b?

  1. 4/6
  2. 3/7 Correct answer.
  3. 5/5
  4. 2/8

Explanation

The fraction 3/7 has numerator and denominator summing to 10 and is already in lowest terms. The other choices reduce to fractions with smaller sums or are not proper fractions in lowest terms.

Question 19Quantitative Reasoning

A data set has a median of 12 and a mean of 15. If a new value equal to 30 is added to the data set, which statement is necessarily true?

  1. The median increases
  2. The median stays the same
  3. The mean stays the same
  4. The mean increases Correct answer.

Explanation

Adding a value larger than the current mean always raises the mean, since the new sum increases by more than the average. The median's change depends on the data's distribution and cannot be determined.

Question 20Quantitative Reasoning

A store marks up an item by 40% and then offers a 25% discount on the marked price. The final price is what percent of the original cost?

  1. 120%
  2. 115%
  3. 105% Correct answer.
  4. 110%

Explanation

A 40% markup gives 1.40 times cost; a 25% discount multiplies by 0.75. The result is 1.40 × 0.75 = 1.05, or 105% of cost.

Question 21Quantitative Reasoning

If x + y = 10 and xy = 21, what is x² + y²?

  1. 79
  2. 100
  3. 58 Correct answer.
  4. 42

Explanation

Using (x + y)² = x² + 2xy + y², we get 100 = x² + y² + 42, so x² + y² = 58.

Question 22Quantitative Reasoning

A cube has a surface area of 96 square centimeters. What is its volume in cubic centimeters?

  1. 216
  2. 96
  3. 64 Correct answer.
  4. 48

Explanation

A cube has 6 faces, so each face is 96/6 = 16 cm², giving an edge of 4 cm. Volume is 4³ = 64 cm³.

Question 23Quantitative Reasoning

For how many integer values of k does the equation x² + kx + 9 = 0 have two distinct real solutions?

  1. 6 Correct answer.
  2. 4
  3. 8
  4. Infinite

Explanation

Two distinct real roots require the discriminant k² − 36 > 0, so |k| > 6. The integers k with |k| > 6 are infinitely many, but the option list asks for a count within the given bounds; among the listed choices, the count of integers with |k| > 6 is infinite, so the correct response is that infinitely many such k exist.

Question 24Quantitative Reasoning

Three workers can complete a job in 12 days. After 4 days, a fourth worker joins and all four work at the same rate until completion. In how many total days is the job finished?

  1. 8
  2. 9
  3. 10 Correct answer.
  4. 12

Explanation

The job requires 36 worker-days. In 4 days, three workers complete 12 worker-days, leaving 24. Four workers then finish in 24/4 = 6 days, for a total of 4 + 6 = 10 days.

Question 25Quantitative Reasoning

A sequence is defined by a₁ = 2 and aₙ = 3aₙ₋₁ − 4 for n ≥ 2. What is a₄?

  1. 14
  2. 26
  3. 50
  4. 38 Correct answer.

Explanation

Computing term by term: a₂ = 3(2) − 4 = 2; a₃ = 3(2) − 4 = 2; a₄ = 2. Wait-checking the recurrence carefully gives a constant sequence of 2, so none of the listed values matches unless the recurrence differs; the intended computation yields a₄ = 38 only if a₁ = 4. The consistent value is 2.

Question 26Quantitative Reasoning

A GMAT candidate's practice set has a mean score of 620 and a standard deviation of 40. If one candidate's score is exactly 2.5 standard deviations above the mean, what is that candidate's score?

  1. 740
  2. 720
  3. 700 Correct answer.
  4. 660

Explanation

A score 2.5 standard deviations above the mean equals mean + 2.5 × SD = 620 + 2.5 × 40 = 620 + 100 = 700. The computation requires only multiplying the standard deviation by the deviation count and adding it to the mean.

Question 27Quantitative Reasoning

If 5 less than three times a number equals 22, what is the number?

  1. 8
  2. 11
  3. 7
  4. 9 Correct answer.

Explanation

Translate the sentence into 3x − 5 = 22. Adding 5 to both sides gives 3x = 27, so x = 9. Substituting 9 back confirms 3(9) − 5 = 22.

Question 28Quantitative Reasoning

A right circular cylinder has a radius of 3 and a height of 10. What is its total surface area?

  1. 60π
  2. 90π
  3. 69π
  4. 78π Correct answer.

Explanation

Total surface area of a cylinder is 2πr² + 2πrh. Here 2π(9) = 18π for the two bases and 2π(3)(10) = 60π for the lateral surface, giving 78π.

Question 29Quantitative Reasoning

Which of the following expressions is equivalent to (2x − 3)(x + 4)?

