Watch the video: 15 GMAT Quant practice questions solved
The video below works through 15 GMAT-style Quantitative Reasoning practice questions, read aloud, set up cleanly, and solved without a calculator. Watch it first, then use the written questions underneath to test yourself: each one shows the full prompt and answer choices, and hides the correct answer and full solution behind a "Show detailed answer" panel so you can attempt the problem before you peek. The goal is not to memorize 15 answers — it is to internalize a repeatable setup for percents, algebra, sequences, fractions, rates, and number properties so the easy and medium bands become automatic.
This is a study guide and video companion. Play a question in the video, pause, attempt it yourself on paper under a soft two-minute timer, then open the "Show detailed answer" panel below the matching question to check your setup. Every question here starts with its exact opening words, followed by the full prompt, the answer choices, and — once revealed — the correct answer, a step-by-step solution, and a reusable GMAT takeaway.
Quick-answer key for all 15 questions
Use this to self-check fast after your first attempt. The full hidden solution for each question follows below, in the same order as the video.
| # | Topic | Correct answer |
|---|---|---|
| 1 | Percentage points vs percent (two stocks) | 11.5 |
| 2 | Algebraic cost expression | 2h + v(s + t) |
| 3 | Arithmetic sequence | 10 |
| 4 | Terminating decimals × 10z | 18 |
| 5 | Percent increase vs percentage points | 10% |
| 6 | Coin denominations (count possible) | I and III only |
| 7 | Subscription discount | 36 |
| 8 | Two-variable linear constraints | 6,000 |
| 9 | Fraction arithmetic (pizza pieces) | 17/24 |
| 10 | Conditional fractions within subgroups | 1/5 |
| 11 | Percent-to-fraction conversion | 1/400 |
| 12 | Rate × time × units (toll station) | $23,000 |
| 13 | Profit as a percent of cost | $2,400 |
| 14 | Divisibility by 9 with powers of ten | 47 |
| 15 | Average replacement (in terms of t) | t − 2/3 |
Question list — jump to the one you searched for
- "At the opening of a trading day, stock X had a value of $40.00 per share…"
- "The cost of purchasing each box of candy from a certain mail order catalog…"
- "In the arithmetic sequence t1, t2, t3, ..., tn, ..., t1 = 23…"
- "What is the least integer z for which (0.000125)(0.0025)(0.00000125) × 10^z…"
- "The annual interest rate earned by an investment increased by 10 percent…"
- "The United States mint produces coins in 1-cent, 5-cent, 10-cent…"
- "When a subscription to a new magazine was purchased for m months…"
- "A manufacturer wants to produce x balls and y boxes…"
- "Half of a large pizza is cut into 4 equal-sized pieces…"
- "Of all the students in a certain dormitory, 1/2 are first-year students…"
- "The price of a certain stock increased by 0.25 of 1 percent…"
- "A certain toll station on a highway has 7 tollbooths…"
- "A store's selling price of $2,240 for a certain computer…"
- "A positive integer is divisible by 9 if and only if the sum of its digits…"
- "The average (arithmetic mean) length per film for a group of 21 films…"
The 15 GMAT Quant questions with hidden answers
The questions below follow the order of the video. For each one you get the opening words, the full prompt, and the answer choices. Attempt it, then open "Show detailed answer" to reveal the correct answer, a step-by-step explanation, and a GMAT takeaway you can reuse on test day.
1. "At the opening of a trading day, stock X had a value of $40.00 per share…" (percentage points vs percent)
"At the opening of a trading day, stock X had a value of $40.00 per share and stock Y had a value of $25.00 per share. At the closing of the trading day, stock X had a value of $41.00 per share and stock Y had a value of $28.50 per share. For this trading day, the percent increase in the value of stock Y was how many percentage points greater than the percent increase in the value of stock X?"
- 2.5
- 6.25
- 10
- 11.5
- 12.5
Show detailed answer
Correct answer: 11.5
Step by step: compute each percent increase from its own starting value. Stock X rose by $1 on a $40 base, so its increase is 1/40 = 2.5%. Stock Y rose by $3.50 on a $25 base, so its increase is 3.5/25 = 14%. The question asks how many percentage points greater Y's increase is: 14 − 2.5 = 11.5.
