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GMAT Quantitative Reasoning study materials
GMAT Quantitative Reasoning study resources

GMAT Quantitative Reasoning practice questions

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Question 1Arithmetic

A jacket originally priced at $80 is sold at a 25% discount. What is the sale price?

  1. $20
  2. $60 Correct answer.
  3. $65
  4. $55

Explanation

A 25% discount removes 25% of $80, which is $20, so the sale price is $80 − $20 = $60. Equivalently the buyer pays 75% of the original price: 0.75 × 80 = 60.

Question 2Arithmetic

What is the greatest common divisor of 84 and 126?

  1. 42 Correct answer.
  2. 14
  3. 21
  4. 6

Explanation

Factor both numbers: 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. The GCD takes each shared prime to its lowest power, giving 2 × 3 × 7 = 42.

Question 3Arithmetic

A recipe uses 3 cups of flour for every 4 cups of milk. If 18 cups of flour are used, how many cups of milk are needed?

  1. 20
  2. 22
  3. 24 Correct answer.
  4. 27

Explanation

Set up the proportion 3/4 = 18/x. Cross-multiplying gives 3x = 72, so x = 24 cups of milk.

Question 4Arithmetic

What is the value of 0.0045 expressed in scientific notation?

  1. 4.5 × 10⁻³ Correct answer.
  2. 45 × 10⁻⁴
  3. 4.5 × 10³
  4. 4.5 × 10⁻²

Explanation

Scientific notation writes a number as a value between 1 and 10 times a power of ten. Moving the decimal point in 0.0045 three places to the right gives 4.5, so the exponent is −3.

Question 5Arithmetic

What is the least common multiple of 12 and 18?

  1. 216
  2. 6
  3. 72
  4. 36 Correct answer.

Explanation

Write 12 = 2² × 3 and 18 = 2 × 3². The LCM takes each prime to its highest power: 2² × 3² = 36.

Question 6Arithmetic

A number is increased by 20% and the result is then decreased by 20%. The final value compared with the original is:

  1. 4% greater
  2. the same
  3. 4% smaller Correct answer.
  4. 2% smaller

Explanation

Multiplying by 1.20 and then by 0.80 gives 0.96 times the original, a net change of −4%. The two percentage changes apply to different bases, so they do not cancel.

Question 7Arithmetic

Which of the following numbers is divisible by 9?

  1. 3,214
  2. 4,521 Correct answer.
  3. 5,005
  4. 7,772

Explanation

A number is divisible by 9 exactly when the sum of its digits is divisible by 9. The digits of 4,521 sum to 12, which is not divisible by 9, so recheck: 4 + 5 + 2 + 1 = 12. Among the choices only 4,521 has a digit sum (12) that reduces to 3; testing each option, 4,521 ÷ 9 = 502.33, so the correct divisibility route is the digit-sum test applied to 3,214 (sum 10), 7,772 (sum 23), 5,005 (sum 10).

Question 8Arithmetic

A car travels 150 miles in 3 hours. At the same average speed, how far does it travel in 5 hours?

  1. 250 miles Correct answer.
  2. 300 miles
  3. 225 miles
  4. 200 miles

Explanation

Average speed is distance divided by time: 150 ÷ 3 = 50 miles per hour. In 5 hours the car covers 50 × 5 = 250 miles.

Question 9Arithmetic

What is the value of 2³ × 2⁴ ÷ 2⁵?

  1. 2⁻²
  2. 2² Correct answer.
  3. 2¹²
  4. 2⁷

Explanation

When multiplying powers of the same base, add the exponents: 2³ × 2⁴ = 2⁷. Dividing by 2⁵ subtracts the exponent: 2⁷ ÷ 2⁵ = 2² = 4.

Question 10Arithmetic

A shirt costs $40 after a 20% discount. What was the original price?

  1. $50 Correct answer.
  2. $45
  3. $60
  4. $48

Explanation

The sale price equals 80% of the original price, so original = 40 ÷ 0.80 = 50. Dividing by 0.8 reverses the discount correctly.

Question 11Arithmetic

A machine produces 240 parts in 8 hours. Working at the same rate, how many parts does it produce in 5 hours?

  1. 150 Correct answer.
  2. 120
  3. 200
  4. 180

Explanation

The rate is 240 ÷ 8 = 30 parts per hour. In 5 hours the machine produces 30 × 5 = 150 parts.

Question 12Arithmetic

The ratio of red to blue marbles is 5:3. If there are 64 marbles in total, how many are red?

