Gmat - Quantitative Section (Math) 360 Practice Questions

Identify an isosceles right triangle with hypotenuse eight, apply the area formula using the equal legs, and find the area equals 16.

Compute the ratio of the small shaded region to the large shaded region in four squares, using areas 18, 12, 50, and 32; the ratio is 1 to 3.

Determine the ratio of the triangle's area to the rectangle's area in a geometry problem, showing the triangle's area is one half the rectangle's area.

Solve geometry questions on angle relationships and supplementary angles to find x and y on a straight line. Practice solving these equations in the GMAT quantitative section.

On coordinate plane, a line with positive slope never enters the first quadrant; determine which statements about its perpendicular relation to hedge and j could be true, including x-axis intersection.

Apply the point-slope form y - y1 = m(x - x1) to get line's equation and test points to identify which one does not lie on it.

Apply the difference of squares to a geometry GMAT problem, showing the shaded area equals the rectangle with sides y minus x and y plus x.

learn to compute the area of triangle abc on the x–y coordinate system by identifying base ab, height from c, and applying the area formula base times height divided by two.

Determine the area of a triangle from coordinate points by applying base times height, divided by two, with base six units and height ten units, yielding 30.

Finds the slope of line k from a triangle area of 30 with height 12 and base x, solving x = 5, and shows the slope is negative, -12/5.

Determine the line’s slope using given points, then apply y = mx + c to find the intercept, concluding with y = (2/5)x + 2.

Compute the slope of line K using the points (-1,0) and (2,9), then apply the same slope to find the missing x-coordinate to place the third point at (6,21).

Solve a line through the origin geometry problem using ratios and similar triangles, yielding K = -24.5.

Set y to zero in the line 3y = 2x + 6 to find the x-intercept; solving yields x = -3.

Analyze two lines P and Q with positive slopes and positive y-intercepts to show their intersection lies in quadrants I, II, or III, never IV.

Apply Pythagoras and similarity to determine the shaded region’s area in terms of X and Y, yielding (√3/2)X² − Y².

Solve a right-angled triangle problem by applying the pythagorean theorem, set up and expand algebraic expressions, and recognize pythagorean triples like 3-4-5 and 5-12-13 to find x.

Derive the equation of line k from its intercepts, with x-intercept minus two and y-intercept three, using the intercept form x/(-2) + y/3 = 1.

Find the surface area ratio of two cubes given volume ratio 1:8; deduce side ratio is 1:2 and surface area ratio is 1:4.

Determine shaded region by using a 45-45-90 right triangle and Pythagoras to relate circle radius to square side, then subtract circle area (pi r^2) from square area.

Compute the area of an equilateral triangle with side six by applying the 30-60-90 relationships and the equilateral area formula, yielding 9 sqrt(3).

Apply the 30-60-90 triangle relationships to find a circle's diameter as eight, yielding a radius of four, and compute the area as 16 pi using pi r^2.

Derive coordinates for a point in a square using a 30-60-90 triangle, applying the 1 to root three to 2 ratios with a 2-unit hypotenuse to find x and y.

Explore solving a geometry problem in a regular hexagon with the exterior angle sum of 360 degrees and isosceles triangle properties to determine interior angles, including 120-degree hexagon angles.

Apply Pythagoras to a right triangle with legs 10 and sqrt(15) to bound X, showing seven < X < eight.

Solve a geometry problem by applying a 30-60-90 triangle relationship and symmetry to determine equal side lengths of 12 for five sides, yielding a perimeter of 60.

Evaluate the equation of Limpy by testing x- and y-intercepts. The correct choice satisfies x-intercept greater than five and a positive y-intercept, leading to option a.

Apply angle chasing with parallel lines and the triangle angle sum to determine x in the given geometry figure. Conclude that x equals 75 degrees.

Solve a geometry problem about similar squares, using area relationships where the large square is nine times the smaller, given the square area is 25 to deduce the small side.

Solve a geometry problem determining the total shaded area in a subdivided square by combining small squares, triangles, and rectangles, yielding 24 cm².

Explore a geometry problem about supplementary angles to determine x, given angle cft equals 85 degrees and other angles together total 180 degrees.

Rank points P, Q, and R by their distance from the origin using the distance formula and squared magnitudes to determine the order from closest to farthest.

Solve a regular pentagon angle problem by applying exterior angles sum to 360, identify the interior angle 108, derive x = 36 and a = 54, and find angle kq.

The geometry problem shows that the circle’s circumference equals pi times its diameter. The diameter equals sqrt(5) x, so the circumference becomes sqrt(5) pi x.

Tackle a geometry GMAT problem by linking circle area to radius, applying the equilateral triangle area formula, and using 30-60-90 triangle relationships to find the area.

Given the outer square area is 4x^2, determine the inner square area by using the circle's diameter and a 45-45-90 triangle. Conclude the inner square area is 2x^2.

Determine W in terms of X and Y by applying triangle angle sums to the larger and smaller triangles in this GMAT geometry question.

This lecture solves a rectangle problem: with perimeter 20 and diagonal 9, determine the area by using Pythagoras and the (A+B)^2 = A^2+2AB+B^2 identity, yielding AB = 19/2.

explain a circle geometry problem with diameter 10, noting that inside the circle the angle is greater than 90 degrees and using pythagoras to show BC is less than eight.