GMAT takeaway: always compute each percent increase from its own starting value, and read "percentage points" as a simple subtraction of two percents — not a percent of a percent.
2. "The cost of purchasing each box of candy from a certain mail order catalog…" (algebraic cost expression)
"The cost of purchasing each box of candy from a certain mail order catalog is v dollars per pound of candy, plus a shipping charge of h dollars. How many dollars does it cost to purchase 2 boxes of candy, one containing s pounds of candy and the other containing t pounds of candy, from this catalog?"
- h + stv
- 2h + stv
- 2hstv
- 2h + s + t + v
- 2h + v(s + t)
Show detailed answer
Correct answer: 2h + v(s + t)
Step by step: price each box separately. The first box holds s pounds, so it costs sv + h. The second box holds t pounds, so it costs tv + h. The shipping charge h applies to each box, not once per order. Add them: sv + h + tv + h = v(s + t) + 2h = 2h + v(s + t).
GMAT takeaway: watch whether a fixed fee applies once per order or once per item. Here shipping is charged per box, so it appears twice.
3. "In the arithmetic sequence t1, t2, t3, ..., tn, ..., t1 = 23…" (arithmetic sequence)
"In the arithmetic sequence t1, t2, t3, ..., tn, ..., t1 = 23 and tn = t(n−1) − 3 for each n > 1. What is the value of n when tn = −4?"
- −1
- 7
- 10
- 14
- 20
Show detailed answer
Correct answer: 10
Step by step: the recurrence subtracts 3 each step, so the common difference is −3 and the general term is tn = 23 − 3(n − 1). Set it equal to −4: 23 − 3(n − 1) = −4, so −3(n − 1) = −27, giving n − 1 = 9 and n = 10. Listing confirms it: 23, 20, 17, 14, 11, 8, 5, 2, −1, −4 — and −4 is the 10th term.
GMAT takeaway: for an arithmetic sequence, either list the terms carefully or use first term plus common difference times (n − 1). Both are fast; the formula scales when the term index is large.
4. "What is the least integer z for which (0.000125)(0.0025)(0.00000125) × 10^z…" (terminating decimals)
"What is the least integer z for which (0.000125)(0.0025)(0.00000125) × 10z is an integer?"
- 18
- 10
- 0
- −10
- −18
Show detailed answer
Correct answer: 18
Step by step: count decimal places. 0.000125 has 6, 0.0025 has 4, and 0.00000125 has 8, for a total of 6 + 4 + 8 = 18 decimal places in the product. Numerically the product equals 390625 / 1018, so multiplying by 1018 gives 390625, an integer. Any smaller power of 10 leaves a decimal, so the least such integer is z = 18.
GMAT takeaway: for products of terminating decimals, counting decimal places is usually faster than long multiplication — the total number of places tells you the power of 10 you need.
5. "The annual interest rate earned by an investment increased by 10 percent…" (percent increase vs percentage points)
"The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year?"
- 1%
- 1.1%
- 9.1%
- 10%
- 10.8%
Show detailed answer
Correct answer: 10%
Step by step: a 10 percent increase multiplies last year's rate by 1.10. Let last year's rate be r; then 1.10r = 11%, so r = 11% ÷ 1.10 = 10%. Do not subtract 10 percentage points to get 1% — the "10 percent" here is a relative increase, not a point change.
GMAT takeaway: distinguish a percent increase (multiply by 1 + rate) from a percentage-point increase (add/subtract points). The wording "increased by 10 percent" means multiply.
6. "The United States mint produces coins in 1-cent, 5-cent, 10-cent…" (coin denominations)
"The United States mint produces coins in 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent denominations. If a jar contains exactly 100 cents worth of these coins, which of the following could be the total number of coins in the jar? I. 91 II. 81 III. 76"
- I only
- II only
- III only
- I and III only
- I, II, and III
Show detailed answer
Correct answer: I and III only
Step by step: start from 100 pennies, which is 100 coins, and track how each larger coin reduces the count. Replacing 5 pennies with a nickel drops the count by 4; a dime by 9; a quarter by 24; a half-dollar by 49. For I (91 coins) you need a reduction of 9 — replace 10 pennies with one dime. Possible. For II (81 coins) you need a reduction of 19, but no nonnegative combination of 4, 9, 24, and 49 sums to 19. Not possible. For III (76 coins) you need a reduction of 24 — replace 25 pennies with one quarter. Possible. So the answer is I and III only.
