GMAT- Data Sufficiency 250 Questions and their solutions

analyze data sufficiency for the inequality 3x < 2y with positive integers using statements. show that neither alone is enough, but together they prove the answer is yes (option c).

In this data sufficiency lecture, evaluate rounding X to the nearest tenth and integer to decide if X is at least 2.55, with statement one sufficient and statement two not.

Analyze a GMAT data sufficiency problem about an aquarium with three fish types to determine the ratio of groups to angelfish; show that the second statement alone is enough.

This lecture explains data-sufficiency concepts using rounding to the nearest tenth and nearest integer, with X around 2.55, showing statement one is sufficient while statement two is not.

Calculate the probability of drawing a black or white ball from a box. Using the second statement alone is sufficient to give white or black probability as 5/6.

Analyze a GMAT data sufficiency problem about a cube, using surface area and opposite-vertex distance to determine the side length, with each statement sufficient to compute the volume.

Examine two statements about positive integers x and y and show that neither alone is sufficient, but together they are, yielding the answer C.

Analyze a circle data-sufficiency problem where a right triangle area 18 yields r^2 = 36, showing a single statement suffices; arc-length reasoning with theta pi/2 confirms second statement is enough.

Master data sufficiency concepts by analyzing rounding rules to the nearest tenth and nearest integer, concluding that statement one is sufficient while statement two is not.

Explore data-sufficiency reasoning for P and Q using comparisons of squares and cubes; determine that statement two alone suffices to conclude P > Q, yielding answer B.

Analyze data sufficiency for exponential inequalities using even and odd powers and negative values. Show that statement two alone suffices to decide x^5 > y^5.

analyze whether x is bigger than y using inequalities in this data sufficiency question, and determine that statement 1 alone is sufficient while statements 2 and 3 are not.

determine the probability of drawing a red or white ball from a box of white, red, and green balls; since green probability is 1/3, red or white equals 2/3.

Evaluate the two data sufficiency statements about Jill's paintings; they prove insufficient to determine the exact number, with combined information yielding 27 or 28.

Analyze data sufficiency for area comparison: determine when S1 alone suffices to compare triangle and rectangle areas, while S2 alone may not provide enough information.

This data sufficiency question analyzes the signs of J and K and their quadrant placements. Neither statement alone nor together determines the exact quadrant, so the answer is E.

Analyze data sufficiency question 15, where an isosceles right triangle and a square of side three determine P, the square’s diagonal, with either statement alone sufficing.

Demonstrates data-sufficiency reasoning for W, X, Y, Z with nonzero product; the first statement makes the product WXYZ equal to one, while the second statement is not sufficient.

Analyze data sufficiency for whether K is prime by examining cases with factors of K and primes between 150 and 200, showing that single or combined statements may be insufficient.

Analyze data sufficiency for a water barrel that is 40 percent full; both statements fail to determine the barrel's volume, so neither alone provides the needed information.

Analyze a GMAT data sufficiency question on seating Lisa and Philip next to each other among GAO employees; show why statement alone is insufficient and both together yield exact probability.

Analyze a data-sufficiency problem with black, white, and yellow balls to determine the probability of drawing black or white, noting that the second statement alone suffices.

In data sufficiency question 20, statement one alone determines X equals five. Statement two alone yields two possible values, so it is not sufficient.

Determine the ratio in this data sufficiency question: the first statement fails to determine it, while the second, that Ann planted 10 percent more than Bob, yields the ratio 10:11.

Solve a data sufficiency problem about Bobby and Mickey, where Maggie is 15 years older, to determine if a single statement suffices; statement 1 is enough, statement 2 is not.

Evaluate data sufficiency for Bill's four test scores, showing that neither statement alone yields the average and that additional information is needed to determine the overall mean.

Analyze a data sufficiency question on the ratio x:y; the first statement alone determines the ratio, while the second statement alone is insufficient to find x:y.

Apply data sufficiency reasoning to determine if CA can be found. Individually, statements 1 and 2 are insufficient, but together they suffice to compute CA via Pythagoras in the circle.

Determine the price per widget w from a 480 total cost in this data sufficiency problem using two conditional statements; each statement alone suffices to find w.

Derive Y from X equals 3 plus 2Y and X minus 3W, showing each statement alone yields Y equals 3/2, thus data sufficiency.

Determine that neither statement alone suffices, and together they yield two possible values for X (2 or 3), leaving X's value undetermined.

Statement one is not enough to find x minus y. Solving x^2+x=12 gives x equal to -4 or 3, and with x+y=12 it remains ambiguous, so data sufficiency fails.

