GMAT Quantitative Questions: 15 Practice Problems & Answers

GMAT Quantitative Reasoning questions test arithmetic and elementary algebra, but rarely in a form you would meet in a school textbook. The section gives you 21 Problem Solving questions in 45 minutes, without a calculator, and rewards choosing a short, reliable method more than heavy computation. The fastest way to understand the section is to work through real-style questions, so this guide combines a short overview with 15 original practice questions across the main topics, each with a full explanation.

For a complete overview of the section, its curriculum and pacing, see our Quantitative Reasoning guide. Word problems have their own article with 10 worked examples, so the practice set below focuses on the other question types.

What GMAT Quantitative questions look like

Every question in the Quantitative Reasoning section is a Problem Solving question: a question followed by five answer choices, exactly one of which is correct. Key facts:

• 21 questions in 45 minutes, so about 2 minutes 9 seconds per question on average.
• No calculator. Numbers are chosen so that clean arithmetic, estimation or algebra gets you there.
• Arithmetic and algebra only. Geometry is no longer tested, and Data Sufficiency has moved to the Data Insights section. Our comparison of the current and the classic GMAT explains what changed.
• Adaptive. The section is computer adaptive: the exam uses your responses to previous questions to select the next ones and estimate your ability level. That does not mean every question is harder than the last.
• Two styles of question. Some are pure calculations or equations; many are word problems that hide the same algebra inside a short scenario.

The Quant section score runs from 60 to 90 and carries the same weight in your Total Score as Verbal Reasoning and Data Insights. For the full exam format, see our guide to the GMAT exam pattern and question format.

Topics tested in GMAT Quant

GMAC describes the section as arithmetic and elementary algebra; statistics, counting and probability are treated as part of arithmetic in its study materials, and are listed separately here only to organize the practice. GMAC does not publish how many questions come from each topic, and the mix varies between test-takers, so no single topic is guaranteed to appear. Number properties, percents, ratios and algebra are the foundations most other questions build on, which makes them a good place to start.

How to approach a GMAT Quant question

1. Read the question to the end first. Note exactly what is asked (x, x², a + b) and any condition such as “x is positive” or “n is an integer”.
2. Look at the answer choices. Their spread tells you whether an estimate is enough and whether picking numbers or testing choices could be faster than algebra.
3. Choose a method. Direct algebra, a common base, factoring, picking numbers or working backwards from the choices. Prefer the method with the fewest steps you can do reliably.
4. Write a short setup before you calculate. One line of notation prevents most misreads.
5. Check against the question. Confirm that you answered what was asked and that your answer meets every condition.

For time-saving techniques such as picking numbers and backsolving, see our word problems guide and our article on GMAT strategies.

15 GMAT Quantitative practice questions with explanations

The questions are grouped by topic and labeled with an approximate difficulty. Try each one in about two minutes before reading the explanation, and do not use a calculator.

Question 1: Number properties (Easy)

If n is a positive integer and n² is divisible by 72, what is the smallest possible value of n?

(A) 6
(B) 12
(C) 24
(D) 36
(E) 72

Explanation. Factor 72 = 2³ × 3². For n² to contain 2³, n must contain at least 2² (because squaring doubles every exponent: 2² becomes 2⁴). For 3², n needs 3¹. So the smallest n is 2² × 3 = 12, and 12² = 144 = 2 × 72. Choice (A) is the trap: 6² = 36 is not divisible by 72.

Answer: (B).

Question 2: Percents and ratios (Medium)

The ratio of a to b is 3 : 5, and b is 40% greater than c. What is the ratio of a to c?

(A) 9 : 25
(B) 3 : 5
(C) 7 : 5
(D) 21 : 25
(E) 25 : 21

Explanation. Link both relationships through b. From a : b = 3 : 5, a = 0.6b. From “b is 40% greater than c”, b = 1.4c. So a = 0.6 × 1.4c = 0.84c, and a : c = 84 : 100 = 21 : 25. Picking numbers works too: let c = 100, so b = 140 and a = 84. Choice (E) reverses the ratio, (B) ignores the second relationship, and (A) treats “40% greater” as if it were 40% less (b = 0.6c).

Answer: (D).

Question 3: Exponents (Medium)

If 4^x × 2^x+3 = 8⁵, what is the value of x?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Explanation. Rewrite everything in base 2: 4^x = 2^2x and 8⁵ = 2¹⁵. Then 2^2x × 2^x+3 = 2^3x+3 = 2¹⁵, so 3x + 3 = 15 and x = 4. Converting to a common base is the standard move whenever bases are powers of the same number.

Answer: (C).

Question 4: Roots (Medium)

√50 + √18 − √8 = ?

