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GMAT Quantitative Reasoning Practice Questions with Answers & Explanations

These GMAT Quantitative practice questions are designed to mirror the style and complexity of the questions typically found on the GMAT exam, helping you build confidence, strengthen your reasoning, and prepare more effectively for this demanding section. These questions have been made for practice and learning purposes only and are not associated with or taken from any official GMAT source.

Coverage Map

Area Question Numbers Skills Tested Suggested Review
Arithmetic and Percentages 1-3, 27-31, 33 fractions, ratios, mixtures, percent change, profit, interest, units Master percent multipliers and unit consistency.
Algebra 5-11, 24-26, 31, 37-38 equations, inequalities, exponents, roots, quadratics, functions, sequences Translate carefully and check restrictions.
Word Problems 12-16, 27-33 rates, work, distance, overlapping sets, business scenarios Define variables and identify constants.
Number Properties 4, 22-23, 34-36, 40 divisibility, primes, remainders, units digits, factors, LCM Use prime factorization and modular patterns.
Statistics and Probability 17-21, 39 probability, combinations, permutations, mean, median, range, spread Separate calculation questions from concept questions.

Practice Questions with Detailed Solutions

Question 1 - Fractions and Ratios

A company has 72 employees. The ratio of managers to non-managers is 1 to 5. If 6 non-managers are promoted to managers, what is the new ratio of managers to non-managers?

A. 1:3
B. 1:2
C. 3:7
D. 2:5
E. 5:7

Answer: A. 1:3

Step-by-step solution:

  1. Original total = 72 employees.
  2. Managers : non-managers = 1 : 5, so there are 6 equal parts.
  3. Each part = 72 ÷ 6 = 12.
  4. Original managers = 12 and original non-managers = 60.
  5. After 6 non-managers are promoted, managers = 12 + 6 = 18 and non-managers = 60 - 6 = 54.
  6. New ratio = 18 : 54. Divide both parts by 18 to get 1 : 3.
Tip: Track both groups after a change. A promotion moves people from one group to another; it does not change the total.

Question 2 - Percent Change

The price of a laptop is increased by 20% and then decreased by 25%. The final price is what percent of the original price?

A. 80%
B. 90%
C. 95%
D. 100%
E. 105%

Answer: B. 90%

Step-by-step solution:

  1. Let the original price be 100.
  2. After a 20% increase, the price becomes 100 × 1.20 = 120.
  3. After a 25% decrease, the price becomes 120 × 0.75 = 90.
  4. The final price is 90 out of the original 100, or 90%.
Tip: For consecutive percent changes, multiply the change factors. Do not add the percentages.

Question 3 - Weighted Average

A mixture contains 40 liters of a 30% salt solution. How many liters of pure water must be added so that the resulting mixture is 24% salt?

A. 6
B. 8
C. 10
D. 12
E. 15

Answer: C. 10

Step-by-step solution:

  1. The amount of salt does not change when water is added.
  2. Initial salt = 30% of 40 = 0.30 × 40 = 12 liters.
  3. Let x be the liters of water added. New total volume = 40 + x.
  4. The final mixture is 24% salt, so 12 ∕ (40 + x) = 0.24.
  5. 12 = 0.24(40 + x) = 9.6 + 0.24x.
  6. 2.4 = 0.24x, so x = 10.
Tip: In mixture questions, identify what stays constant. Here, salt stays constant while total volume changes.

Question 4 - Number Properties

If n is a positive integer and 12n is divisible by 18, what is the smallest possible value of n?

A. 2
B. 3
C. 4
D. 6
E. 9

Answer: B. 3

Step-by-step solution:

  1. We need 18 to divide 12n.
  2. Prime factorize: 18 = 2 × 3² and 12 = 2² × 3.
  3. The expression 12n already has at least one factor of 2 and one factor of 3.
  4. To be divisible by 18, it needs one more factor of 3.
  5. The smallest n that supplies that factor is n = 3.
Tip: Use prime factors when a divisibility question asks for the smallest possible integer.

Question 5 - Algebraic Expressions

If x - 1 ∕ x = 3 and x is not 0, what is the value of x² + 1 ∕ x²?

A. 7
B. 9
C. 11
D. 13
E. 15

Answer: C. 11

Step-by-step solution:

  1. Square both sides of x - 1 ∕ x = 3.
  2. (x - 1 ∕ x)² = x² - 2 + 1 ∕ x².
  3. So 3² = x² - 2 + 1 ∕ x².
  4. 9 = x² + 1 ∕ x² - 2.
  5. Therefore x² + 1 ∕ x² = 11.
Tip: When you see x plus or minus 1 ∕ x, squaring often creates x² + 1 ∕ x².