Analyze a data sufficiency question on Canadians, Americans, and Mexicans with C:M 3:2, showing that first and second statements alone and together fail to fix the number of Americans.

Determine the average of four numbers A, B, C, D using two data sufficiency statements; show that each statement alone is insufficient, and together they do not determine A+B+C+D.

This data sufficiency lecture uses 30-60-90 triangle ratios and height to find the area of triangle EBC. Statement 1 alone suffices (and statement 2 also suffices) to yield 12√3.

The lecture uses parity reasoning on data sufficiency with positive integers p and q, showing p^2 q being odd forces p and q odd; statement one suffices.

Determine the slope from Ax + By = C as -A/B; A = 2B yields slope -2, while C = 4B alone is insufficient.

Solve a GMAT data sufficiency question by analyzing two statements to determine x. Both statements alone prove x = 3.

Factor the expression 9x^2 - 30xy + 25y^2 into (3x - 5y)^2 and show that 3x - 5y equals 20 is sufficient, while x+y equals 12 is not.

In a data sufficiency problem of red, green, and blue chips, determine red or green probability; statement 2 is sufficient, since p(r or g) = 1 − p(b) = 6/7.

examine data sufficiency for a, b, and c given b^3 = a and c = a^3, showing that a's sign cannot be determined from either statement alone or both together.

The lecture explains data sufficiency for y greater than x under two statements, y = x + 1 and y = x^2 + 1, showing each statement alone suffices.

Explore a data sufficiency question on whether X plus Y is a multiple of 11 for integers between 10 and 99. Statement two is sufficient; statement one is not.

analyze a data-sufficiency problem using an arithmetic progression of seven days with a total of 126 visitors; determine that each single statement alone suffices to find the first-day count.

this lecture analyzes data sufficiency for x and y, showing statement 1 alone suffices to determine whether x > y, while statement 2 alone is insufficient due to multiple relations.

This data sufficiency lecture analyzes the price of a tape roll with one equation and two variables; statement 1 alone suffices, while statement 2 alone does not.

Solve a data sufficiency circle problem by using area formulas and A minus B and A plus B relationships to determine which statement alone suffices.

Learn data sufficiency skills for GMAT question 45 by examining fraction comparisons and inverse relations to determine when statement two alone is sufficient.

Analyze a GMAT data sufficiency problem about jacket pricing. Compute Jessica’s savings from a sale using original price P, increase A, and discount B, and assess statements' sufficiency.

Determine whether A is less than B. Conclude that statement 1 is not sufficient; statement 2 shows A > B, so statement 2 alone is sufficient.

Analyze data sufficiency question 48 on parity, using statements about 3x+3 and x^2 to show that each statement alone suffices to determine whether x is even.

Analyze how to determine the average of A and B using data sufficiency. Statement 1 is insufficient to find A+B, while statement 2 is sufficient.

Explore data-sufficiency for two integers P and Q: statement one P is a factor of Q, statement two P is a multiple of Q. Individually neither suffices; together they suffice.

Apply fourth and fifth roots to x, distinguishing even versus odd powers. Statement 1 yields two possible values; Statement 2 yields a unique positive value, so the answer is B.

The lecture shows that the angle equals arctan(k/j) from a point and origin; with j = -4 alone, the angle is not determined, and statement two alone is insufficient.

This data sufficiency problem analyzes an isosceles triangle with angles A, B, and C. Using statement two (C = 90) yields A = B = 45, proving sufficiency.

Explore a data sufficiency problem on a line with points A, B, C to determine AB. Statements AC = 10 and BC = 7 yield multiple AB values, so insufficient.

Answering whether y is an integer when x is an integer in a data sufficiency problem. Statement one alone is sufficient, while statement two is not sufficient.

GMAT data sufficiency: apply circle geometry to deduce square area via radius, diameter, and Pythagoras theorem; statement 1 is enough, statement 2 is not, so the answer is A.

Explore GMAT data-sufficiency strategies as you analyze two statements about fractions inversely related to denominators to determine k; neither statement alone nor together yields a unique value.

Solve a GMAT data sufficiency problem to determine T by using two statements about positive integers a, m, and n, and deducing N minus M equals 7 to compute T.

Explore data sufficiency question 59: statement one (x < 6) is not enough, statement two (x < 4) is sufficient, so the correct choice is B.

Examine how statement one, x > 0, and statement two, x^2 > 9, each fail to determine x alone. Together, they imply x > 2, showing both statements are sufficient.

This data sufficiency lecture analyzes W, X, Y with mean 20 and W ≤ X ≤ Y; using statements to test W > 15, together they are sufficient (answer: C).