(A) 2√15
(B) 6√2
(C) 4√5
(D) 8√2
(E) 10√2

Explanation. Simplify each root by pulling out perfect squares: √50 = 5√2, √18 = 3√2 and √8 = 2√2. The total is 5√2 + 3√2 − 2√2 = 6√2. Choice (A) comes from wrongly combining the numbers under the roots (50 + 18 − 8 = 60 = 4 × 15).

Answer: (B).

Question 5: Remainders (Medium)

When the positive integer n is divided by 6, the remainder is 4. What is the remainder when 3n is divided by 6?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Explanation. Write n = 6k + 4. Then 3n = 18k + 12 = 6(3k + 2), which is a multiple of 6, so the remainder is 0. Check with a number: n = 10 gives 3n = 30, and 30 ÷ 6 leaves no remainder. Picking a number like this is a reliable way to confirm remainder questions.

Answer: (A).

Question 6: Absolute value (Medium)

How many integers x satisfy |2x − 5| < 7?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 12

Explanation. Remove the absolute value as a double inequality: −7 < 2x − 5 < 7. Add 5: −2 < 2x < 12. Divide by 2: −1 < x < 6. The integers are 0, 1, 2, 3, 4 and 5, which makes six. Choice (D) counts −1 and 6, which the strict inequality excludes.

Answer: (C).

Question 7: Inequalities (Medium)

If −3 < a < 2 and 1 < b < 4, which of the following could be the value of ab?

(A) −13
(B) −12
(C) −11
(D) 8
(E) 9

Explanation. Test the extremes. The most negative product comes from the most negative a and the largest b: close to −3 × 4 = −12. The largest product comes from the largest a and b: close to 2 × 4 = 8. Because every inequality is strict, ab lies strictly between −12 and 8, so −12 and 8 themselves are impossible. Only −11 fits.

Answer: (C).

Question 8: Quadratics (Medium)

If x² − 5x − 14 = 0 and x > 0, what is the value of x² − 2x?

(A) 14
(B) 21
(C) 28
(D) 35
(E) 49

Explanation. Factor: x² − 5x − 14 = (x − 7)(x + 2), so x = 7 or x = −2. Since x > 0, x = 7, and x² − 2x = 49 − 14 = 35. Read the condition “x > 0” before solving: it tells you which root to keep.

Answer: (D).

Question 9: Systems of equations (Easy)

If 3a + 2b = 17 and 2a + 3b = 13, what is the value of a + b?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Explanation. You do not need a and b separately. Add the two equations: 5a + 5b = 30, so a + b = 6. When the question asks for a combination, look for a way to get that combination directly; here it saves solving the whole system (which gives a = 5, b = 1).

Answer: (C).

Question 10: Functions (Medium)

If f(x) = x² − 3x and f(a + 1) = f(a), what is the value of a?

(A) −2
(B) −1
(C) 0
(D) 1
(E) 2

Explanation. Expand: f(a + 1) = (a + 1)² − 3(a + 1) = a² − a − 2. Setting this equal to a² − 3a gives −a − 2 = −3a, so 2a = 2 and a = 1. Check: f(2) = 4 − 6 = −2 and f(1) = 1 − 3 = −2.

Answer: (D).

Question 11: Sequences (Medium)

In a sequence, a₁ = 3 and a_n = 2a_n−1 − 1 for every n ≥ 2. What is a₆?

(A) 17
(B) 33
(C) 63
(D) 65
(E) 129

Explanation. Build the terms: 3, 5, 9, 17, 33, 65. You may notice the pattern a_n = 2ⁿ + 1, which confirms a₆ = 64 + 1 = 65. Choice (B) is a₅: count the terms carefully.

Answer: (D).

Question 12: Statistics: mean and median (Medium)

The set {2, 5, 9, 12, x} has a mean equal to its median. If x > 12, what is the value of x?

(A) 9
(B) 12
(C) 15
(D) 17
(E) 20

Explanation. Because x > 12, it is the largest value, so the median is the middle value, 9. The mean is (2 + 5 + 9 + 12 + x) ÷ 5 = (28 + x) ÷ 5. Setting this equal to 9 gives 28 + x = 45 and x = 17, which does satisfy x > 12.

Answer: (D).

Question 13: Statistics: standard deviation (Hard)

Which of the following changes to the set {10, 20, 30, 40, 50} would decrease its standard deviation?

(A) Adding the numbers 10 and 50
(B) Adding the number 30
(C) Adding 5 to every number
(D) Multiplying every number by 2
(E) Replacing 50 with 60

Explanation. Standard deviation measures how far values sit from the mean (30). Adding a value equal to the mean leaves the mean unchanged and adds nothing to the sum of squared deviations, but it increases the number of values, so the average squared deviation, and with it the standard deviation, falls. Adding 10 and 50 adds two far-away values (increase); adding 5 to every number shifts the set without changing the spread (no change); doubling every number doubles the spread (increase); replacing 50 with 60 pushes a value further out (increase). GMAT standard deviation questions are conceptual like this: you rarely need to calculate one.