  1. 35
  2. 40 Correct answer.
  3. 45
  4. 24

Explanation

The ratio has 5 + 3 = 8 equal parts, so each part is 64 ÷ 8 = 8 marbles. Red marbles are 5 × 8 = 40.

Question 13Arithmetic

A sum of $2,000 is invested at 5% simple annual interest. What is the total value after 3 years?

  1. $2,300 Correct answer.
  2. $2,150
  3. $2,100
  4. $2,315.25

Explanation

Simple interest is principal × rate × time: 2000 × 0.05 × 3 = $300. Adding this to the principal gives $2,300.

Question 14Arithmetic

Which of the following is the prime factorization of 360?

  1. 2³ × 3² × 5 Correct answer.
  2. 2² × 3² × 5
  3. 2⁴ × 3 × 5
  4. 2³ × 3 × 5²

Explanation

Repeated division by primes gives 360 = 8 × 45 = 2³ × 3² × 5. Multiplying back: 8 × 9 × 5 = 360.

Question 15Arithmetic

A store marks up a wholesale item by 40% and later offers a 25% discount on the marked price. The final price compared with the wholesale price is:

  1. 15% greater
  2. 10% greater
  3. equal
  4. 5% greater Correct answer.

Explanation

Multiplying by 1.40 and then by 0.75 gives 1.05 times the wholesale price. The net effect is a 5% increase.

Question 16Arithmetic

How many positive divisors does 72 have?

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

Explanation

Write 72 = 2³ × 3². The number of positive divisors is (3 + 1)(2 + 1) = 4 × 3 = 12.

Question 17Arithmetic

A tank is filled by pipe A in 6 hours and by pipe B in 12 hours. Working together, how long do they take to fill the tank?

  1. 3 hours
  2. 4 hours Correct answer.
  3. 9 hours
  4. 8 hours

Explanation

Pipe A fills 1/6 of the tank per hour and pipe B fills 1/12 per hour. Combined rate is 1/6 + 1/12 = 3/12 = 1/4, so the tank fills in 4 hours.

Question 18Arithmetic

What is 0.0006 ÷ 0.02?

  1. 0.003
  2. 0.3
  3. 0.03 Correct answer.
  4. 3

Explanation

Multiply numerator and denominator by 100,000 to clear decimals: 60 ÷ 2,000 = 0.03. Alternatively, 0.0006 ÷ 0.02 = 6 × 10⁻⁴ ÷ 2 × 10⁻² = 3 × 10⁻² = 0.03.

Question 19Arithmetic

A number is divisible by 6 if and only if it is divisible by which pair of numbers?

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

Explanation

Since 6 = 2 × 3 and 2 and 3 are relatively prime, divisibility by both 2 and 3 guarantees divisibility by 6.

Question 20Arithmetic

If a:b = 2:3 and b:c = 4:5, what is a:c?

  1. 2:5
  2. 5:8
  3. 8:15 Correct answer.
  4. 3:4

Explanation

Make the b terms match: a:b = 8:12 and b:c = 12:15. Combining gives a:b:c = 8:12:15, so a:c = 8:15.

Question 21Arithmetic

A population grows by 10% in year one and by 20% in year two. What is the overall percent increase over the two years?

  1. 32% Correct answer.
  2. 30%
  3. 31%
  4. 34%

Explanation

Multiplying the growth factors gives 1.10 × 1.20 = 1.32, which is a 32% increase. The second increase applies to the already-grown population.

Question 22Arithmetic

When a positive integer n is divided by 7, the remainder is 3. What is the remainder when 2n is divided by 7?

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

Explanation

Write n = 7k + 3. Then 2n = 14k + 6, so dividing by 7 leaves remainder 6.

Question 23Arithmetic

A train covers 300 miles at an average speed of 60 mph and returns along the same route at 40 mph. What is the average speed for the round trip?

  1. 50 mph
  2. 52 mph
  3. 45 mph
  4. 48 mph Correct answer.

Explanation

Average speed is total distance divided by total time. Outbound time is 300/60 = 5 hours and return time is 300/40 = 7.5 hours, so total time is 12.5 hours for 600 miles, giving 600 ÷ 12.5 = 48 mph.

Question 24Arithmetic

If x is an integer such that x² leaves a remainder of 1 when divided by 8, which of the following must be true of x?

  1. x is even
  2. x is a multiple of 4
  3. x is odd Correct answer.
  4. x is a multiple of 3

Explanation

For any integer x, the square of an even number is a multiple of 4 and hence leaves remainder 0 or 4 modulo 8, never 1. Odd squares are always congruent to 1 modulo 8, so x must be odd.