Analyze a GMAT data sufficiency question with positive numbers P and Q, applying sum and diff identities to show statement two suffices to determine the value.

Assess data sufficiency for question 63 by testing root and integer constraints, concluding that statement 1 alone suffices to determine the answer while statement 2 is not sufficient.

Analyze how line intercepts determine sufficiency in a GMAT data-sufficiency problem. Each statement about the x-intercepts and y-intercepts alone proves sufficient to determine the value.

This data-sufficiency exercise uses tokens and tent costs to solve for x and y, representing 3-token and 4-token tents; only statements combined yield a unique solution.

Explore a data-sufficiency GMAT problem on compound interest, using A = P(1 + r/m)^(7m) to assess if statements about principal and rate alone suffice, showing both are insufficient.

Determine that statement two alone suffices to conclude that P is less than Q, so P is not bigger than Q.

Explains how triangle side lengths x+2, x-3, and y-1 determine the largest angle, showing AB biggest implies angle C largest, and that statement x minus y equals 1 is sufficient.

Determine the value of 1/x minus 1/y using GMAT data sufficiency; statement one suffices, while statement two provides no usable relation.

Using cross multiplication, the lecture explains that for nonzero W, X, Y, Z, WZ = XY suffices to decide W/X = Y/Z; WY = XZ alone is not enough.

the lecture analyzes a gmat data sufficiency ratio problem solved by cross multiplication, showing statement 1 is enough and statement 2 is not.

Explore data sufficiency in a gmat problem where A and B’s joint rate yields 200 widgets in four hours. Show that each statement alone suffices to determine the required time.

Learn to solve GMAT data sufficiency questions by analyzing price per banana through proportional reasoning, testing statements about quantities A, B, R, and S to determine if combined info suffices.

This data sufficiency lecture analyzes a GMAT problem about brooms costing 78.30 with 8% tax, asking the price per broom excluding tax, and shows that each statement alone is sufficient.

Analyze speed, distance, and time relationships in a GMAT data sufficiency problem, and determine that statement one yields t = 6 hours, while statement two is insufficient.

This data sufficiency lecture analyzes four distinct positive integers with mean between 3 and 4, showing a single statement can't determine the range, and even both statements are inconclusive.

Explore data sufficiency for a coordinate geometry problem with quadrilateral ABCDE. Show that statement 1 is not enough to decide the area, while statement 2 suffices under the parallelogram condition.

Analyze data sufficiency for a multi-segment trip by calculating average speed from total distance and total duration, using given statements to determine if enough information exists.

Explore a data sufficiency challenge where two teachers distribute cookies evenly to 24 and 18 students, using the lowest common multiple to determine possible totals and assess statement sufficiency.

Examine a GMAT data-sufficiency problem with two equations in x and y, showing that neither statement alone nor combined yields a unique value for x.

Explore data sufficiency for the expression x^2−y^2 by applying the identity (x−y)(x+y). See how statement 1 (x+y=16) is insufficient, while statement 2 (x−y=0) yields zero and is sufficient.

This data sufficiency lecture analyzes problem 82, showing statement one is not enough, while statement two alone is sufficient, yielding 17/5 as the value.

Explore how line slope and quadrant placement affect whether a line passes through quadrant three, using statements about positive and negative slopes and angle types.

Combining statements about the triangle's area and a 60-degree angle determines the circle’s radius and thus its circumference.

Evaluate data sufficiency criteria for whether ABCDE is a rectangle by testing angle conditions and side parallels. Show that both statements, alone or together, fail to provide sufficient information.

Using the ratio mammals:reptiles:birds = 11:8:5, statement 1 yields X = 4, so five X equals 20 birds, and statement 2 similarly confirms X = 4.

evaluate data sufficiency for a GMAT problem with x and y as consecutive odd integers, x<y, and xy negative; conclude statement one is sufficient, statement two is not.

analyze how x and y signs place the point in quadrants and determine when x*y is positive. demonstrate that each statement alone is sufficient for the data sufficiency question.

analyze a GMAT data sufficiency ratio problem w:x:y = 1:3 and two statements, showing that each statement alone is sufficient.

Analyze data sufficiency for positive integers X and Y, focusing on X times Y and X plus Y are even, and show statement two is insufficient alone but sufficient jointly.

Assess a data sufficiency problem with X and Y to determine if X is less than Y, noting that statement one is insufficient and statement two is definitive.

In gmat data sufficiency question 92, analyze two statements to decide if A exceeds C; statement two alone is sufficient, while statement one is not.