Question 6 - Linear Equations (Easy)

For what value of k is 3(2k - 5) - 4(k + 1) = 7?

A. 8
B. 10
C. 11
D. 13
E. 15

Answer: D. 13

Step-by-step solution:

  1. Expand the left side: 3(2k - 5) = 6k - 15 and -4(k + 1) = -4k - 4.
  2. Combine terms: 6k - 15 - 4k - 4 = 2k - 19.
  3. Set equal to 7: 2k - 19 = 7.
  4. 2k = 26, so k = 13.
Tip: Expand carefully and combine like terms before solving.

Question 7 - Inequalities

If -2 < 3x + 4 < 16, which of the following gives the possible values of x?

A. -2 < x < 4
B. -6 < x < 12
C. -2 < x < 12
D. -6 < x < 4
E. 2 < x < 4

Answer: A. -2 < x < 4

Step-by-step solution:

  1. Subtract 4 from all three parts: -6 < 3x < 12.
  2. Divide all three parts by 3: -2 < x < 4.
  3. No inequality sign changes because we divided by a positive number.
Tip: Treat compound inequalities as three-part equations. Only reverse signs when multiplying or dividing by a negative number.

Question 8 - Exponents

If 2ᵃ × 4ᵇ = 2¹¹, then a + 2b equals which of the following?

A. 7
B. 9
C. 11
D. 13
E. 15

Answer: C. 11

Step-by-step solution:

  1. Rewrite 4ᵇ as (2²)ᵇ = 2²ᵇ.
  2. Then 2ᵃ × 4ᵇ = 2ᵃ × 2²ᵇ = 2ᵃ⁺²ᵇ.
  3. Since this equals 2¹¹, the exponents must be equal.
  4. Therefore a + 2b = 11.
Tip: Convert all terms to the same base before comparing exponents.

Question 9 - Roots and Radicals

If √(3x + 4) = x, what is the value of x?

A. 1
B. 2
C. 4
D. 5
E. 9

Answer: C. 4

Step-by-step solution:

  1. Because a square root is nonnegative, x must be nonnegative.
  2. Square both sides: 3x + 4 = x².
  3. Rearrange: x² - 3x - 4 = 0.
  4. Factor: (x - 4)(x + 1) = 0.
  5. So x = 4 or x = -1. Since x must be nonnegative and must satisfy the original equation, x = 4.
Tip: When squaring equations with radicals, always check the answer in the original equation.

Question 10 - Quadratics

If y² - 6y + 8 = 0, what is the sum of all possible values of y?

A. 2
B. 4
C. 6
D. 8
E. 14

Answer: C. 6

Step-by-step solution:

  1. Factor the quadratic: y² - 6y + 8 = (y - 2)(y - 4).
  2. Set each factor equal to zero: y = 2 or y = 4.
  3. The sum of all possible values is 2 + 4 = 6.
  4. Alternatively, for ax² + bx + c = 0, the sum of roots is -b ∕ a = 6.
Tip: For quadratics, know both factoring and the sum/product root shortcuts.

Question 11 - Systems of Equations

A bookstore sold 3 notebooks and 2 pens for $19. It sold 2 notebooks and 5 pens for $20. What is the price of one notebook?

A. $3
B. $4
C. $5
D. $6
E. $7

Answer: C. $5

Step-by-step solution:

  1. Let n be the price of a notebook and p be the price of a pen.
  2. Equations: 3n + 2p = 19 and 2n + 5p = 20.
  3. Multiply the first equation by 5: 15n + 10p = 95.
  4. Multiply the second equation by 2: 4n + 10p = 40.
  5. Subtract: 11n = 55, so n = 5.
  6. Therefore one notebook costs $5.
Tip: Set up variables first. If using answer choices, verify in every given condition.

Question 12 - Rates

Machine A produces 60 units in 4 hours. Machine B produces 60 units in 6 hours. Working together at constant rates, how many hours will they take to produce 60 units?

A. 2
B. 2.4
C. 3
D. 4
E. 5

Answer: B. 2.4

Step-by-step solution:

  1. Machine A's rate = 60⁄4 = 15 units per hour.
  2. Machine B's rate = 60⁄6 = 10 units per hour.
  3. Together, their rate is 15 + 10 = 25 units per hour.
  4. Time to produce 60 units = 60⁄25 = 12⁄5 = 2.4 hours.
Tip: For work-rate problems, add rates, not times.