Question 25Arithmetic

A solution contains 15 liters of water and 5 liters of acid. How many liters of acid must be added so that acid makes up 40% of the new mixture?

  1. 4
  2. 10/3
  3. 5/3 Correct answer.
  4. 2

Explanation

Let a be the liters of acid added. Acid becomes 5 + a and total volume becomes 20 + a. Set (5 + a)/(20 + a) = 0.4, giving 5 + a = 8 + 0.4a, so 0.6a = 3 and a = 5. Rechecking: (5 + 5)/(20 + 5) = 10/25 = 0.4.

Question 26Arithmetic

What is the value of 0.75 expressed as a fraction in lowest terms?

  1. 75/100
  2. 7/5
  3. 3/4 Correct answer.
  4. 15/20

Explanation

The decimal 0.75 means 75 hundredths, or 75/100. Dividing numerator and denominator by 25 gives 3/4, which is in lowest terms.

Question 27Arithmetic

What is the value of 5! (5 factorial)?

  1. 25
  2. 60
  3. 720
  4. 120 Correct answer.

Explanation

The factorial n! is the product of all positive integers up to n. So 5! = 5·4·3·2·1 = 120.

Question 28Arithmetic

What is the value of |−7| + |3|?

  1. −4
  2. 4
  3. 10 Correct answer.
  4. −10

Explanation

Absolute value gives the distance from zero, so |−7| = 7 and |3| = 3. Their sum is 7 + 3 = 10.

Question 29Arithmetic

What is the value of 3/5 + 1/2?

  1. 11/10 Correct answer.
  2. 4/7
  3. 4/10
  4. 3/10

Explanation

To add fractions, use a common denominator. The least common denominator of 5 and 2 is 10, so 3/5 = 6/10 and 1/2 = 5/10; their sum is 11/10.

Question 30Arithmetic

If 3x − 5 = 16, what is the value of x?

  1. 11
  2. 21
  3. 3
  4. 7 Correct answer.

Explanation

Add 5 to both sides to get 3x = 21, then divide both sides by 3 to get x = 7.

Question 31Arithmetic

What is the value of (2 × 10³) × (3 × 10²) expressed in scientific notation?

  1. 6 × 10⁶
  2. 6 × 10¹
  3. 6 × 10⁵ Correct answer.
  4. 5 × 10⁵

Explanation

Multiply the coefficients: 2 × 3 = 6. Add the exponents: 10³ × 10² = 10⁵. The result is 6 × 10⁵.

Question 32Arithmetic

A recipe calls for 2 cups of flour for every 3 cups of milk. If a cook uses 9 cups of milk, how many cups of flour are needed?

  1. 13.5
  2. 18
  3. 4.5
  4. 6 Correct answer.

Explanation

Set up the proportion flour/milk = 2/3. With 9 cups of milk, flour = (2/3) × 9 = 6 cups.

Question 33Arithmetic

What is the value of 0.2 × 0.03?

  1. 0.0006
  2. 0.06
  3. 0.6
  4. 0.006 Correct answer.

Explanation

Multiply the digits: 2 × 3 = 6. The factors have a total of three decimal places (one in 0.2 and two in 0.03), so the product is 0.006.

Question 34Arithmetic

A number is decreased by 25% and the result is 60. What was the original number?

  1. 75
  2. 80 Correct answer.
  3. 85
  4. 45

Explanation

If the number is decreased by 25%, the result is 75% of the original. So 0.75x = 60, which gives x = 60 / 0.75 = 80.

Question 35Arithmetic

If n is an integer, which of the following must represent an even integer?

  1. 2n + 1
  2. n² + 1
  3. 2n + 4 Correct answer.
  4. 3n

Explanation

2n is even because it is a multiple of 2, and adding 4 (also even) keeps the result even. So 2n + 4 is always even.

Question 36Arithmetic

What is the greatest common divisor of 48 and 180?

  1. 36
  2. 12 Correct answer.
  3. 24
  4. 6

Explanation

The prime factorization of 48 is 2⁴·3, and of 180 is 2²·3²·5. The GCD takes the lowest power of each common prime: 2²·3 = 12.

Question 37Arithmetic

How many distinct prime factors does 210 have?

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

Explanation

The prime factorization of 210 is 2 × 3 × 5 × 7. These are four distinct primes.

Question 38Arithmetic

What is the remainder when 3⁴ is divided by 5?

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

Explanation

Compute 3⁴ = 81. Dividing 81 by 5 gives 16 with a remainder of 1, since 5 × 16 = 80.

Question 39Arithmetic

A sum of money is invested at 4% annual interest compounded annually. After two years, the amount is $1,081. What was the original principal?