Present a data sufficiency scenario with five friends' amounts, using total and median concepts to decide who has the most money, and show that each statement alone suffices.

Analyze data sufficiency question 94 by testing whether x and y satisfy the given conditions through algebraic manipulation, and show that statement two alone is sufficient.

Explore data sufficiency using a 20-number set with 19 values between 40 and 50, comparing median and mean, and show that the second statement is sufficient.

Analyze remainder problems in data sufficiency by expressing numbers as four k plus R and examining modulo eight, showing statement 1 suffices while statement 2 does not, answer a.

Analyze data sufficiency for comparing standard deviations of datasets K and L, using statements about multiples of three and nine, and determine that statements alone are insufficient.

Combine two data statements to determine M+K for a square and related right triangles, using the area relation and the difference of squares (M-K)(M+K)=144.

Determine x minus y using data sufficiency; statement one gives x minus y = 6, so sufficient; statement two gives x minus y = plus or minus 6, not sufficient.

Assess sufficiency for the data sufficiency question in a gmat course on x^2 plus 1/x^2; statement one yields 2, statement two yields 1, so both alone are sufficient.

Explain how slope signs arise from angles between lines, distinguish acute and obtuse angles, and show that combined statements in data sufficiency yield the answer c.

The lecture analyzes data-sufficiency for whether quadrilateral abcde is a square. Alone, each statement is insufficient; together, they show all angles are 90 degrees and all sides are equal.

Explains a data sufficiency problem with four integers a, b, c, d to determine the mean and median, shows that the statements (including mode) yield the median at three.

In an isosceles triangle, equal sides mean the height bisects the base and the angles; each statement alone suffices to decide side equality and area relation.

Explore a data sufficiency question where statement 1 yields four x-values and statement 2 yields two; combined, they still leave two possibilities, so neither alone nor together suffices.

Analyze a data sufficiency problem about selecting two black socks from 36 without replacement. The first statement yields a solvable probability, while the second statement offers insufficient information.

Illustrates data sufficiency using a 4:5 male-to-female ratio. Statement 1 provides no new information, while statement 2 yields X=20, giving 80 male students.

This data sufficiency question uses three rope pieces X, Y, Z with X shortest, given Y+Z=6 and X+Y=3; two statements are not sufficient because three variables need three equations.

Analyze data sufficiency for probability questions by evaluating independent trials, computing at least-one event probabilities and complements, and comparing statements to determine sufficiency.

Analyze a geometric setup with right angles, parallel lines, and similar triangles to determine data sufficiency for question 110. Conclude that statement two alone is sufficient to solve the problem.

Use midpoint and similar triangles to find B's height from C. Statement 1 gives B=20 ft when C=40 ft and is sufficient; statement 2 with 60 degrees is insufficient.

Determine the sufficiency in a GMAT data sufficiency question 112 by testing each statement. Show that statement two alone yields X+3Y = 12, with X, Y, W positive, proving sufficiency.

Examine data sufficiency for divisibility by 12 using statements about X being divisible by 27 and by 6, and assess whether X/12 is an integer.

Determine if abc is divisible by three using the digit-sum rule in a data-sufficiency framework; analyze statements: 8b divisible by 3, and a+b (or c) is a multiple of 3.

Master data sufficiency for a GMAT problem on compound interest with monthly compounding, showing that statements 1 and 2 together are sufficient.

Explore data sufficiency in a GMAT problem using a square, a midpoint, and angle conditions to show when statements fail and when combined yield equal sides and a fixed angle.

Determine that statement 1 alone suffices to decide if Bob has the most votes, while statement 2 alone is not sufficient.

Analyze data sufficiency question 118 by solving |6-3x|=x-2 with case work and check x values. Conclude that statement 1 is sufficient, statement 2 is not, so the answer is A.

Evaluate data sufficiency for W, X, Y as consecutive integers; show statement 1 yields sufficiency, while statement 2 does not guarantee consecutiveness.

Gmat data sufficiency lecture demonstrates determining A squared plus C squared from two statements about A, B, and C; neither statement alone is enough, but together they are sufficient.

Examine a data sufficiency scenario with addition, subtraction, multiplication, and division to determine the value of one gunma and assess if the statements together or separately suffice.

Analyze two statements about boys and girls to determine the probability of selecting a boy; individually insufficient, but together they yield a solvable data sufficiency equation.

This data sufficiency lesson tackles a price puzzle where parking tickets cost half of orchestra tickets, balcony to orchestra is 3:2, and statements reveal orchestra price 30 and balcony 15.

This data sufficiency lesson analyzes a GMAT problem about paint cans, where small cans cost 30 and large cans cost 8, testing whether statements alone suffice.