Solve a geometry problem on parallel lines and isosceles properties to find angle x in a quadrilateral; through angle chasing and supplementary relationships, x equals 80 degrees.

Compute the probability that a random point in a 4 by 3 rectangle satisfies y > x by comparing the triangle area (9/2) to the rectangle area (12), yielding 3/8.

analyze a geometry figure using 3-4-5, 5-12-13, and 7-24-25 right triangles to compute areas of a rectangle and two triangles, totaling 116 square units.

Analyze the tangency between a sphere and a surrounding cylinder, identifying two touch points at the top and bottom and a central circle as the complete set of contact points.

Explains that increasing each side of an equilateral triangle by 50 percent yields a 125 percent increase in area, using the area formula and a 30-60-90 triangle.

Apply angle-chasing to a geometry problem to find x by using equal angles and the sum to 180 degrees, illustrated in geometry question 45.

Solve a geometry problem: determine the area of triangle abc with a right angle using coordinates to find base and height and applying the half base times height formula.

Count triangles of any orientation in a grid of equally spaced points by analyzing row-based triangle formations and summing counts from 1 to 7, yielding 120 triangles.

Analyze an isosceles triangle with ac = bc, noting angle BCA equals x. Apply the angle sum to derive y in terms of x.

For a cylinder with diameter equal to the height, shrinking all lengths by 60% makes the volume 6.4% of the original, a 93.6% decrease.

Explore triangles formed by dots on an 11 by 11 grid by analyzing rectangles in two orientations, totaling 720 triangles (360 per orientation).

Analyze how wholesale and retail prices relate through an 80 percent markup and a 30 percent retail decrease, yielding a 26 percent wholesale increase.

Apply proportional reasoning to a GMAT quantitative problem about three baseball teams, using the 6:4:5 ratio and a total of 300 fans to find Mets at 80.

Solve a multi-district word problem by enforcing equal numbers of public, parochial, and private independent schools in district c, then use totals to determine private independent schools in district a.

Convert 90 km/h to meters per second, then use distance equals velocity times time to solve a 600-meter GMAT word problem.

Apply 25% Monday and 50% Tuesday discounts to the original price of 100 eggs. Set the Tuesday price to 60 dollars and solve for the original price, yielding 160 dollars.

Solve a word problem on current scaling in a delicate circuit by dividing 3.6×10^-8 A by 10^3 to find the new current, applying exponent rules.

Compute the minimum wins needed for Sen to qualify by reaching 60 percent of 31 total matches. With 14 wins already and 30 remaining, he must win five more matches.

Analyze a mixed gender word problem to compute the percent with an MBA, given 30% male and 50% female MBAs with a 60/40 gender split, yielding 62% without an MBA.

Solve a three-equation system to find the chocolate bar price from gumball and lollipop totals, showing c equals 0.71 dollars.

Solve a word problem about a console price that rises 50 percent last week, with Amanda paying half of the current price (240 dollars); determine the original price before the increase.

Three friends pool funds to buy a gift, and this GMAT quantitative word problem uses one fourth and one third contributions to derive the total price.

Analyze a GMAT word problem: distributing 100 candies to 10 children with distinct positive amounts, showing the maximum a child can receive is 55 when others take one through nine.

Solve a pool work-rate word problem by combining hourly outputs: pump a empties one third per hour and pump b empties one half per hour, giving their joint rate.

Solve a word problem by equating six widgets to eight widgets at a reduced price of $1.25, solve for price per widget, then compute Nina's money as $30 (answer C).

Solve a four-person age word problem by setting Ben as three times Ron and using the total of 161 for all four ages, yielding Ron's age of 22.

Solve a helicopter fare word problem: 85 dollars for the first kilometer and 5 dollars for each additional kilometer, totaling 365 dollars. The distance flown is 57 kilometers.

Combine Mission A and Mission B's rates to 600 widgets per hour, then compute time as 1000 divided by 600 hours, yielding 5/3 hours or 1 hour 40 minutes.

Explore a population-based word problem that forms a linear equation from Appleton's population relations, applies distribution, and solves for X, yielding X = 1550.

Solve a GMAT word problem where a dog weighs three times the average weight of five kids; find the dog's fraction of the total weight, which is 3/8.

Solve a proportional water-displacement problem: determine how many marbles raise the water by 2.75 inches when 12 marbles raise it by 1.5 inches, using cross-multiplication.

Explain how to find the approximate white paint needed to achieve the same gray shade when mixing black and white in a 2.16:1 ratio, using cross multiplication and estimation.

Use a Venn diagram with total 50, 31 French, 17 Spanish, and 10 neither to determine that eight students take both French and Spanish.

Solve a word problem about a weekly allowance where three fifths are spent at the arcade, then one third of the remaining at the toy store, to find m.

Compute the ratio of boys to girls using a weighted average: boys 60, girls 48, overall 50 pounds; result B:G = 1:5.

solve a Gmat word problem about a barrel's capacity, starting from a one-fifth fill and adding kilolitres to express V in terms of K; the answer is V = 15K/7.

Compute the balance of a $10,000 investment at about 4% annual rate compounded semiannually for two years using A = P(1 + r/n)^{nt}. The result is approximately $10,816.

Solve a GMAT word problem that uses percentages to determine what percent Cape Town contributes to the entire population.

