Free GMAT Quantitative Reasoning Exam Flashcards

21 multiple-choice Problem Solving questions in 45 minutes, each with five answer choices. Quantitative Reasoning is one of three 45-minute sections. You may take the three sections in any order and take one optional 10-minute break after the first or the second section.

No calculator is permitted on Quantitative Reasoning. GMAC provides an on-screen calculator only in Data Insights. Every Quant item has to be handled with mental arithmetic, scratch work and estimation.

Only Problem Solving appears here; Data Sufficiency now sits in Data Insights. GMAC describes the section as algebraic and arithmetic foundational knowledge, so Euclidean geometry (angles, triangles, circles, area, volume) is absent. Coordinate-plane graphing survives inside the algebra content area.

All three GMAT sections are computer adaptive. The first question is medium difficulty, and each later question is selected from your earlier answers. You cannot skip a question, and you must confirm each answer before the next one appears.

Bookmark any question you are unsure about. Once every question in the section has an answer, you may review as many questions as you like, bookmarked or not, and change up to three answers, all inside the section's own 45 minutes.

GMAC applies a penalty for not completing a section. If time expires, your score is reduced to reflect the number of unanswered questions, and mba.com warns it decreases significantly with each blank. An educated guess beats no answer, so make sure all 21 items carry an answer before the clock runs out.

Quant is scored from 60 to 90 and is weighted equally with Verbal Reasoning and Data Insights in the 205-805 Total Score. The section score depends on how many questions you answered, which answers were correct, and each question's difficulty and other statistical characteristics.

45 minutes across 21 questions is about 2 minutes 9 seconds each. The Official Guide advises abandoning any question that runs long: rule out the answer choices you know are wrong, pick the best of the rest, and move on.

You must wait at least 16 calendar days between GMAT appointments and may test at most 5 times in a rolling 12-month period. Test-center and online appointments count together. GMAC has removed the former 8-attempt lifetime limit.

GMAT scores are valid for five years and stay available for reporting for up to 10 years; results older than that cannot be sent. There is no pass or fail - each program decides how it reads a score.

2: last digit is even. 3: digit sum divisible by 3. 4: last two digits divisible by 4. 5: ends in 0 or 5. 6: passes both the 2 and the 3 test. 8: last three digits divisible by 8. 9: digit sum divisible by 9.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 - fifteen of them. 2 is the only even prime and 1 is not prime. To test whether n is prime, trial-divide by the primes up to the square root of n.

Write the prime factorization, add 1 to each exponent, then multiply. 72 = 2^3 x 3^2, so it has (3 + 1)(2 + 1) = 12 positive divisors. The exponents drive the count, not the size of the primes.

For positive integers, dividend = divisor x quotient + remainder with 0 <= remainder < divisor. A remainder of 4 therefore forces a divisor of at least 5. Every integer leaving remainder r on division by d has the form dk + r.

Units digits repeat in cycles. 2 gives 2, 4, 8, 6; 3 gives 3, 9, 7, 1; 7 gives 7, 9, 3, 1; 8 gives 8, 4, 2, 6 - each of length 4. Divide the exponent by 4 and use the remainder, where a remainder of 0 means the fourth term.

a^m x a^n = a^(m+n). a^m / a^n = a^(m-n). (a^m)^n = a^(mn). (ab)^n = a^n x b^n. a^0 = 1 for any nonzero a, and a^(-n) = 1/a^n. Bases must match before exponents may be added or subtracted.

For two positive integers, GCF x LCM = the product of the two numbers, so knowing one gives the other. Build them from prime factorizations: the GCF takes the lowest power of each shared prime, the LCM the highest power of every prime present.

Reduce the fraction first. It terminates only when the denominator's prime factorization contains nothing but 2s and 5s. 7/40 terminates because 40 = 2^3 x 5, while 5/12 repeats because 12 contains a factor of 3.

a^2 - b^2 = (a + b)(a - b). It also converts awkward products into easy ones: 79 x 81 = (80 - 1)(80 + 1) = 6,400 - 1 = 6,399. Look for it whenever one square is subtracted from another.

(a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2. The middle term 2ab is the giveaway. The standard trap is assuming (a + b)^2 equals a^2 + b^2, which holds only when a or b is 0.

If a product equals 0, at least one factor is 0. Move everything to one side, factor, then set each factor to zero. x^2 = 5x becomes x(x - 5) = 0, so x = 0 or x = 5. Dividing both sides by x would silently lose the root x = 0.

For ax^2 + bx + c = 0 with a nonzero, x = (-b +/- sqrt(b^2 - 4ac)) / (2a). The discriminant b^2 - 4ac decides the root count: positive gives two real roots, zero gives exactly one, negative gives none.

For ax^2 + bx + c = 0, the roots sum to -b/a and multiply to c/a. In x^2 - 7x + 12 = 0 they sum to 7 and multiply to 12, so they are 3 and 4. This is faster than the quadratic formula whenever the roots are integers.

Two linear equations in two unknowns have exactly one solution when the lines cross, no solution when they are parallel (same slope, different intercept), and infinitely many when one equation is a multiple of the other and both describe the same line.

Multiplying or dividing both sides of an inequality by a negative number reverses its direction: -2x > 6 becomes x < -3. Adding or subtracting never flips it. Never divide by a variable unless the sign of that variable is known.