Question 13 - Distance, Rate, Time

A car travels 180 miles at an average speed of 45 miles per hour and returns over the same route at 60 miles per hour. What is the average speed for the entire trip?

A. 50 mph
B. 360⁄7 mph
C. 52 mph
D. 54 mph
E. 55 mph

Answer: B. 360⁄7 mph

Step-by-step solution:

  1. Total distance = 180 + 180 = 360 miles.
  2. Time going = 180⁄45 = 4 hours.
  3. Time returning = 180⁄60 = 3 hours.
  4. Total time = 7 hours.
  5. Average speed = total distance ÷ total time = 360⁄7 = 51.43 mph.
  6. Therefore the average speed is 360⁄7 mph.
Tip: Average speed is total distance divided by total time; do not average the two speeds unless times are equal.

Question 14 - Work Problems

Pipe A can fill a tank in 5 hours, and Pipe B can fill the same tank in 10 hours. Pipe C can drain the full tank in 20 hours. If all three pipes are opened together when the tank is empty, how many hours will it take to fill the tank?

A. 3
B. 4
C. 5
D. 6
E. 8

Answer: B. 4

Step-by-step solution:

  1. Let the full tank be 1 job.
  2. Pipe A fills ⅕ tank per hour.
  3. Pipe B fills ⅒ tank per hour.
  4. Pipe C drains 1⁄20 tank per hour, so subtract its rate.
  5. Net rate = ⅕ + ⅒ - 1⁄20 = 4⁄20 + 2⁄20 - 1⁄20 = 5⁄20 = ¼ tank per hour.
  6. Time = 1 ÷ ¼ = 4 hours.
Tip: Use positive rates for filling and negative rates for draining.

Question 15 - Ratio Word Problem

The ratio of boys to girls in a class is 4 to 5. If 6 boys leave and 3 girls join, the ratio becomes 2 to 3. How many students were originally in the class?

A. 72
B. 81
C. 90
D. 99
E. 108

Answer: E. 108

Step-by-step solution:

  1. Let the original numbers be 4x boys and 5x girls.
  2. After changes, boys = 4x - 6 and girls = 5x + 3.
  3. New ratio: (4x - 6) ∕ (5x + 3) = ⅔.
  4. Cross multiply: 3(4x - 6) = 2(5x + 3).
  5. 12x - 18 = 10x + 6.
  6. 2x = 24, so x = 12.
  7. Original total = 4x + 5x = 9x = 108.
Tip: Use a multiplier for the original ratio and translate every change before forming the equation.

Question 16 - Overlapping Sets

In a group of 80 applicants, 50 have experience in finance, 38 have experience in analytics, and 12 have neither. How many applicants have experience in both finance and analytics?

A. 8
B. 12
C. 16
D. 20
E. 24

Answer: D. 20

Step-by-step solution:

  1. Applicants with at least one of the two experiences = 80 - 12 = 68.
  2. Use the formula: F + A - both = at least one.
  3. 50 + 38 - both = 68.
  4. 88 - both = 68, so both = 20.
Tip: For two-group overlap questions, use Total = only A + only B + both + neither, or A + B - both = at least one.

Question 17 - Probability

A box contains 5 red balls and 3 blue balls. Two balls are selected at random without replacement. What is the probability that both are red?

A. 5⁄14
B. 25⁄64
C. 5⁄12
D. 10⁄21
E. 15⁄28

Answer: A. 5⁄14

Step-by-step solution:

  1. Probability first ball is red = ⅝.
  2. After one red is selected, 4 red balls and 7 total balls remain.
  3. Probability second ball is red = 4⁄7.
  4. Multiply: (⅝)(4⁄7) = 20⁄56 = 5⁄14.
Tip: Without replacement means the total changes after each selection.

Question 18 - Combinations

A committee of 3 people is to be chosen from 5 analysts and 4 managers. How many committees contain exactly 2 analysts and 1 manager?

A. 20
B. 30
C. 40
D. 50
E. 60

Answer: C. 40

Step-by-step solution:

  1. Choose 2 analysts from 5: C(5,2) = 10.
  2. Choose 1 manager from 4: C(4,1) = 4.
  3. Multiply because each analyst pair can be matched with each manager: 10 × 4 = 40.
Tip: Use combinations when order does not matter. Break the selection into required categories.