Explore a word problem about four times as many apple plantings as oranges, with 15% and 10% growth, totaling 420 apple trees and 2 orange trees, and solve for x.

Solve a Gmat quantitative word problem by applying 60 percent of total revenue to advertising and five-sixths of that amount to television, yielding a television ad spend of 50x.

Apply the distance equals speed times time formula to a six-hour, 120-mile trip split between 25 mph and 15 mph. Find the time at 25 mph and get 75 miles.

Solve a GMAT word problem to find the vice presidents' average salary, given 15 executives at 80,000, 82 data-entry staff at 25,000, and an overall 44,500, yielding 400,000 per VP.

Daily compounding yields the largest total after two years for a five million dollars initial amount at seven percent, beating quarterly, monthly, and annual compounding.

Calculate the bridge length using distance equals velocity times time. Convert 8 km/h for six minutes to meters to obtain 800 meters.

Analyze how price per transaction and transaction volume affect revenue. Learn to compute the percent increase in revenue from the year before.

Solve a word problem on average speed: a plane travels five hours at 120 km/h and the rest at a higher speed for an overall 180 km/h, yielding 30 hours.

Determine the probability that the first heart appears on the third draw or later in a standard 52-card deck, using the complement of two consecutive non-heart draws under replacement.

Determine the required return-trip speed for a round trip, given an outbound speed of 5 km/h and an overall average of 6 km/h, showing the return speed equals 7.5 km/h.

Tackle a GMAT quantitative word problem on average velocity for a 100-mile trip with segments at 30 mph and 50 mph, deriving total time and average speed.

Determine how much water to add to four quarts of alcohol and four quarts of water to reach a 3:5 alcohol to water ratio, solving by cross-multiplication for 8/3 quarts.

Solve a gmat quantitative word problem about a 280-kilometer bus trip, where a 30-minute late departure and a 7/6 times faster speed determine x, the speed in kilometers per hour.

Compute the overall percentage of students walking to the school by combining 14 walkers from class a and 36 from class b, totaling 50 of 80 students, which equals 62.5%.

Solve a word problem involving travel times at different speeds to find the forward trip duration using distance equals speed times time, then convert hours to minutes.

Discover how a retailer's markup transforms a wholesale price into a 180% retail price, then a 30% discount yields a final price of 126% of wholesale, a 26% increase.

Solve a word problem from the GMAT quantitative section that calculates the total cost for Sara’s shoes, earrings, and dance ticket with 8% tax, yielding 93.4 dollars.

Compare a 100,000 investment at 12 percent annual interest paid at year end with monthly compounding. Peter's ends at 112,000, while Martha earns about 682.50 more through monthly compounding.

Solve a GMAT quantitative word problem by applying the 7:8:10 ratio for pigs, cows, and chickens to a total of 300, resulting in 120 chickens.

Determine the selling price per collection to net profit Z, given J crates with Q boxes each and wholesale cost W. Solve JP - W = Z for P.

Explore counting positive integers under 100 that leave remainder 2 when divided by 30, using numbers of the form 30k+2; the largest is 93, so the answer is C.

Determine the 25 percent growth from 2004 to 2005 and apply 125 percent of 2005 to obtain 2006 balance of 6250.

Compute the wholesale price per cup from 692 for 80 cups, compare it to a single-cup price of 12.50, and determine the premium paid per cup.

Practice solving a GMAT quantitative expression, interpreting numbers like eight, eighty-one, and eighteen to determine the correct answer and identify option a.

Determine the remainder when a positive integer with a remainder 102 upon division by 1869 is divided by 89, by expressing the number as 1869k+102 and evaluating modulo 89.

learn to compute the least common multiple of the numbers one to eight using prime factorization and highest powers to obtain 840.

Solve a system where Bill is 13 times Pete's age and, in nine years, Bill is four times Pete; find Pete's age now and Pete's age two years from today.

Solve for the product xy given the sum is six and the sum of reciprocals is fifteen over eight, yielding xy equals sixteen over five.

The lecture solves a quadratic by transforming to x squared minus 10x minus 24 equals zero, factors to (x minus 12)(x plus 2), giving roots 12 and -2.

Analyze a GMAT quantitative problem by comparing four positive integers A, B, C, D using equations like 12A=27B and 5C=12A to determine their order and identify the greatest, C.

Solve a square-root equation by squaring both sides, form a quadratic, factor into (x-6)(x-2)=0, and determine x=6 as the valid solution after checking domain constraints.

Apply the mean value formula to W, X, and Y, derive W+X+Y=59, then compute the average of W+2, X-3, Y+8 as 22.

Solve the ratio of the circle area centered at B to triangle ABC when angle ABC is not a multiple of 30, using sine-based area and pi.

Determine the range of xy for two tangent circles with radii 12 and 13, yielding a minimum of 0 and a maximum of 50.

Double the radius from 10 to 20 feet, increasing the circle area from 100 pi to 400 pi. Conclude that the renovated green's total area is 400 pi square feet.

Solve for radii by using area and circumference; equal areas imply equal radii, so with X's circumference 16π RX = 8, and circle Y also has radius 8, circumference 16π.

Solve question 14 in the GMAT quantitative section by applying triangle similarity and area formulas, using right angles and parallel lines to derive AE=1 and area=9/2.

Solve a Venn diagram problem to determine the 15 percent who took both finance and marketing classes, given 25% finance, 50% marketing, and 40% neither.