This GMAT data sufficiency lecture analyzes a problem where w/(x+y)=1, demonstrates rearranging and solving, and shows that each statement alone suffices to determine (x+y)/w.

We analyze a GMAT data sufficiency problem with positive x and y, determining that statement one alone suffices and that statement two also suffices.

analyze a gmat data-sufficiency scenario with three sports baseball, basketball, and football, using a 15:12:8 ratio and a no-all-three overlap, showing that given pairwise counts do not determine baseball players.

Apply data sufficiency techniques to question 128, using midpoint properties, a 30-60-90 triangle, parallelism, and triangle similarity to derive the PE to KD ratio, concluding option B.

Evaluate when y^2/(x(x+y)) is positive without cross multiplying, deducing sign cases of x and x+y; assess whether x > -1 or y > -1 alone or together suffices.

Explore data sufficiency question 130 on medians, using two statements; statement one is insufficient, statement two shows B is not the median.

This GMAT data sufficiency lecture analyzes a question involving powers and seventh powers, showing that statement one yields infinitely many possible a values and is not sufficient to determine a.

Solve a GMAT data sufficiency problem: after 20% reductions, determine the sale price gap between hat and shirt; statement 1 alone yields the exact difference, statement 2 alone is insufficient.

This lecture analyzes the parity of integer products in data sufficiency questions, showing that for consecutive integers, even times odd is always even, making the second statement sufficient.

Use data sufficiency to determine the annual percentage rate in a monthly compounded account, given a $10,000 principal, November 2003 interest of $61.83, and December 2008 withdrawal.

Examine a data sufficiency GMAT problem that tests rounding k to the nearest hundredth and thousand to determine the digit b, using two statements to deduce b.

Solve a data sufficiency problem using a blue-red, large-small matrix to determine the blue and large count, showing each statement alone is sufficient.

Evaluate a gmat data-sufficiency problem with a, b, c where b^2+c^2=370; determine a^2+c^2, showing that statements alone are insufficient but together they yield a unique value.

Analyze whether x and y are positive integers yielding a prime product under statement 1 and an even square under statement 2, and show together they deduce x=1 and y=2.

tackle a data sufficiency GMAT problem involving prime factorization and exponents, analyzing two statements and their intersection to determine sufficiency.

Master data sufficiency with power-based expressions, applying exponent rules to simplify X^a + X^a + X^a and related products. Deduce X from statements, as the example shows X = 3.

Examine data sufficiency for consecutive positive integers and when the mean is an integer. Statement 1, the range is even, suffices; statement 2, the median is an integer, also suffices.

Learn GMAT data sufficiency techniques to find B minus A in a city-count problem, showing how the second statement determines the difference and yields six.

With 42 students, seniors exceed four times freshmen and freshmen exceed seven. The only solution is eight freshmen and thirty-four seniors.

Examine how a quadrilateral ABCDE is identified as a square by equal sides, 90-degree angles, and equal diagonals, highlighting that a square is a special rectangle.

Analyze data sufficiency for question 145 by evaluating the sign behavior of powers, noting even powers are positive and odd powers are negative, and whether statement one suffices.

Analyze a two-statement data sufficiency problem about bags of marbles where one bag has one more marble, totaling 2001, and use the statements to determine X.

Determine the counts of red and blue balls in the eight-ball box from the first statement, which yields five red and three blue, so the answer is A.

Analyze data sufficiency in a GMAT problem involving a prime B and a chosen operation. Evaluate plus, minus, multiplication, and division to determine when the equation holds.

analyze data sufficiency for positive integers x and y, evaluating two statements on inequalities to decide if x is bigger than 3y; statement two is sufficient, statement one is not.

Data sufficiency analysis shows that neither statement alone suffices, but together they show X is positive and Y is negative, making XY negative.

analyze data sufficiency for integers x and y with x = y + 1, comparing x^x, y^y, and x^y, and show that together they prove x^x > y^y.

Assess data sufficiency for comparing slopes of lines K and J using intercepts, parallelism, and obtuse angles, illustrating multiple cases and often inconclusive results.

This lecture demonstrates solving a gmat data sufficiency question by rewriting the inequality, analyzing the positive denominator and the numerator with a derivative, and concluding statement two suffices.

Evaluate a data sufficiency problem comparing the cube root of X with the fifth root of X (X ≠ 0), highlighting sign effects and concluding the statements are not sufficient.

Data sufficiency for the GMAT is explored through ratio and percentage reasoning to test each statement. The session shows that statement one alone suffices to determine the number of girls.