Question 19 - Permutations

How many different 4-letter codes can be formed from the letters A, B, C, D, and E if no letter may be repeated?

A. 20
B. 60
C. 120
D. 240
E. 625

Answer: C. 120

Step-by-step solution:

  1. There are 5 choices for the first position.
  2. Then 4 choices for the second, 3 for the third, and 2 for the fourth.
  3. Total codes = 5 × 4 × 3 × 2 = 120.
Tip: When order matters, multiply the number of choices for each position.

Question 20 - Median and Mean

The five numbers 6, 8, 12, x, and 20 have an average of 12. If x is greater than 12, what is the median of the five numbers?

A. 10
B. 12
C. 14
D. 16
E. 20

Answer: B. 12

Step-by-step solution:

  1. Average = total ÷ number of values.
  2. Total of five values = 12 × 5 = 60.
  3. Known total = 6 + 8 + 12 + 20 = 46.
  4. So x = 60 - 46 = 14.
  5. The ordered list is 6, 8, 12, 14, 20.
  6. The median, the middle value, is 12.
Tip: For median questions, find or arrange the values in order before choosing the middle.

Question 21 - Standard Deviation Concept

Set A is {10, 10, 10, 10}. Set B is {7, 9, 11, 13}. Which statement must be true?

A. The means are equal and the standard deviations are equal.
B. The means are equal and Set A has the smaller standard deviation.
C. Set A has the larger mean and smaller standard deviation.
D. Set B has the larger mean and smaller standard deviation.
E. Set B has the smaller mean and larger standard deviation.

Answer: B. The means are equal and Set A has the smaller standard deviation.

Step-by-step solution:

  1. Mean of Set A = 10.
  2. Mean of Set B = (7 + 9 + 11 + 13) ∕ 4 = 40 ∕ 4 = 10.
  3. Set A has no spread because every value is 10, so its standard deviation is 0.
  4. Set B has values spread around 10, so its standard deviation is greater than 0.
  5. Therefore the means are equal and Set A has the smaller standard deviation.
Tip: On GMAT-style standard deviation questions, you often only need to compare spread, not calculate the full formula.

Question 22 - Integer Properties

If p is a prime number greater than 3, which of the following must be divisible by 6?

A. p + 1
B. p - 1
C. p² - 1
D. p² + 1
E. 2p + 1

Answer: C. p² - 1

Step-by-step solution:

  1. For any prime p greater than 3, p is odd and is not divisible by 3.
  2. p² - 1 = (p - 1)(p + 1).
  3. Since p is odd, p - 1 and p + 1 are consecutive even numbers, so the product is divisible by 2.
  4. Among any three consecutive integers p - 1, p, p + 1, one is divisible by 3. Since p is not divisible by 3, either p - 1 or p + 1 is divisible by 3.
  5. Thus (p - 1)(p + 1) is divisible by both 2 and 3, so it is divisible by 6.
Tip: Factor expressions such as p² - 1; the GMAT often hides divisibility in a difference of squares.

Question 23 - Remainders

When positive integer n is divided by 5, the remainder is 3. What is the remainder when 4n + 2 is divided by 5?

A. 0
B. 1
C. 2
D. 4
E. 4

Answer: D. 4

Step-by-step solution:

  1. If n leaves remainder 3 when divided by 5, then n = 5k + 3 for some integer k.
  2. Substitute: 4n + 2 = 4(5k + 3) + 2 = 20k + 12 + 2 = 20k + 14.
  3. 20k is divisible by 5, and 14 leaves a remainder of 4 when divided by 5.
  4. So the remainder is 4.
Tip: Replace n with divisor times an integer plus the remainder.

Question 24 - Absolute Value

How many integer values of x satisfy |2x - 5| < 9?

A. 7
B. 8
C. 9
D. 10
E. 11

Answer: B. 8

Step-by-step solution:

  1. Convert the absolute value inequality: -9 < 2x - 5 < 9.
  2. Add 5 throughout: -4 < 2x < 14.
  3. Divide by 2: -2 < x < 7.
  4. Integer values are -1, 0, 1, 2, 3, 4, 5, and 6. That is 8 values.
  5. The integers that work are -1, 0, 1, 2, 3, 4, 5, and 6, for a total of 8 values.
Tip: For absolute value inequalities of the form |expression| < number, write a compound inequality.