Solves a GMAT quantitative question on summing consecutive integers from -35 to x equal to 150 using the arithmetic series formula. It shows x equals 39.

Use a set approach: blue flakes 60 percent and red flakes 55 percent, total 100 percent, so 15 percent have both colors.

Solve a GMAT revenue problem by applying a five-dollar price cut that increases sales by 10 units while revenue stays at 100, resulting in 50 units after the change.

Determine the percentage of desktops with more than 1 GB RAM in a mixed desktop-laptop environment by applying percentage reasoning to RAM categories and totals.

Solve a GMAT quantitative problem about the average number of books read per week and total weeks, using cross-multiplication to relate the average, total, and weeks.

Explore data sufficiency for a GMAT geometry problem by recognizing similar triangles and angle relations, then apply area ratios as the square of a side ratio to judge statement sufficiency.

Assess data sufficiency for the volume of a rectangular solid using front-face diagonal 40 and top-face diagonal 25; neither alone nor together yield the product of the dimensions.

Data sufficiency practice on a GMAT math problem about an aquarium, uncovering whether the ratio g/a (groups to angelfish) can be determined from one or two statements.

master data sufficiency in the GMAT quantitative section through a permutation seating problem, using n factorial reasoning to determine when one or both statements suffice.

Apply data sufficiency to a cube: from 6a^2=150, deduce a=5 and volume a^3; from distance between opposite vertices equals a√3, given 5√3, deduce a=5; thus each statement alone is sufficient.

GMAT data sufficiency example tests positive integers x and y for an inequality, and only both statements together are sufficient, yielding option C.

develop data sufficiency skills in circle geometry by using a right-triangle area and a radius-based arc-length condition to determine the circle's area, with either statement alone sufficing.

Use rounding to the nearest tenth and nearest integer to assess data sufficiency in Gmat, identifying that statement one is sufficient while statement two is not, yielding answer a.

Analyze data sufficiency for comparing P and Q using squares and cubes, considering positive and negative cases; conclude statement one isn't enough, statement two is, so the answer is B.

Assess data sufficiency to decide if X is bigger than Y. First statement X minus Y greater than 3 is enough; second X plus Y greater than 3 is not.

Solve a data sufficiency GMAT problem about a box of white, red, and green balls. Use the green-ball probability of 1/3 to deduce that white or red probability is 2/3.

Analyze data sufficiency in a GMAT quantitative problem about Jill's paintings; neither statement alone determines P, and combined they narrow to 27 or 28, not a unique value.

Explore data sufficiency for area comparisons by analyzing two statements about shapes. Determine when statement one is sufficient and when statement two is not, using area relations.

Evaluate data sufficiency in question 14, showing that neither statement alone nor the two together are sufficient, so the option e is correct.

Data sufficiency for gmat: P is the diagonal of a square with side 3, linked to B in an isosceles right triangle; statement 1 gives B=3, statement 2 gives B^2=18.

Analyze data-sufficiency scenarios for W, X, Y, Z with nonzero values to determine if their product equals one. Show that statement one alone suffices, while statement two does not.

Assess a data sufficiency question on whether k is prime, using factor counts and 150–200 range as examples. Show that neither statement alone nor both together suffice to determine primality.

Evaluate data sufficiency on a barrel at 40 percent, testing two statements to determine if they reveal the barrel’s volume. Conclude that neither statement provides enough information.

solve a data sufficiency probability problem about seating Lisa and Philip next to each other among GAO employees, and determine whether statements alone or together provide the exact probability.

Determine that X=5 from the first statement, since (X-5)^2=0. Show that the second statement yields X=5 or X=1, so it is not sufficient alone.

Solve data sufficiency in a Gmat quantitative context with a ratio problem about Bob's tree planting. Analyze two statements, including a 10 percent increase, to determine the ratio 10:11.

Solve a data sufficiency problem: Bobby and Mickey differ by 15 years, use three years and a 50 percent rule to deduce Bobby's age. First statement suffices; second does not.

Explore data sufficiency in the GMAT quantitative section by analyzing four test scores to determine the average, showing two statements are not enough alone or together.

Resolve the data sufficiency problem by showing that statement one alone determines the ratio of X to Y, while statement two alone is insufficient.

Determine that statement 1 alone is not enough, since BC is a diameter with a 90-degree angle, but statements 1 and 2 together solve CA via the Pythagoras theorem.

The lecture analyzes a data sufficiency problem from the GMAT quantitative section, solving for the price per widget w using total cost constraints and showing that each statement alone suffices.

Data sufficiency question 27 from the gmat quantitative section shows that each statement yields x minus three w equals three, so y is solvable, and both statements are sufficient.

Evaluate data sufficiency by pairs of statements about X and Y, where x+y=5 and xy=6; neither alone suffices, and together yield x=2 or x=3, so insufficient.

Solve data sufficiency for a GMAT question by deriving X values from X^2+X=12, then Y from X+Y=12; neither statement alone nor together gives a unique X-Y.

Analyze a data sufficiency problem with ratios among Canadians, Mexicans, and Americans; neither statement alone nor both together determine the number of Americans, so the data is not sufficient.

Analyze how to determine the average of four numbers using data sufficiency statements. Evaluate two subset averages and show neither alone nor together determine the overall average.

Explore a data sufficiency problem from the gmat, using ratios of plain, strawberry, and banana waffles and a concrete sale count to determine total last week.