Assess data sufficiency for K by analyzing whether K is an integer or fraction, the primality of possible values, and constraints from even powers and square numbers.

Analyze a GMAT data sufficiency question where Y equals X to the minus three; show that neither statement alone nor both together determine the relation without extra information.

Solve a data sufficiency problem to find the ratio of the areas of the larger and smaller circles by deriving radii from collinear points and using cross-multiplication with two statements.

Explore data sufficiency in circle geometry, applying diameter properties and the cosine rule to determine the circle area from a single statement.

Combine the statements to deduce x equals -3 by using x^2 = 9 and |x| = -x to constrain the sign, confirming only -3 satisfies both.

Determine the volume of a rectangular solid using its bottom and front face areas under integer constraints. Combine both statements to deduce B=7 and C=4, yielding a volume of 224.

Assess a GMAT data-sufficiency problem comparing Judith and Quincy’s investments with 2012 and 2013 percentage changes. Statement two alone suffices to determine which investment is larger by 2013.

Analyze how to find the area of triangle abc inscribed in a circle of radius six, with isosceles case ab = ac, using the sine rule and area formula.

Analyze a four-player card game where players hold eight cards from a 52-card deck; face cards are worth 20 points. Prove that two statements fail to confirm Charles's highest total.

Analyze data sufficiency questions with X and Y as positive integers, examining parity and primality in X^2Y^2, and show that statement 1 alone is sufficient while statement 2 is not.

Analyze a data sufficiency scenario with a line of positive slope at least three units from the origin to see if it passes quadrant II; conclude more information is needed.

Assess data-sufficiency for a GMAT problem about the percentage of female employees who are college graduates, showing that neither statement alone nor their combination yields the exact percentage.

Evaluate data sufficiency for P(A and B) > 1/3 when A and B are not independent, using P(A)=0.8 and P(B)=0.7. Statement 1 yields P(A and B)=0.56, which exceeds 1/3, while statement 2 is insufficient, so the answer is a.

Determine the probability a bulb is defective from a shipment of 720 bulbs using the ratio of defective to non-defective bulbs; statement one gives 1:60, but without X, not enough.

Analyze a GMAT data sufficiency problem with pennies, nickels, and quarters totaling $1.37; evaluate whether counts of pennies or quarters determine the probability of drawing an illegal coin.

Use the complement method to find the probability that outcome A occurs at least once in nine independent trials. With P(A per trial)=1/3, P(A)=1-(2/3)^9.

Analyze a GMAT data sufficiency question by evaluating two statements: R + J = 360,000 and 360,000 = 2J; combine them to solve for both salaries.

Learn how to solve a GMAT data sufficiency question on the average of X and Y by combining two statements to determine X+Y without solving X, Y, or K.

Assess whether quadrilateral abcde is a square using data sufficiency statements; determine that neither statement alone nor together suffices, so the answer is a.

Estimate the probability that a specific student sits at the extreme right in a random seating of engineers, using odd primes and leftmost-seat symmetry.

Determine whether a line with slope -3/2 passes through a given point by computing the intercept from a known point and checking the target, with each statement alone sufficient.

Solve data sufficiency problems in GMAT style by using the triangle angle sum of 180 to determine X, with statement one sufficient to find X while statement two is not.

explain data sufficiency for comparing two nonzero integers x and y using two statements; analyze x^2, |x|, and positivity, show how combined reasoning determines whether x is greater than y.

Analyze when x squared exceeds y squared by applying the difference of squares, showing that knowing both x+y<0 and x−y<0 makes (x−y)(x+y)>0, yielding sufficiency.

Explain how data sufficiency uses the mean of a set of positive multiples of five under k to force an even set size. Conclude the only feasible value is 48.

This data-sufficiency walkthrough uses the coordinate plane with lines y=x and y=x+1 to compare P and Q; the first condition is not sufficient, while the second alone is sufficient.

Compute the lighthouse brick area using 2πrh with r = 14 ft and height from 274 steps of 8 inches, yielding about 16,000 square feet.

Analyze a GMAT data sufficiency question on exponent comparisons, use signs and even/odd powers to assess positivity, and conclude that statements one and two together are not sufficient.

Solve data-sufficiency: probability of selecting a boy when boys to girls are in a 7:5 ratio. Statement two suffices, giving 7/12; statement one is not enough.

Analyze a data sufficiency question about Carl's age, showing how one variable and one equation from two statements let you solve the age in nine years.

Explore data sufficiency in problem 186 by analyzing division rules: remainders are less than divisors, prime checks for factors, and how combining F, A, D, N, and R narrows possibilities.