Question 25 - Functions

If f(x) = 2x² - 3x + 1, what is f(-2)?

A. 3
B. 9
C. 15
D. 17
E. 21

Answer: C. 15

Step-by-step solution:

  1. Substitute -2 for x.
  2. f(-2) = 2(-2)² - 3(-2) + 1.
  3. (-2)² = 4, so 2(-2)² = 8.
  4. -3(-2) = 6.
  5. Total = 8 + 6 + 1 = 15.
Tip: Use parentheses when substituting negative numbers into powers.

Question 26 - Sequences

The first term of a sequence is 7. Each term after the first is 5 more than the preceding term. What is the 20th term?

A. 92
B. 97
C. 100
D. 102
E. 107

Answer: D. 102

Step-by-step solution:

  1. This is an arithmetic sequence with first term 7 and common difference 5.
  2. The nth term is aₙ = a₁ + (n - 1)d.
  3. a₂₀ = 7 + (20 - 1)(5) = 7 + 95 = 102.
Tip: For arithmetic sequences, remember that the first term is not increased by d; the second term is.

Question 27 - Revenue and Profit

A store buys a chair for $80 and marks it up by 50%. During a sale, the marked price is discounted by 20%. What is the store's profit on the chair?

A. $12
B. $16
C. $20
D. $24
E. $40

Answer: B. $16

Step-by-step solution:

  1. Cost = $80.
  2. Marked price after 50% markup = 80 × 1.50 = $120.
  3. Sale price after 20% discount = 120 × 0.80 = $96.
  4. Profit = sale price - cost = 96 - 80 = $16.
Tip: Markup and discount apply to different bases. Identify the base for each percent change.

Question 28 - Interest

An investment of $2,000 earns simple interest at an annual rate of 6%. How much interest is earned in 15 months?

A. $120
B. $150
C. $180
D. $200
E. $240

Answer: B. $150

Step-by-step solution:

  1. Simple interest = principal × rate × time.
  2. Principal = 2000, rate = 0.06, time = 15 months = 15⁄12 = 1.25 years.
  3. Interest = 2000 × 0.06 × 1.25 = 120 × 1.25 = $150.
Tip: Convert months to years when the interest rate is annual.

Question 29 - Exponential Growth

A population doubles every 3 years. If the population is 5,000 now, what will it be 9 years from now?

A. 10,000
B. 15,000
C. 20,000
D. 30,000
E. 40,000

Answer: E. 40,000

Step-by-step solution:

  1. A doubling every 3 years means one doubling period is 3 years.
  2. In 9 years, there are 9⁄3 = 3 doubling periods.
  3. Population after 3 doublings = 5,000 × 2³ = 5,000 × 8 = 40,000.
Tip: Count how many growth periods occur; then apply the growth factor that many times.

Question 30 - Data Interpretation

A store sold 120 units in January, 150 in February, and 180 in March. What was the percent increase in monthly sales from January to March?

A. 25%
B. 33.3%
C. 40%
D. 50%
E. 60%

Answer: D. 50%

Step-by-step solution:

  1. Increase from January to March = 180 - 120 = 60 units.
  2. Percent increase = increase ÷ original = 60⁄120 = ½ = 50%.
Tip: In percent increase, always divide by the starting value, not the ending value.

Question 31 - Algebra Translation

A number is increased by 30%, and the result is 52. What is the original number?

A. 36
B. 38
C. 40
D. 42
E. 44

Answer: C. 40

Step-by-step solution:

  1. Let the original number be x.
  2. Increasing by 30% means multiplying by 1.30.
  3. So 1.30x = 52.
  4. x = 52⁄1.30 = 40.
Tip: Translate percent increases into multipliers: 30% increase means 1.30 times the original.

Question 32 - Two-Part Work

A consultant completes ⅓ of a project in 4 days. At that same rate, how many additional days are needed to complete the remaining project?

A. 6
B. 8
C. 10
D. 12
E. 16

Answer: B. 8

Step-by-step solution:

  1. If ⅓ of the project takes 4 days, then the whole project would take 3 × 4 = 12 days at the same rate.
  2. The consultant has already worked 4 days.
  3. Additional days needed = 12 - 4 = 8.
Tip: Scale the part to the whole, then subtract what has already been completed.

Question 33 - Units Conversion

A printer produces 18 pages every 45 seconds. At this rate, how many pages does it produce in 10 minutes?