Answer: (B).

Question 14: Counting (Medium)

How many three-digit positive integers have three different digits, all of them odd?

(A) 60
(B) 75
(C) 100
(D) 120
(E) 125

Explanation. There are five odd digits (1, 3, 5, 7, 9), and none of them is 0, so every arrangement is a valid three-digit number. Choose the hundreds digit in 5 ways, the tens digit in 4 and the units digit in 3: 5 × 4 × 3 = 60. Choice (E), 5³ = 125, allows repeated digits.

Answer: (A).

Question 15: Probability (Hard)

A bag contains 4 red and 6 blue marbles. Two marbles are drawn at random without replacement. What is the probability that they are the same color?

(A) 1/3
(B) 2/5
(C) 7/15
(D) 8/15
(E) 13/25

Explanation. Count pairs. Total pairs: 10 × 9 ÷ 2 = 45. Two red: 4 × 3 ÷ 2 = 6. Two blue: 6 × 5 ÷ 2 = 15. So the probability is (6 + 15) ÷ 45 = 21/45 = 7/15. Choice (E), 13/25, is the answer with replacement: (4/10)² + (6/10)² = 0.52. “Without replacement” changes the denominator on the second draw.

Answer: (C).

Answer key

1 B, 2 D, 3 C, 4 B, 5 A, 6 C, 7 C, 8 D, 9 C, 10 D, 11 D, 12 D, 13 B, 14 A, 15 C.

Common mistakes on GMAT Quant

• Answering a different question. Solving for x when the question asks for x² or a + b.
• Ignoring conditions. Missing “positive”, “integer” or “different digits”, which often rules out an answer that otherwise looks right.
• Strict versus inclusive inequalities. Counting the endpoints when the inequality is “less than”.
• Calculating when you could simplify. Multiplying out large numbers instead of factoring or converting to a common base.
• Replacement in probability. Treating draws “without replacement” as independent.
• Sinking time into one question. Spending four minutes on a question costs you time you need for the rest of the section.

Timing on GMAT Quant

With 45 minutes for 21 questions, the average is about 2 minutes 9 seconds per question, but treat it as a reference rather than a deadline: Question 9 above should take under a minute, while a hard probability question may take close to three. Two simple checkpoints help: aim to finish question 7 by about the 15-minute mark and question 14 by about the 30-minute mark. These checkpoints do not create extra time; they help you stay close to the average pace and notice early if you are falling behind.

If you reach your personal cut-off without a clear path, eliminate the choices you can, select your best answer, bookmark the question and move on. The GMAT does not let you skip a question, but once you have answered every question in the section, you can return to bookmarked questions if time remains and change up to three answers. Never leave questions unanswered at the end: unanswered questions carry a significant score penalty.

How to practise GMAT Quant questions

• Start by topic, untimed. Work through one topic at a time until the standard methods feel automatic.
• Move to mixed, timed sets. On test day nothing tells you which topic a question belongs to, so practise recognizing it yourself.
• Review every mistake by cause. Was it a missing concept, a wrong method, a calculation slip or time? Each needs a different fix; see how to measure your GMAT prep progress.
• Use official questions too. GMAC’s free Official Starter Kit includes official practice questions and two full-length practice exams.
• Plan the work. Our guide on how to prepare for the GMAT sets out phases, timelines and an example study week.

Frequently asked questions

How many Quantitative questions are on the GMAT?

The Quantitative Reasoning section has 21 questions in 45 minutes. All of them are Problem Solving questions with five answer choices.

Is geometry on GMAT Quant?

No. The current GMAT does not test geometry in the Quantitative Reasoning section. It focuses on arithmetic and algebra, including number properties, percents, ratios, statistics, counting and probability.

Can I use a calculator on GMAT Quant?

No. A calculator is not available in Quantitative Reasoning. An on-screen calculator is available only in the Data Insights section, and you cannot bring your own.

Are Data Sufficiency questions part of Quant?

Not any more. Data Sufficiency questions now appear in the Data Insights section, together with Multi-Source Reasoning, Table Analysis, Graphics Interpretation and Two-Part Analysis.

Which Quant topics are hardest?

It depends on your background, but many test-takers find probability, counting, statistics concepts and number properties hardest because they reward a precise setup rather than routine calculation. Your diagnostic results are the best guide to where to focus.

Key takeaways

• GMAT Quant has 21 Problem Solving questions in 45 minutes, with no calculator and no geometry.
• The section tests arithmetic (including number properties, percents, ratios, statistics, counting and probability) and elementary algebra, often through word problems.
• Read the whole question and the answer choices before choosing a method; the shortest reliable route usually wins.
• Use the average time as a reference, answer every question and save review time for a few bookmarked questions.

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