This data sufficiency lecture analyzes a coin problem with quarters and dimes totaling 1.70, showing that with x+y<9, the only solution is x=6 and y=2, so statement one suffices.

Explore a data sufficiency question on divisibility by four and eight, where a positive integer n with square-root reasoning leads to the conclusion that each statement alone is sufficient.

this lecture demonstrates a data sufficiency problem with integers x and y nonzero; statement 1 (x+y=0) makes the expression equal to 1 and is sufficient, statement 2 is not.

Explore the closure properties of a set K of integers: if x in K then 2x in K, and if x and y in K then x+y in K.

Solve a GMAT data sufficiency question using an isosceles triangle with angle relations, exterior angles, and x-values, showing that each statement alone is sufficient.

Analyze data sufficiency for question 192 using distance equals speed times time on a 120-mile trip. Conclude: statement 1 is not enough; statement 2 yields a unique solution.

Analyze a GMAT data-sufficiency problem with 11 consecutive even integers. With mean zero, if 10 is in the set the probability is 1/11; otherwise zero.

Analyzing a GMAT data sufficiency question about a minus b and x, the lecture shows statement one is not enough and both statements yield a unique value for x.

Analyze a GMAT data sufficiency problem about a circle, radius, and a 30–60–90 triangle, using AB = 12 to determine the radius and circle area.

Analyze a GMAT data sufficiency question by applying modulus inequalities and number line reasoning to compare cases, evaluate two statements, and identify the resulting X-range intersections.

In this data sufficiency lecture for GMAT question 197, the instructor uses a slope and a line through the origin to show statement 1 is not enough.

Solve a data sufficiency GMAT style problem about selecting two socks without replacement to determine whether each statement alone suffices to find the probability that both socks are black.

Assess whether divisibility of XY or WY by six yields enough to determine W, X, Y as positive integers with product 24. Both statements alone and together are not sufficient.

analyze the data sufficiency of a probability problem: determine whether the chance of at least one success exceeds 1/5 by testing prime n values and combining conditions, concluding insufficiency.

Apply the law of cosines to a data sufficiency question, deducing BC equals 6 in an isosceles BCE triangle with angles 30 and 60, enabling solution of the problem.

Solve a GMAT data sufficiency problem using consecutive odd integers; determine y minus x equals 2, and use statement 2 with eight numbers to make it solvable.

Explore data sufficiency concepts through a two-statement problem using positive integers A, B, C, D to decide whether J > K by comparing A·D and B·C.

Identify the slope of line k from x-intercept 3 and y-intercept -2 in the xy plane; use opposite over adjacent, yielding a positive slope of 2/3.

Examine a GMAT data sufficiency problem with integers X and Y and two statements, and determine that each statement alone is sufficient.

Evaluate data sufficiency for the probability of selecting a boy from a class; alone, B+G=35 or the ratio B:G=3:4 are insufficient, but together they yield a determinate probability.

Evaluate data sufficiency in geometry by analyzing circle and square intersections to compare areas; determine when single or combined statements are insufficient.

Analyze the random seating of 15 employees, determining the probability that Andrew sits to the right of Georgia, which equals one-half.

Statement 1 yields K = ±1/5, not a unique value, and statement 2 implies K is 0 or 1. Together, these two do not determine K.

Explore data sufficiency for a power-based inequality problem, analyze signs of 8^(6−A) and 8^5−A, and show neither statement alone nor together uniquely determines A.

Learn how to solve a data sufficiency problem with quadratic inequalities, identify roots at 1 and 3, and determine that statement 1 alone is sufficient while statement 2 is not.

Determine the percent of hospital patients in intensive care by combining gender distribution with care proportions, which yields 23 percent and shows the data are sufficient.

Determine Y in this data-sufficiency problem by showing statement 1 alone is insufficient; combine with the parallel lines to deduce X = 30 and Y = 30.

Explore data sufficiency by solving for x with a single equation, showing that each statement alone suffices to determine the value. This illustrates that one unknown requires one equation.

Analyze a GMAT data-sufficiency problem on a 30-60-90 triangle, showing that without a side length the problem is unsolvable, and that statement 2 yields BC, giving answer B.

Analyzes a GMAT data-sufficiency problem with W, X, Y; statement one is not sufficient, statement two is not sufficient, and together they remain indeterminate.

Solve a GMAT data sufficiency problem to determine the unique split: 400 women and 200 men in a 600-employee company, with 25% and 17% participation in the voluntary equity program.

Analyze two data-sufficiency statements about dress shirts and non-dress shirts to deduce the total number of shirts using percentages.

