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).

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.

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 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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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 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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.