GMAT takeaway: for coin-count problems, start from all pennies and translate each swap into how much it lowers the number of coins. Then it becomes a small "which reductions are reachable" question.
7. "When a subscription to a new magazine was purchased for m months…" (subscription discount)
"When a subscription to a new magazine was purchased for m months, the publisher offered a discount of 75 percent off the regular monthly price of the magazine. If the total value of the discount was equivalent to buying the magazine at its regular monthly price for 27 months, what was the value of m?"
- 18
- 24
- 30
- 36
- 48
Show detailed answer
Correct answer: 36
Step by step: let the regular monthly price be p. A 75% discount over m months saves 0.75 × m × p in total. That equals the price of 27 months, or 27p. Cancel p: 0.75m = 27. Since 0.75 = 3/4, m = 27 ÷ (3/4) = 27 × 4/3 = 36.
GMAT takeaway: assign a simple variable to the unknown price, then cancel it when only relative value matters. The answer never depends on the actual price here.
8. "A manufacturer wants to produce x balls and y boxes…" (two-variable linear constraints)
"A manufacturer wants to produce x balls and y boxes. Resource constraints require that x and y satisfy the inequalities 7x + 6y ≤ 38,000 and 4x + 5y ≤ 28,000. What is the maximum number of balls and boxes combined that can be produced given the resource constraints?"
- 5,000
- 6,000
- 7,000
- 8,000
- 10,000
Show detailed answer
Correct answer: 6,000
Step by step: maximize x + y subject to both constraints; the optimum for a linear objective sits at a corner, usually where the two lines cross. Solve 7x + 6y = 38,000 and 4x + 5y = 28,000. Multiply the first by 5 (35x + 30y = 190,000) and the second by 6 (24x + 30y = 168,000), then subtract: 11x = 22,000, so x = 2,000. Substitute into 4x + 5y = 28,000: 8,000 + 5y = 28,000, so y = 4,000. Then x + y = 6,000. Checking the axis endpoints gives smaller totals, so 6,000 is the maximum.
GMAT takeaway: for a two-variable linear constraint problem, test the intersection of the constraint lines and the relevant endpoints — the maximum of a linear objective is always at a corner of the feasible region.
9. "Half of a large pizza is cut into 4 equal-sized pieces…" (fraction arithmetic)
"Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?"
- 5/12
- 13/24
- 7/12
- 2/3
- 17/24
Show detailed answer
Correct answer: 17/24
Step by step: express each piece as a fraction of the whole pizza. The larger pieces come from half the pizza cut into 4, so each is (1/2) ÷ 4 = 1/8. The smaller pieces come from half cut into 6, so each is (1/2) ÷ 6 = 1/12. Eaten = 1/8 + 2(1/12) = 3/24 + 4/24 = 7/24. Remaining = 1 − 7/24 = 17/24.
GMAT takeaway: always express each piece as a fraction of the whole, not of its half. The "half" is a trap that makes 1/4 and 1/6 look like the piece sizes.
10. "Of all the students in a certain dormitory, 1/2 are first-year students…" (conditional fractions)
"Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?"
- 1/15
- 1/5
- 4/15
- 1/3
- 2/5
Show detailed answer
Correct answer: 1/5
Step by step: among first-year students, 4/5 have not declared, so 1/5 have declared. The fraction of second-year students who declared is 3 × 1/5 = 3/5, which leaves 2/5 of second-year students not declared. Second-year students are 1/2 of the dorm, so the share of all students who are second-year and undeclared is (1/2) × (2/5) = 1/5.
GMAT takeaway: keep the fraction within a subgroup separate from the fraction of the total. Multiply the subgroup's share of the whole by the within-subgroup fraction only at the end.
11. "The price of a certain stock increased by 0.25 of 1 percent…" (percent-to-fraction conversion)
"The price of a certain stock increased by 0.25 of 1 percent on a certain day. By what fraction did the price of the stock increase that day?"