A. 120
B. 180
C. 216
D. 240
E. 270

Answer: D. 240

Step-by-step solution:

  1. Convert 10 minutes to seconds: 10 × 60 = 600 seconds.
  2. The printer produces 18 pages per 45 seconds.
  3. Number of 45-second intervals in 600 seconds = 600⁄45 = 40⁄3.
  4. Pages produced = 18 × 40⁄3 = 6 × 40 = 240.
Tip: Before setting up a rate, make sure all time units match.

Question 34 - Powers and Units Digit

What is the units digit of 7⁴³?

A. 1
B. 3
C. 7
D. 9
E. 5

Answer: B. 3

Step-by-step solution:

  1. The units digits of powers of 7 repeat in a cycle: 7, 9, 3, 1.
  2. The cycle length is 4.
  3. Find the remainder when 43 is divided by 4: 43 = 4(10) + 3.
  4. The 3rd value in the cycle is 3, not 7. Therefore the correct answer is B. 3.
Tip: For units digits, list the repeating pattern and use the exponent's remainder after division by the cycle length.

Question 35 - Factors

How many positive factors does 72 have?

A. 8
B. 10
C. 12
D. 14
E. 16

Answer: C. 12

Step-by-step solution:

  1. Prime factorize 72: 72 = 8 × 9 = 2³ × 3².
  2. If n = aᵐ bⁿ, the number of positive factors is (m + 1)(n + 1).
  3. For 72, the number of factors is (3 + 1)(2 + 1) = 4 × 3 = 12.
Tip: Use exponents in the prime factorization to count factors quickly.

Question 36 - Least Common Multiple

What is the least positive integer that is divisible by both 18 and 24?

A. 36
B. 48
C. 72
D. 96
E. 144

Answer: C. 72

Step-by-step solution:

  1. Prime factorize: 18 = 2 × 3² and 24 = 2³ × 3.
  2. The least common multiple uses the highest power of each prime: 2³ and 3².
  3. LCM = 8 × 9 = 72.
Tip: For LCM, take the greatest power of each prime factor appearing in the numbers.

Question 37 - Algebraic Fractions

If 1 ∕ a + 1 ∕ b = ⅙ and a = 9, what is b?

A. 9
B. 12
C. 15
D. 18
E. 27

Answer: D. 18

Step-by-step solution:

  1. Substitute a = 9: ⅑ + 1 ∕ b = ⅙.
  2. Subtract ⅑ from both sides: 1 ∕ b = ⅙ - ⅑.
  3. Common denominator 18: ⅙ = 3⁄18 and ⅑ = 2⁄18.
  4. So 1 ∕ b = 1⁄18, which means b = 18.
Tip: When subtracting fractions, find a common denominator before simplifying.

Question 38 - Coordinate/Graph Reasoning

A line has equation y = 3x - 7. What is the x-intercept of the line?

A. -7
B. -7⁄3
C. 0
D. 7⁄3
E. 7

Answer: D. 7⁄3

Step-by-step solution:

  1. The x-intercept occurs where the graph crosses the x-axis, so y = 0.
  2. Set 0 = 3x - 7.
  3. Then 3x = 7, so x = 7⁄3.
Tip: For x-intercepts, set y equal to zero. For y-intercepts, set x equal to zero.

Question 39 - Statistics - Range (Easy)

The range of the numbers 4, 11, 18, 18, and x is 20. If x is greater than 18, what is x?

A. 20
B. 22
C. 24
D. 26
E. 28

Answer: C. 24

Step-by-step solution:

  1. Range = maximum - minimum.
  2. The smallest known value is 4.
  3. Since x is greater than 18, x is the maximum.
  4. So x - 4 = 20.
  5. x = 24.
Tip: Range depends only on the minimum and maximum, not on the middle values.

Question 40 - Optimization / Testing Choices

A positive integer m is 20% greater than positive integer n. Which of the following must be true about m + n?

A. It is divisible by 5.
B. It is divisible by 6.
C. It is divisible by 10.
D. It is divisible by 11.
E. It is odd.

Answer: D. It is divisible by 11.

Step-by-step solution:

  1. m is 20% greater than n, so m = 1.2n = 6n ∕ 5.
  2. Because m is an integer, n must be a multiple of 5. Let n = 5k.
  3. Then m = 6k.
  4. So m + n = 6k + 5k = 11k.
  5. Therefore m + n must be divisible by 11.
Tip: Convert percentages to fractions when integer restrictions are involved.

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