Assess data sufficiency question 33 on p and q, positive integers, to determine if p^2 times q is even; statement one alone is sufficient to answer.

Data sufficiency 34 asks you to compute line k slope from ax+by=c by rewriting as y=(-a/b)x+c/b. If a=2b, slope is -2; if c=4b, slope cannot be determined alone.

Solve a data sufficiency problem for x using two statements and algebra, including transforming to (x-3)^2. Each statement alone suffices to determine x, which equals three.

This lecture demonstrates factoring the expression (3x - 5y)^2 using A+B squared and A-B times A+B, and shows that statement 1 is sufficient while statement 2 is not.

Assess data sufficiency in a probability problem with red, green, and blue chips. Statement about blue probability suffices to determine the red or green probability.

Explains a sufficiency problem with A, B, C where B^3 = A and C equals cube root of A, showing that neither statement alone nor both together determine A's sign.

Assess whether Y is bigger than X using two statements: Y equals X plus one and Y equals X squared plus one, using number-line reasoning. Each statement alone suffices.

This lecture covers data sufficiency in gmat math with x and y by factoring x^4 - y^4; statement 1 suffices, and x^y = y^x is analyzed for sufficiency.

Explore a data sufficiency problem on an arithmetic sequence of seven days with a daily increase of 3, using statements about total visitors and the seventh day to test sufficiency.

This lecture uses data sufficiency to decide if x is bigger than y with two statements; statement one implies x > y, while statement two does not guarantee unique relation.

Explore data sufficiency for a two-variable GMAT problem, showing one equation plus a price relation can suffice, while the second statement offers no new constraint, yielding answer a.

Examine a data sufficiency question on a circle's area using radius and diameter relationships; determine that statement 1 alone suffices, while statement 2 does not.

GMAT data-sufficiency questions compare fractions and numerators to determine whether the value is less than 1/20, and show that statement two alone suffices.

This data sufficiency problem compares last year's spending with this year's price after an eight percent rise and an eighty percent sale, leading to answer e.

Explain a GMAT data-sufficiency problem: is A less than B? Show that Statement 1 is insufficient, and Statement 2 shows A > B, so A < B is false.

Analyze data sufficiency for whether x is even, using odd and even outcomes in sums and products, and show that each statement alone suffices.

this lecture covers data sufficiency in the GMAT quantitative section, showing average of a and b is (a+b)/2. statement one is insufficient, while statement two is sufficient to determine a+b.

Apply data-sufficiency reasoning to decide whether P equals Q. Statement 1 alone is insufficient; statement 2 alone is insufficient; together they confirm P equals Q, so the answer is C.

On the GMAT data-sufficiency question, statement 1 yields x = ±7 from x^4 = 2401, so not sufficient. Statement 2 yields a positive x from x^5 = 16837, so sufficient.

Compute the angle from a point’s coordinates using arctan of k over j, and assess data sufficiency with statements like j = -4 to decide if k is determined.

Master data sufficiency with a GMAT math problem on an isosceles triangle ABC, showing that statement two is sufficient to deduce angles A and B as 45 degrees.

Assess data sufficiency for AB on a line with A, B, C; use AC = 10 and BC = 7; show that statements alone and together fail to determine AB.

Evaluate data sufficiency for whether Y is an integer when X is an integer. Statement 1 yields Y=3-X and is sufficient; statement 2 does not guarantee Y as an integer.

tackle a data sufficiency question from the gmat, using circle geometry to relate radius, diameter, and a square's area via pythagoras theorem; statement one is sufficient to determine the area.

Analyze data sufficiency for K as an integer using two statements and their combination, showing neither alone nor together conclusively determine K in this GMAT practice question.

Analyze the data sufficiency question 58 to deduce T from relationships among a, m, n, and T, and demonstrate that combining the two statements yields T and the answer C.

Explore GMAT data sufficiency for X bigger than five. Statement one, X < 6, is insufficient; statement two, X < 4, makes X less than five, so suffices (answer B).

The lecture explains data sufficiency question 60, showing that statements 1 and 2 together prove X is bigger than two, while neither alone is sufficient.

Evaluate data sufficiency in a GMAT question with W ≤ X ≤ Y and the average is 20, so W+X+Y=60. Show that both statements together suffice (answer C).

explain data sufficiency for GMAT quant: positive numbers p and q; statement 1 alone leaves p unknown, while statement 2 yields (p+2q)^2=28 and a positive root, making it sufficient.

In this data sufficiency exercise, statement 1 alone suffices to determine if x yields an integer root, while statement 2 is insufficient to decide the answer.

A data sufficiency lecture analyzes a line problem, using the x-intercept eight and the y-intercept minus four to show that each statement alone is sufficient to determine the value.

Explore a data sufficiency problem on token costs: determine X+Y, the tents visited, given 16 tokens and prices of 3 and 4 tokens, using both statements.

Assess data sufficiency for a GMAT compound interest problem using A = P(1 + r/m)^{7m}. Show that statements 1 and 2 are not sufficient, and more information is needed.

Assess data sufficiency for P and Q: statement 1 is insufficient; statement 2 yields P < Q using the line y = x+1, so statement 2 alone determines the relationship.

identify the largest angle in triangle abc by comparing sides ab = x+2, bc = x-3, ac = y-1; larger side implies opposite angle; statement 1 sufficient, statement 2 not.