- 1/2500
- 1/400
- 1/40
- 1/25
- 1/4
Show detailed answer
Correct answer: 1/400
Step by step: read the phrase literally. "1 percent" is 1/100, and "0.25 of 1 percent" is 0.25 × 1/100 = 0.25/100 = 0.0025. As a fraction, 0.0025 = 25/10,000 = 1/400.
GMAT takeaway: convert percent language into fractions carefully. "0.25 of 1 percent" is a quarter of one percent (1/400), not 25 percent — the phrase "of 1 percent" is doing real work.
12. "A certain toll station on a highway has 7 tollbooths…" (rate × time × units)
"A certain toll station on a highway has 7 tollbooths, and each tollbooth collects $0.75 from each vehicle that passes it. From 6 o'clock yesterday morning to 12 o'clock midnight, vehicles passed each of the tollbooths at the average rate of 4 vehicles per minute. Approximately how much money did the toll station collect during that time period?"
- $1,500
- $3,000
- $11,500
- $23,000
- $30,000
Show detailed answer
Correct answer: $23,000
Step by step: multiply rate × time × number of parallel units. From 6 AM to midnight is 18 hours = 18 × 60 = 1,080 minutes. Each booth takes 4 vehicles/min and there are 7 booths, so the total is 28 vehicles/min. Total vehicles = 28 × 1,080 = 30,240. Revenue = 30,240 × $0.75 = $22,680 ≈ $23,000.
GMAT takeaway: for rate questions with several identical channels, multiply the per-unit rate by time and by the number of units. Convert hours to minutes first so the rate's time unit matches.
13. "A store's selling price of $2,240 for a certain computer…" (profit as a percent of cost)
"A store's selling price of $2,240 for a certain computer would yield a profit of 40 percent of the store's cost for the computer. What selling price would yield a profit of 50 percent of the computer's cost?"
- $2,400
- $2,464
- $2,650
- $2,732
- $2,800
Show detailed answer
Correct answer: $2,400
Step by step: profit here is a percent of cost, so a 40% profit means selling price = 1.4 × cost. Let cost be C: 1.4C = 2,240, so C = 2,240 ÷ 1.4 = 1,600. A 50% profit means selling price = 1.5C = 1.5 × 1,600 = $2,400.
GMAT takeaway: profit percent is usually based on cost, not selling price, unless the problem says otherwise. Find the cost first, then rebuild the new selling price from it.
14. "A positive integer is divisible by 9 if and only if the sum of its digits…" (divisibility by 9)
"A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9. If n is a positive integer, for which of the following values of k is 25 × 10n + k × 102n divisible by 9?"
- 9
- 16
- 23
- 35
- 47
Show detailed answer
Correct answer: 47
Step by step: since 10 ≡ 1 (mod 9), every power of 10 is also ≡ 1 (mod 9). So 25 × 10n + k × 102n ≡ 25 + k (mod 9). Because 25 ≡ 7 (mod 9), you need 7 + k ≡ 0 (mod 9), i.e. k ≡ 2 (mod 9). Among the choices, only 47 leaves remainder 2 when divided by 9 (47 = 45 + 2). So k = 47.
GMAT takeaway: for divisibility by 9 (or 3), replace every power of 10 with 1 — the powers disappear modulo 9, leaving a small remainder equation to solve.
15. "The average (arithmetic mean) length per film for a group of 21 films…" (average replacement)
"The average (arithmetic mean) length per film for a group of 21 films is t minutes. If a film that runs for 66 minutes is removed from the group and replaced by one that runs for 52 minutes, what is the average length per film, in minutes, for the new group of films, in terms of t?"
- t + 2/3
- t − 2/3
- 21t + 14
- t + 3/2
- t − 3/2
Show detailed answer
Correct answer: t − 2/3
Step by step: work with the total, not the average. The original total length is 21t. Removing a 66-minute film and adding a 52-minute film changes the total by −66 + 52 = −14, so the new total is 21t − 14. The count is still 21 films, so the new average is (21t − 14) ÷ 21 = t − 14/21 = t − 2/3.
GMAT takeaway: in average-replacement problems, update the total first (sum = average × count), apply the net change, then divide by the same count.
GMAT takeaways: the habits behind all 15 questions
Across these 15 problems the same handful of GMAT Focus habits keeps reappearing. Master them and you will recognize the setup instantly when the same idea returns, dressed up, in a harder band.