For a positive a, |x| < a means -a < x < a, one interval. |x| > a means x < -a or x > a, two intervals. Apply the rule to the whole expression inside the bars: |x - 3| < 2 gives 1 < x < 5.

f(x) is a rule, not a multiplication. To evaluate f(g(x)), work the inner function first and feed its output into f. Order matters, so f(g(2)) rarely equals g(f(2)). A function's domain is the set of inputs that return a real value.

Slope m = (y2 - y1) / (x2 - x1). In y = mx + b the constant b is the y-intercept; set y = 0 to find the x-intercept. A positive slope rises left to right, a negative slope falls, a horizontal line has slope 0, and a vertical line's slope is undefined.

'Is' means equals, 'of' means multiply, 'more than' and 'sum' mean add, and 'per' means divide. 'x is 5 less than y' becomes x = y - 5, not 5 - y. Name the quantity the question actually asks for before you begin solving.

Multiply by a fraction equal to 1, arranged so the unwanted unit cancels. Kilometers per hour to meters per second means multiplying by 1,000/3,600, which is 5/18, so 72 km/h = 20 m/s. Convert everything to one unit system before computing.

A ratio a : b means the quantities are ak and bk for some positive k, and the total is (a + b)k. A ratio on its own never fixes the actual amounts, so a 3 : 5 split stays 3k and 5k until an actual total or difference is supplied.

Percent change = (new value - original value) / original value x 100, and the denominator is always the original. A rise from 40 to 50 is a 25% increase, while the fall from 50 back to 40 is a 20% decrease.

Multiply the factors rather than adding the percents. A 15% increase followed by a 20% discount gives 1.15 x 0.80 = 0.92, an 8% net decrease. Adding +15% and -20% to get -5% is the classic trap.

'x is 20% of y' means x = 0.2y. 'x is 20% more than y' means x = 1.2y. 'x is 20% less than y' means x = 0.8y. Identify which quantity the percent is taken of before writing the equation.

1/8 = 0.125 = 12.5%. 1/6 = 16.67%. 1/5 = 20%. 1/4 = 25%. 1/3 = 33.33%. 3/8 = 37.5%. 5/8 = 62.5%. 2/3 = 66.67%. 3/4 = 75%. 7/8 = 87.5%. Recognizing these on sight replaces long division under time pressure.

Distance = rate x time. Average speed is total distance divided by total time, never the average of the two speeds. Driving 60 km at 60 km/h and then 60 km at 30 km/h takes 3 hours for 120 km, an average of 40 km/h rather than 45.

Rates add, times do not. If one worker finishes in a hours and another in b hours, 1/T = 1/a + 1/b, so T = ab / (a + b). Workers needing 6 and 3 hours alone finish together in 18/9 = 2 hours.

Moving toward each other or in opposite directions, add the speeds; moving in the same direction, subtract them. A boat travels downstream at boat + current and upstream at boat - current, and the same rule covers headwind and tailwind.

Track the substance, not just the total volume. Amount of solute = volume x concentration, and those amounts add. A weighted average always falls between the two component values and sits closer to the one carrying the larger weight.

Profit = revenue - cost. Percent markup divides that profit by the cost, while percent margin divides the same profit by the selling price. An item costing $80 sold for $100 carries a 25% markup but a 20% margin, so check the base.

Mean is the sum divided by the count. Median is the middle value once the list is ordered, or the average of the two middle values when the count is even. Mode is the most frequent value, and a list may have several modes or none.

In any evenly spaced list the mean equals the median, and both equal (first + last) / 2. The sum is then mean x count. The integers 11 through 40 average 25.5 and sum to 25.5 x 30 = 765.

Range is largest minus smallest. Standard deviation measures spread about the mean. Adding the same constant to every term leaves the standard deviation unchanged, while multiplying every term by k multiplies it by |k|. A list of identical values has standard deviation 0.

Read the answer choices first. When they are far apart, round and bound the arithmetic; when they cluster, compute exactly. Rounding both factors up overstates a product, so keep track of the direction of every rounding error.

For two groups, Total = A + B - Both + Neither, because anyone in both was counted twice. Equivalently, the size of A or B equals |A| + |B| - |A and B|. A two-circle Venn diagram or a 2x2 table keeps the categories straight.

If one stage has m outcomes and the next has n, the pair of stages has m x n outcomes. Arranging n distinct objects in a row gives n! orderings, and 0! = 1. Multiply across independent choices and add across mutually exclusive cases.

When order does not matter use combinations: C(n, r) = n! / (r! (n - r)!). When order matters use permutations: P(n, r) = n! / (n - r)!. Committees and handshakes are combinations; rankings, seating orders and passwords are permutations.

With equally likely outcomes, P(E) = favorable outcomes / total outcomes, always between 0 and 1. P(not E) = 1 - P(E). Whenever a question asks for 'at least one', computing 1 - P(none) is usually the fastest route.

P(A or B) = P(A) + P(B) - P(A and B); the overlap term drops out only when the events are mutually exclusive. For independent events P(A and B) = P(A) x P(B). Dependent events need the probability of the second given the first.

Arithmetic: a_n = a_1 + (n - 1)d, and n terms sum to n(a_1 + a_n) / 2. Geometric: a_n = a_1 x r^(n - 1). Mind the (n - 1): a sequence starting at 4 with d = 3 has 10th term 4 + 27 = 31.