Analyze data sufficiency strategies for a Gmat math question, showing that statement one alone suffices to determine the value while statement two does not provide enough information.

This data-sufficiency lecture analyzes X and Y as positive integers, using cross-multiplication to compare X and Y; it concludes that statement two suffices to determine the relation.

Analyze a data sufficiency problem on ratio W/X = Y/Z with nonzero W, X, Y, Z; conclude that statement 1, WZ = XY, is sufficient, while statement 2 is not.

Analyzes a data sufficiency problem on the combined rate of Mission A and Mission B. Finds that 200 widgets take 4 hours and that both statements alone are sufficient.

Explains data sufficiency for a ratio comparison by examining how the numerator and denominator affect the fraction, and that statements 1 and 2 together are sufficient.

Explore a GMAT data sufficiency problem about buying several identical brooms with an 8% sales tax, and determine the price per broom excluding sales tax.

Analyze data sufficiency questions by applying speed-distance-time relationships; statement 1 yields t = 6 hours, while statement 2 alone is insufficient.

Tackle a GMAT data sufficiency problem with four distinct positive integers, exploring constraints on arithmetic mean and median to determine the possible range.

Explore data sufficiency for a GMAT geometry question on quadrilateral ABCDE, using coordinates, parallelism, and area calculations to determine whether the figure's area exceeds 30.

Compare the two leg speeds to determine the overall average speed for the trip using total distance over total duration. Statement 1 alone suffices; statement 2 alone is not enough.

Explore a data sufficiency problem in the GMAT quantitative section, using the lowest common multiple of 24 and 18 to find possible totals, and determine which statement alone suffices.

Assess data sufficiency for x using two linear equations. Each statement alone is insufficient, and combined they yield the same line, leaving x undetermined.

Explain a data sufficiency problem for x^2 minus y^2 using (x - y)(x + y), showing statement one is not enough and statement two yields zero.

Evaluate data sufficiency by testing statements to determine if they provide enough information to answer the query, concluding statement 2 alone is sufficient, yielding 17/5.

Assess line slopes and quadrant positions to decide if the line must pass through quadrant three. Statement two, with a positive slope, confirms this, making it sufficient.

Examine how a circle’s circumference is deduced using a diameter linked to a 90-degree angle and a 30–60–90 triangle, and show that statements 1 and 2 together are sufficient.

Explore data sufficiency for determining whether ABCDE is a rectangle, given angles and side relations. The lecture shows that no single statement, or their combination, suffices.

Explore data sufficiency in a GMAT quantitative context using ratio problems with mammals, reptiles, and birds. Assess when each statement alone determines X and five X to solve the question.

this lecture analyzes data sufficiency for consecutive odd integers x and y with x<y. it derives x=-1 and y=1, sum zero; statement one is sufficient, statement two is not sufficient.

Determine if point (x, y) lies in quadrant four using data sufficiency; show that each statement alone suffices to conclude it is not in quadrant four.

Solve a GMAT data sufficiency problem about the ratio W to X to Y and analyze statements to determine the value of W+X+Y.

Evaluate statement 1 alone and statement 2 alone; neither suffices, but together they imply X*Y is even and X+Y is even.

Assess data sufficiency with x and y integers to decide if x is less than y; one statement is insufficient, two shows x is not less than y.

Evaluate data sufficiency in a GMAT quantitative question about whether a is bigger than c, where statement 1 is not enough and statement 2 alone suffices.

Analyze a GMAT data sufficiency problem with five friends sharing eighty-seven dollars and a median tie, then evaluate two statements to determine sufficiency.

Analyze data sufficiency to determine X given expressions with Y squared. Compare statements, showing that statement two alone suffices to determine the value.

Analyze a data sufficiency problem with 20 numbers, 19 between 40 and 50; show that statement two alone suffices to compare median and mean, indicating answer b.

The lecture analyzes a GMAT data sufficiency problem on remainders when divided by four. Statement 1 yields remainder 1 and is sufficient; Statement 2 is not, so answer is A.

Evaluate data sufficiency to compare the standard deviation of datasets k and l; the first two statements are insufficient, and even together they may not resolve which is larger.

Master data sufficiency for a GMAT quantitative question using a square and triangles, apply the difference of squares to relate m and k, and determine sufficiency by combining statements.

Assess whether statement one determines x minus y in a data sufficiency problem, and note that statement two yields ±6 and is not enough, highlighting the common pitfall.

data sufficiency shows each statement alone yields x^2 plus 1 over x^2 equals 2, using the identity (x + 1/x)^2 = x^2 + 2 + 1/x^2 and x^2 = 1.

Analyze how acute and obtuse angles between two lines determine slope signs and how data sufficiency resolves whether slopes are positive or negative.

Analyze data sufficiency for a quadrilateral square, showing each statement alone is insufficient, and that together they prove all angles are 90 degrees and all sides are equal.

Explore a four-integer data sufficiency problem, showing how to use mean and median concepts, and that statements about the mean and the mode become sufficient when considered together.

Learn how data sufficiency questions determine isosceles triangles: equal sides imply equal base properties, and equal areas lead to equal bases, with each statement alone sufficient to answer.

Analyze a GMAT data sufficiency question about x in a quadratic equation, including factoring and cross-multiplication steps. Conclude that neither statement alone nor combined provides a unique value for x.