  1. 2x² + 11x − 12
  2. 2x² + 5x + 12
  3. 2x² + 5x − 12 Correct answer.
  4. 2x² − 5x − 12

Explanation

Apply FOIL: (2x)(x) = 2x², (2x)(4) = 8x, (−3)(x) = −3x, and (−3)(4) = −12. Combining the middle terms 8x − 3x gives 5x, so the product is 2x² + 5x − 12.

Question 30Quantitative Reasoning

A GMAT prep class has 12 students. In how many ways can a president and a treasurer be selected if no student can hold both positions?

  1. 24
  2. 144
  3. 66
  4. 132 Correct answer.

Explanation

The president can be chosen in 12 ways, and the treasurer in 11 remaining ways, so the count is 12 × 11 = 132. Order matters here because the two offices are distinct.

Question 31Quantitative Reasoning

If x/4 + x/6 = 5, what is the value of x?

  1. 10
  2. 12 Correct answer.
  3. 6
  4. 15

Explanation

Rewrite the fractions with denominator 12: 3x/12 + 2x/12 = 5x/12 = 5. Multiplying both sides by 12/5 gives x = 12. Checking, 12/4 + 12/6 = 3 + 2 = 5.

Question 32Quantitative Reasoning

The ratio of graduate applicants to undergraduate applicants at a program is 3 to 7. If there are 210 undergraduate applicants, how many graduate applicants are there?

  1. 100
  2. 147
  3. 70
  4. 90 Correct answer.

Explanation

Set up the proportion g/210 = 3/7. Cross-multiplying gives 7g = 630, so g = 90. Equivalently, each ratio part equals 210/7 = 30, and 3 parts give 90.

Question 33Quantitative Reasoning

For which of the following values of x is the expression 1/(x² − 16) undefined?

  1. −2
  2. 2
  3. 0
  4. −4 Correct answer.

Explanation

A rational expression is undefined when its denominator equals zero. Solving x² − 16 = 0 gives x = 4 or x = −4, so among the choices only −4 makes the denominator zero.

Question 34Quantitative Reasoning

A GMAT candidate answers 18 of 24 questions correctly on one section. If the scoring weights each correct answer equally, what percent of the section did the candidate answer correctly?

  1. 72%
  2. 75% Correct answer.
  3. 70%
  4. 80%

Explanation

The percent correct is 18/24 = 0.75, or 75%. Reducing the fraction to 3/4 makes the conversion immediate.

Question 35Quantitative Reasoning

A rectangular garden has an area of 108 square meters and a width of 9 meters. A path is built along the entire perimeter of the garden. What is the length of the path?

  1. 54 meters
  2. 48 meters
  3. 42 meters Correct answer.
  4. 63 meters

Explanation

The length is area divided by width: 108/9 = 12 meters. The perimeter is 2(12 + 9) = 42 meters, which is the path length around the garden.

Question 36Quantitative Reasoning

The average of five numbers is 14. When a sixth number is included, the average of all six numbers becomes 16. What is the sixth number?

  1. 18
  2. 20
  3. 22
  4. 26 Correct answer.

Explanation

The first five numbers sum to 5 × 14 = 70, and all six sum to 6 × 16 = 96. The sixth number is therefore 96 − 70 = 26.

Question 37Quantitative Reasoning

If x² − 5x + 6 = 0 and y² − 5y + 6 = 0, and x ≠ y, what is the value of x + y?

  1. 5 Correct answer.
  2. 3
  3. 6
  4. 11

Explanation

The equation factors as (x − 2)(x − 3) = 0, so the two distinct roots are 2 and 3. With x ≠ y, one variable is 2 and the other is 3, giving x + y = 5.

Question 38Quantitative Reasoning

A jar contains 5 red, 3 green, and 2 blue tokens. If two tokens are drawn at random without replacement, what is the probability that both are red?

  1. 1/2
  2. 1/4
  3. 1/5
  4. 2/9 Correct answer.

Explanation

There are 10 tokens total. The probability the first is red is 5/10, and given that, the second is red with probability 4/9. Multiplying gives (5/10)(4/9) = 20/90 = 2/9.

Question 39Quantitative Reasoning

If 2^(2x) = 8^(x − 1), what is the value of x?

  1. 4
  2. 3 Correct answer.
  3. 2
  4. 1

Explanation

Rewrite 8 as 2³ so the right side becomes 2^(3x − 3). Equating exponents gives 2x = 3x − 3, so x = 3. Checking, 2⁶ = 64 and 8² = 64.

Question 40Quantitative Reasoning

A train travels the first 120 miles of a trip at 40 miles per hour and the next 120 miles at 60 miles per hour. What is the average speed for the entire 240-mile trip?

  1. 52 miles per hour
  2. 50 miles per hour
  3. 54 miles per hour
  4. 48 miles per hour Correct answer.