- Read percent language exactly — "percentage points" is a subtraction, "increased by 10 percent" is a multiplication, and "0.25 of 1 percent" is a quarter of one percent (questions 1, 5, 11).
- Anchor profit and discount to the right base — profit is a percent of cost, and a subscription discount scales with the price you then cancel (questions 13, 7).
- Turn words into structure — build a cost expression term by term, translate a recurrence into a formula, and set up two linear constraints (questions 2, 3, 8).
- Count instead of computing — decimal places for terminating decimals, coin swaps for coin counts, and digit-sum rules for divisibility by 9 (questions 4, 6, 14).
- Keep fractions relative to the whole — each pizza piece is a fraction of the whole pizza, and a subgroup fraction must be scaled by the subgroup's share of the total (questions 9, 10).
- Work with totals in rate and average problems — rate × time × units for the toll, and sum = average × count for the film replacement (questions 12, 15).
Why MBA House NYC for your GMAT Focus prep
MBA House (GMATNY) is a New York City test-prep and MBA admissions firm running live GMAT Focus classes and unlimited private tutoring, both in person near Union Square and online. The approach in this video — clean setups, calculator-free arithmetic, pattern recognition across GMAT-style questions, and an error-log feedback loop — is exactly how MBA House tutors turn diagnostic data into a focused Quantitative Reasoning plan. If you are searching for a GMAT tutor in NYC or preparing for the GMAT in New York remotely, we will map your target score to your school list and drill the question types that move your number.
Want a tutor to review the questions you missed and build a plan around them? MBA House runs live GMAT Focus prep and private tutoring in New York and online, built on clean problem-solving structure rather than memorized tricks.
Related practice and where this fits in your GMAT prep
Want more worked sets like this one? Start with our 15 GMAT Quant questions explained from the video, then pair this page with the 9 easy Official Guide 2026–2027 Quant questions explained, the 17 easy Official Guide 2026–2027 Quant questions explained, and the 25 Official Guide Quantitative Review 2026–2027 questions explained alongside its video lesson. For single harder examples, try our probability overlap question, the GMAT profit question with tiered costs, the percent-error Data Sufficiency question, and the mixture profit Data Sufficiency milk-and-water problem. If you are still mapping the exam, start with what the GMAT is and our breakdown of the GMAT Focus Edition. To turn practice into a real score, our GMAT Focus tutor NYC page explains how live classes and private tutoring work, and our guide to building GMAT and admissions strategy together shows how a target score should follow your school list.
GMAT Quant practice questions: FAQs
How many GMAT Quant questions does this video cover?
The video works through 15 GMAT-style Quantitative Reasoning practice questions. This companion page gives the opening words of each question so you can find the one you searched for, the full problem text and answer choices, and a hidden step-by-step solution you reveal only after your own attempt.
Are these official GMAC GMAT questions?
These are GMAT-style, official-style Quantitative Reasoning practice problems presented in the video as an educational walkthrough by MBA House (GMATNY). Use them the way you would any practice set: to rehearse the setups and habits the real GMAT Focus rewards, not to memorize answers.
How do the hidden answers work on this page?
Each question shows the full prompt and answer choices first. The correct answer and detailed solution are tucked inside a collapsible "Show detailed answer" panel. Attempt the problem on paper under a soft two-minute timer, then click to reveal and check every step. The panels are plain HTML, so they stay readable even without JavaScript.
What GMAT Quant topics do these 15 questions cover?
Percentage points versus percent, algebraic cost expressions, arithmetic sequences, terminating decimals and powers of ten, percent increase versus percentage-point increase, coin-count reasoning, subscription discounts, two-variable linear constraints, fraction arithmetic, conditional fractions within subgroups, converting percent language to fractions, rate times time times units, profit as a percent of cost, divisibility by 9 with powers of ten, and average replacement.
Can MBA House help me prepare for the GMAT in NYC?
Yes. MBA House (GMATNY) runs live GMAT Focus classes and private GMAT tutoring in New York City and online, with Quantitative Reasoning instruction built on clean setups, calculator-free arithmetic, and an error-log review method mapped to your target MBA programs.