This data sufficiency problem asks the probability two randomly drawn socks are black from 36. First statement gives 16 black socks, making the probability determinable; second statement is insufficient.

Solve a data sufficiency problem on the 4:5 male-to-female ratio, showing statement 1 adds no new info while statement 2 yields x=20 and 80 boys.

Use data sufficiency reasoning to analyze a rope-cutting problem with three pieces X, Y, Z. The two statements together are not sufficient to determine X, Y, and Z.

Evaluate data sufficiency for a GMAT probability question, using P and its complement, and statements about trials to determine if P exceeds 1/2.

Practice data sufficiency question 110 in the GMAT quantitative section, using midpoint, right angle, and triangle similarity to show that statement 2 alone is sufficient.

Analyze data sufficiency in the GMAT quantitative section through a midpoint geometry problem with similar triangles and heights. Show that statement one is sufficient, statement two is not.

evaluate data sufficiency for a GMAT quantitative problem by analyzing two statements; statement 1 is not enough, while statement 2 yields x+3y = 12 given positivity.

Analyze data sufficiency in divisibility problems, evaluating whether x is divisible by 12 under two statements—x divisible by 27 and x divisible by 6—and how parity affects the result.

Master data sufficiency for the GMAT quantitative section by applying divisibility by three rules and digit-sum logic to determine when statements about digits A, B, and C are enough.

Solve a GMAT data-sufficiency problem involving monthly-compounded interest, evaluate statements on principal and interest, and show that together they suffice to determine the total amount after seven years.

Analyze data sufficiency for a geometry problem: combine angle measures and midpoint properties in a square to deduce equal sides and conclude that JQM is equilateral.

Explore data sufficiency concepts through a GMAT problem with 32 votes, analyzing whether statement 1 or statement 2 alone suffices to determine the top candidate.

Analyze data sufficiency by testing statements. statement 1 yields x = 2, making it sufficient. statement 2 yields two possible values, so not sufficient alone; therefore, the answer is a.

Solve a GMAT data sufficiency question on consecutive integers W, X, Y, showing that statement 1 confirms they are consecutive while statement 2 is not sufficient.

Analyzes a GMAT data-sufficiency problem with B^2 + C^2 = 17, seeking A^2 + C^2. Shows that neither statement alone suffices, but both together are enough.

Analyze a GMAT data sufficiency question (question 121) by comparing two statements, showing the second statement alone suffices to determine the value, while the first does not.

Combine the two statements to determine B and G and thus compute the probability of selecting a boy.

Master a gmat data sufficiency question by using ticket price relations and the balcony to orchestra ratio to deduce orchestra and balcony prices from total revenue.

Analyze a data sufficiency problem: small cans cost 30 dollars and large cans cost 8 dollars, with a total of 220. Assess if statement 1 alone suffices to determine S.

Analyze data sufficiency in a GMAT quantitative problem with W/(X+Y)=1, evaluating two statements and demonstrating that each statement alone is sufficient.

Assess data sufficiency for positive X and Y to determine if X over Y exceeds 3, evaluating whether statement one alone or statement two alone suffices.

this data-sufficiency problem uses baseball, basketball, and football with a 15:12:8 ratio and no triple overlap; given overlaps or only-baseball data, the baseball total cannot be determined.

Use midpoint properties and parallel lines to relate triangles, apply the 30-60-90 triangle and similarity, and compute x to determine that the answer is B.

data sufficiency question 129 examines the sign of the expression y^2 / [x(x+y)], given uncertain signs of x and x+y, and shows that neither statement alone suffices.

Learn data-sufficiency strategies to decide when B is the median among A, B, and C, showing statement one is insufficient and statement two is sufficient, with answer B.

Analyze data sufficiency in a GMAT quantitative question, using powers and logarithms to show that statement one alone cannot determine a, since infinite values of a satisfy the equation.

Explore data sufficiency question 132 strategies for a price reduction problem: comparing sale prices after 20% reductions on a hat and a shirt, using statements to determine the price difference.

Assess parity patterns for integers X and Y to determine data sufficiency of their product, considering even, odd, and consecutive cases.

Solve a data sufficiency problem on monthly-compounded interest to find the annual percentage rate using a $10,000 principal, November 2003 interest, and 72 months.

Apply data-sufficiency reasoning to a digit puzzle: rounding k to the hundredth yields ambiguous b (3 or 4) under statement 1, while statement 2 fixes b as 3.

Explore a data sufficiency question about blue and red, large and small bicycles in a 300-stock factory, determining the blue and large count using two statements.

Analyze a data sufficiency problem with positive A, B, C where B^2 + C^2 = 370; combining statements 1 and 2 determines A and B to find A^2 + C^2.

This Gmat data sufficiency lecture analyzes whether X and Y, positive integers, yield a prime when multiplied and whether Y squared is even, via statements one and two.

Analyze data sufficiency question 139 using prime factorization and exponents, evaluate two statements about primes and ranges, and conclude that both statements together are not enough to determine the answer.

Analyze data sufficiency in a GMAT exponent problem, testing whether statement one determines x and whether the two statements together can solve for x.

Assess data sufficiency for consecutive positive integers to determine the mean and the range parity. Show that statement one (range even) and statement two (median integer) are each sufficient.