Evaluate GMAT data sufficiency questions on divisibility by three, showing statement 1 is sufficient and statement 2 is not, with algebraic reasoning for X and Y.

in this data sufficiency problem for GMAT, 2x - y = 75, the statement x = 3y alone suffices, and the second statement alone also suffices to determine x.

Combine the price relation and the total to solve for the trader price, showing that the board price equals trader price plus 7500 and they sum to 15000.

Solve a GMAT data sufficiency problem about car ownership among 80 students by using gender-based ownership statements to determine the total number who own cars.

Analyze a data sufficiency question on a quadratic intercept, test X=2, Y=0, and determine that statements 1 and 2 together are sufficient, yielding answer C.

Demonstrate data sufficiency on a GMAT style five-number problem where the average is 20, and assess whether the three smallest numbers' average is determinable.

Analyze a four-hour round trip between Arlington and Burlington to compute average speed in this GMAT data sufficiency lesson, showing that statement two alone suffices.

Analyze a data sufficiency problem determining what percent of paintings are by Jane from a 3 to 7 ratio, noting that each statement suffices.

Determine how adding a fifth child affects the average weight, given the four-child average is 60, and use data-sufficiency statements to see if the change is determinable.

This data sufficiency lecture uses a Jill and Jack height scenario to determine if x is bigger than y, showing first statement alone proves x is not bigger than y.

Learn to solve GMAT data sufficiency question 229 about socks and ties by evaluating statement 1 (ratio) and statement 2 (total), showing that together they determine the counts.

Analyze a data sufficiency scenario where Valdez harbor handles 240 percent of Duluth's cargo and Northfork Harbor's cargo is 15 percent greater than Duluth's; together, statements determine Northfork Harbor's tonnage.

Provides a data sufficiency approach to dollars per mile by converting hours to minutes using statement 1; statement 2 offers no relevant data.

Analyze a data sufficiency problem with two sprocket producers totaling 250,000. Demonstrate that statement two alone yields y = 50,000, proving sufficiency.

Combine X ≥ 3 and X < 4 to determine X, given X is an integer; together they show X equals 3.

Analyze a GMAT data sufficiency problem on ratios of plain, strawberry, and banana waffles, and decide whether one or two statements suffice to determine total sales.

solve a GMAT data sufficiency question about the modulus of y; determine that statement 1 is not enough, while statement 2 is sufficient.

Analyze data sufficiency question 236 by solving for y via cross multiplication in statement 1, and conclude that statement 2 also provides enough information, so either statement alone is sufficient.

Use data sufficiency to determine the price per dunnart by combining box price and item count. The two statements are sufficient when considered together.

This data-sufficiency example combines 400 male and 800 female voters, with 60% of females voting, to show 880 of 1500 residents voted, about 58.7%.

Analyze a data sufficiency question on primes where N-1 equals a square of an integer. Statement two alone determines X as seven, making N seven and confirming the answer.

Demonstrates data sufficiency for GMAT using X and Y; analyzes two statements to decide sufficiency, concluding statement one is sufficient and statement two is not.

evaluate a gmat data sufficiency problem: statement 1 alone makes the cube root of x plus y^2 an integer; statement 2 is insufficient; answer a.

Use divisibility by nine and the sum of digits to solve data-sufficiency questions. If W+X+Y+Z=13, the remainder is 4; if W+X+Y+Z+5 is divisible by nine, the remainder is also 4.

Explore a GMAT data sufficiency problem: determine x^4 − y^4 for positive integers x > y; statement 1 yields 140, and statement 2 with x^y = y^x is also sufficient.

Explore data sufficiency for deciding whether z is divisible by 9, using the digit sum of 10^n−19 and z+981 being a multiple of 9; both statements suffice.

Explore a data-sufficiency problem: X is a positive integer. Statement 1 makes the sum of any two factors even; statement 2 makes X prime; together they show X equals three.

Analyze data sufficiency for a GMAT question involving X, W, Z and power expressions; determine sufficiency of statements and conclude that statement 1 is sufficient while statement 2 is not.

explore a data sufficiency question about whether an expression in x, a positive integer greater than two, is odd or even, using parity rules and prime-factor insights.

Analyze data sufficiency for a GMAT style question on divisibility and remainders with positive integers, comparing statement one and statement two to determine which suffices.

Apply data sufficiency to determine X: statement 1 yields X from the average expression, making it sufficient; statement 2 sets the median to minus five, also determining X.

Explore a GMAT data sufficiency question comparing page indexing rates X and Y, evaluate each statement and their combination to determine if X is greater than three times Y.