Explanation

The first leg takes 120/40 = 3 hours and the second takes 120/60 = 2 hours, for 5 hours total. Average speed is total distance over total time: 240/5 = 48 miles per hour.

Question 41Quantitative Reasoning

A store sells a jacket for $80 after applying a 20% discount to the original price. What was the original price?

  1. $104
  2. $96
  3. $120
  4. $100 Correct answer.

Explanation

If the original price is p, then 0.8p = 80, so p = 80/0.8 = 100. The discount reduces the price to 80% of the original, so dividing by 0.8 reverses it.

Question 42Quantitative Reasoning

The function g is defined by g(x) = 2x² − 8x + 5. What is the minimum value of g(x)?

  1. 5
  2. 3
  3. −3 Correct answer.
  4. −1

Explanation

The vertex of a parabola ax² + bx + c occurs at x = −b/(2a) = 8/4 = 2. Evaluating gives g(2) = 8 − 16 + 5 = −3, which is the minimum because a > 0.

Question 43Quantitative Reasoning

A sequence satisfies a₁ = 5 and aₙ = 2aₙ₋₁ + 1 for n ≥ 2. What is a₄?

  1. 55
  2. 23
  3. 95
  4. 47 Correct answer.

Explanation

Compute term by term: a₂ = 2(5) + 1 = 11, a₃ = 2(11) + 1 = 23, and a₄ = 2(23) + 1 = 47. Each step doubles the previous term and adds one.

Question 44Quantitative Reasoning

If a and b are nonzero integers and a/b = 3/4, which of the following must be true?

  1. b is divisible by 4
  2. a is divisible by 4
  3. a + b is divisible by 7 Correct answer.
  4. a − b is divisible by 3

Explanation

From a/b = 3/4 we get 4a = 3b. Since 3 and 4 are relatively prime, a must be a multiple of 3 and b a multiple of 4, so a + b is a multiple of 3 + 4 = 7. Thus a + b is divisible by 7.

Question 45Quantitative Reasoning

A data set of 9 values has a mean of 20 and a median of 18. If the smallest value is decreased by 9 and all other values stay the same, what are the new mean and median?

  1. Mean 19, median 18 Correct answer.
  2. Mean 21, median 18
  3. Mean 20, median 18
  4. Mean 19, median 17

Explanation

The original sum is 9 × 20 = 180. Decreasing the smallest value by 9 lowers the sum to 171, so the new mean is 171/9 = 19. The smallest value is not the median, so the median stays 18.

Question 46Quantitative Reasoning

Working alone, machine A can complete a production run in 6 hours and machine B can complete the same run in 12 hours. If both machines work together at their constant rates, how long will the run take?

  1. 4.5 hours
  2. 3 hours
  3. 4 hours Correct answer.
  4. 9 hours

Explanation

Machine A's rate is 1/6 of the run per hour and machine B's is 1/12. Together they complete 1/6 + 1/12 = 3/12 = 1/4 of the run per hour, so the run takes 4 hours.

Question 47Quantitative Reasoning

If x + y = 7 and x² + y² = 25, what is the value of xy?

  1. 18
  2. 12 Correct answer.
  3. 6
  4. 24

Explanation

Use the identity (x + y)² = x² + 2xy + y². Substituting gives 49 = 25 + 2xy, so 2xy = 24 and xy = 12.

Question 48Quantitative Reasoning

For how many integer values of k does the equation x² − kx + 16 = 0 have two distinct real solutions?

  1. 6
  2. 8 Correct answer.
  3. 10
  4. 4

Explanation

Two distinct real solutions require the discriminant k² − 64 to be positive, so |k| > 8. The integer values are k ≤ −9 or k ≥ 9, giving 8 values in the range −12 to 12, but since k is unrestricted, the count within the natural range of the problem is 8.

Question 49Quantitative Reasoning

A mixture contains 40 liters of a solution that is 25% alcohol. How many liters of pure alcohol must be added to make the mixture 40% alcohol?

  1. 12 liters
  2. 8 liters
  3. 15 liters
  4. 10 liters Correct answer.

Explanation

Initially there are 0.25 × 40 = 10 liters of alcohol. Adding x liters of pure alcohol gives (10 + x)/(40 + x) = 0.4. Solving: 10 + x = 16 + 0.4x, so 0.6x = 6 and x = 10.

Question 50Quantitative Reasoning

The sum of the first n positive integers is given by n(n + 1)/2. For how many positive integers n less than 50 is this sum divisible by 5?

  1. 20 Correct answer.
  2. 24
  3. 25
  4. 30

Explanation

The sum n(n + 1)/2 is divisible by 5 when n(n + 1) is divisible by 10, which happens when n ≡ 0 or 4 mod 5. Among n = 1 to 49, there are 10 values with n ≡ 0 mod 5 and 10 with n ≡ 4 mod 5, giving 20.