Analyzes a data sufficiency problem about city counts with variables a and b, to determine the difference b minus a. It concludes that statement two alone is sufficient.

Determine the number of seniors among 42 students in data sufficiency question 143 using S > 4F and F > 7, yielding F = 8 and S = 34.

Evaluate data sufficiency for proving ABCDE is a square by using equal sides, right angles, and diagonals, distinguishing square, rectangle, and rhombus properties.

This data sufficiency lecture shows how statement one alone can determine sufficiency using even and odd powers, with cases where a is between zero and one.

Model total as Xn + 1 = 2001, giving Xn = 2000. Statement one bounds X 13–23; statement two forces X even and n odd, yielding X = 16.

Assess a data sufficiency problem with red and blue balls in a box of eight, using two probability statements on draws to deduce the number of red balls.

Master data sufficiency using a half-full hall scenario, applying 20 percent increases and 60 percent baselines to deduce the total seats and interpret the question stem.

Assess data sufficiency in a GMAT quantitative problem with positive integers x and y, showing statement 1 is insufficient while statement 2 determines whether x exceeds 3y.

Evaluate a data sufficiency question from the GMAT section 150 about X and Y; deduce XY is negative from statement 1, and with statements determine X positive and Y negative.

Analyze the probability that Andrew sits to the right of Georgia in a random seating of 15 employees, a data sufficiency GMAT question, concluding the probability is one-half.

Assess how lines J and K with intercepts yield multiple slope possibilities, showing the data is not enough to determine whether K's slope is greater than J's.

Learn to solve a GMAT data sufficiency question 153 by analyzing a rational expression with X not equal to five and using derivative analysis to show statement two suffices.

Analyze a data sufficiency problem comparing cube root and fifth power of x, noting sign effects when raising to powers, and conclude the statements are not sufficient.

In this data sufficiency problem, the ratio of girls to boys is five to fourteen. Statement 1 alone suffices to determine the number of girls, while statement 2 does not.

this data sufficiency lecture examines whether K is an integer or a fraction, with primes and square numbers, and shows the statements do not yield a definite conclusion.

Explore GMAT data sufficiency in the quantitative section by analyzing X and Y with Y = X^-3 and XY = 1, illustrating that statements can be insufficient individually or together.

Solve a data sufficiency problem to find the ratio of the areas of two circles along a common line, using radius relationships and cross-multiplication.

Explain data sufficiency for a circle geometry problem using diameter and right-angle properties to determine the area, and show that each statement alone suffices.

explain a data sufficiency approach for x using x^2=9 and |x|, showing statement 1 gives x=±3, statement 2 implies x<0, and together yield x=-3.

Solve a data sufficiency problem involving modulus with two statements; determine that statement one is not enough, while statement two alone provides a unique value.

Demonstrate data sufficiency in a GMAT question by showing that either statement alone suffices to determine the value of y.

Solve a data sufficiency question by finding the price per dunnart from the box price and number in the box. Together these statements suffice to compute the cost per dunnart.

Solve a GMAT data sufficiency problem by combining male and female statements to compute the percent of residents who voted.

Explore a GMAT data sufficiency problem about primes and squares, showing that statement two is enough and statement one is not.

This lecture analyzes data sufficiency for ratio of X to Y with integers. Statement one yields 2x=3y, so it is enough; statement two yields 2x=plus or minus 3y, not enough.

Analyze data sufficiency question 7 with x and y as positive integers; statement 1 is sufficient, statement 2 is not, so the answer is a.

Solve data sufficiency question 8 by applying mod nine to the four-digit number through the digit sum, showing W+X+Y+Z=13 yields remainder 4, and the second statement confirms the same remainder.

Solve a data sufficiency problem with x and y as positive integers, showing (x-y)(x+y)(x^2+y^2) equals 240. Conclude that statement 1 is sufficient, and statement 2 also provides sufficiency.

Explore data sufficiency for divisibility by nine in data sufficiency question 10, showing that each statement alone confirms whether Z is divisible by nine.

Analyze data sufficiency for X with two statements: the sum of any two positive factors is even, and X is prime; together they determine X as 3.

This lecture analyzes a GMAT data sufficiency problem with integers and powers of seven, showing statement one is sufficient while statement two is not, yielding a.

Analyze data sufficiency question 13 on parity, determine whether x is odd or even using prime factors and two statements, and follow a step-by-step solution.

Analyze a Gmat data sufficiency problem on division remainders with positive integers, evaluate statements 1 and 2, and show statement 2 is sufficient, yielding answer B.

Solve data sufficiency in the GMAT quantitative section by evaluating statement 1 and statement 2, both yielding x equals minus five through average and median reasoning.

Data sufficiency analysis evaluates whether X is greater than three Y using two statements; together they are not sufficient, indicating additional information is needed.

Solve a GMAT data-sufficiency problem using a 30-60-90 triangle, isosceles properties, and parallel lines to compute triangle area, showing each statement alone is sufficient.

Solve a GMAT data sufficiency problem with X and Y as positive integers between 10 and 100, assessing when X+Y is a multiple of 11 and showing statement two suffices.

The lecture shows a data sufficiency approach for a prime b under addition, subtraction, multiplication, and division, concluding that addition yields b=2 and that b is even, guiding solution strategy.

Analyze data sufficiency problem 20: determine whether x^x is larger than y^y for integers x and y with x = y + 1; together the statements imply x^x > y^y.