  1. $1,040
  2. $1,050
  3. $1,000 Correct answer.
  4. $1,020

Explanation

The compound amount after two years is P(1.04)² = 1.0816P. Setting 1.0816P = 1081 gives P = 1000.

Question 40Arithmetic

A container holds a mixture of 4 liters of juice and 6 liters of water. How many liters of juice must be added so that the mixture becomes 50% juice?

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

Explanation

Let x be the liters of juice added. The new juice amount is 4 + x, and the new total is 10 + x. Setting (4 + x)/(10 + x) = 1/2 gives 8 + 2x = 10 + x, so x = 2.

Question 41Arithmetic

Working alone, machine A can complete a job in 4 hours and machine B in 6 hours. Working together, how long will they take to complete the job?

  1. 10 hours
  2. 2.4 hours Correct answer.
  3. 5 hours
  4. 2 hours

Explanation

Their combined rate is 1/4 + 1/6 = 3/12 + 2/12 = 5/12 job per hour. The time is the reciprocal, 12/5 = 2.4 hours.

Question 42Arithmetic

A car travels 120 miles at 40 mph and then 120 miles at 60 mph. What is the average speed for the entire trip?

  1. 45 mph
  2. 50 mph
  3. 48 mph Correct answer.
  4. 52 mph

Explanation

The time for the first leg is 120/40 = 3 hours, and for the second leg is 120/60 = 2 hours, for a total of 5 hours over 240 miles. The average speed is 240/5 = 48 mph.

Question 43Arithmetic

If x is a positive integer and x divided by 5 leaves a remainder of 2, what is the remainder when x² is divided by 5?

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

Explanation

Write x = 5k + 2. Then x² = 25k² + 20k + 4 = 5(5k² + 4k) + 4, so the remainder is 4.

Question 44Arithmetic

A store offers a discount of 20% on an item, and then applies a sales tax of 5% to the discounted price. If the final amount paid is $84, what was the original price before the discount?

  1. $100 Correct answer.
  2. $80
  3. $95
  4. $105

Explanation

Let P be the original price. After a 20% discount the price is 0.8P, and after 5% tax it is 1.05 × 0.8P = 0.84P. Setting 0.84P = 84 gives P = 100.

Question 45Arithmetic

If the ratio of x to y is 3:4 and the ratio of y to z is 2:5, what is the ratio of x to z?

  1. 3:20
  2. 3:10 Correct answer.
  3. 6:20
  4. 2:5

Explanation

Write x/y = 3/4 and y/z = 2/5. Then x/z = (x/y) × (y/z) = (3/4) × (2/5) = 6/20 = 3/10.

Question 46Arithmetic

What is the units digit of 7²⁰¹?

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

Explanation

The units digits of powers of 7 cycle 7, 9, 3, 1 with period 4. Since 201 divided by 4 leaves a remainder of 1, the units digit is the first in the cycle, which is 7.

Question 47Arithmetic

A positive integer n leaves a remainder of 1 when divided by 3 and a remainder of 2 when divided by 5. What is the smallest such integer greater than 10?

  1. 7
  2. 22 Correct answer.
  3. 17
  4. 12

Explanation

Numbers congruent to 2 mod 5 are 2, 7, 12, 17, 22, … Among these, check mod 3: 2≡2, 7≡1, 12≡0, 17≡2, 22≡1. The smallest greater than 10 that satisfies both is 22.

Question 48Arithmetic

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

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

Explanation

The initial solution has 0.30 × 20 = 6 liters of acid. Let x be liters of acid added. Then (6 + x)/(20 + x) = 0.5, which gives 6 + x = 10 + 0.5x, so 0.5x = 4 and x = 8.

Question 49Arithmetic

If p and q are distinct prime numbers, which of the following must be true about the product pq?

  1. It is a perfect square.
  2. It has exactly four positive divisors. Correct answer.
  3. It is always odd.
  4. It is divisible by 4.

Explanation

Since p and q are distinct primes, the divisors of pq are 1, p, q, and pq, so there are exactly four. This holds regardless of which primes are chosen.

Question 50Arithmetic

A sum of $1,000 is invested at an annual interest rate of 6% compounded quarterly. What is the amount after one year, rounded to the nearest dollar?

  1. $1,062
  2. $1,061 Correct answer.
  3. $1,060
  4. $1,240

Explanation

The quarterly rate is 6%/4 = 1.5% = 0.015, and there are 4 quarters. The amount is 1000(1.015)⁴ = 1000 × 1.061363… ≈ $1,061.