GMAT Prep Course | Data Sufficiency : 221 Solved Questions

Master data sufficiency with a reusable map to assess each statement and their combination, determining sufficiency and efficiency in solving DS questions.

Explore data sufficiency with a roses and tulips problem. Two unknowns require two equations, so statements alone are insufficient, but together they determine the values; the answer is C.

Solve a data sufficiency cost-per-pound problem with apples and grapes by forming an equation from 12-dollar total for 10 apples and 2 grapes, evaluating statements 1 and 2 for sufficiency.

Learn to determine the median annual salary using data sufficiency by evaluating whether statements alone or together reveal all salaries needed for the middle value.

Assess data sufficiency for converting 250 y to currency x using cross-multiplication and stated currency ratios, evaluating statements 1 and 2 as sufficient individually or together.

Apply data sufficiency rules to printers and scanner price problems. With two unknowns and one equation, one alone is insufficient; two equations make them solvable.

Master GMAT data sufficiency through triangle angle problems and exterior angles. Determine whether statement 1 is sufficient, while statement 2 is not, using a map-based approach.

Uses data sufficiency to solve a GMAT blue-to-purple ratio from 256 marbles with green four times blue; deduces blue 48 and purple 16, giving a 3:1, and shows statements suffice.

Analyze a data sufficiency question on a paint mixture to determine if the yellow quantity meets the required 20 quarts. Demonstrate combining statements to conclude yes, option C.

Analyze a data sufficiency problem with departments X, Y, and Z to identify which received the most funds by combining statements 1 and 2 (X:Y and X:Z).

Solve a data sufficiency question on cans per student by using two statements to find the number of students (16) and compute the average cans donated per student.

Master data sufficiency for GMAT by identifying the median salary in a list of employees, arranging salaries in order, and evaluating statements to determine sufficiency.

Solve a data-sufficiency question on votes for vs against a proposal. Use statements to deduce f = 240 and a = 180, showing alone insufficient but together sufficient (answer C).

Solve a data sufficiency problem from the 2019 and 2020 edition about vanpool passengers, showing that neither statement alone nor together determines the number of men.

Red is 8 of 24, giving red probability of 1/3 for blue marbles. Red alone can't determine blue; with white, red and white together determine blue, yielding C.

Analyze data sufficiency problems by testing statements alone and in combination, using the map to determine what reveals z, and conclude that statements 1 and 2 together are sufficient.

Analyze data sufficiency questions by evaluating statement 1 and statement 2 alone, using a sufficiency map and 10 percent reasoning.

Analyze data sufficiency for a two-class problem: test statements separately and together. Together they determine class A's number of students, so the answer is C.

Assess data sufficiency by comparing February and January heating bills with the 26/25 ratio, showing February is higher; conclude statement 1 is sufficient, statement 2 is not, no combination needed.

Apply data sufficiency to a sequence with first term -8 and common difference 10; neither statement alone suffices, but together determine the term, yielding answer C.

Explore data sufficiency in GMAT style problems by analyzing when individual statements about machine rates alone are insufficient, and how combining statements yields solvable equations for R and S.

Delve into data sufficiency for positive bases with exponents, showing how statements 1 and 2 alone fail but together establish sufficiency in a GMAT problem.

Analyze data sufficiency to determine the range of selling prices; neither statement alone nor combined yields a definitive range, illustrating careful assessment of statements.

Evaluate data sufficiency for three house prices using two statements about gaps between highest, middle, and lowest prices, and analyze when the second-largest price can be determined.

Explore data sufficiency with a 2019–2020 ds problem, showing that neither statement alone suffices. Combine statements 1 and 2 to determine B, yielding the answer C.

Assess data sufficiency in a GMAT problem by evaluating statements about R and W, noting that neither alone nor together guarantee zero, and conclude the data are insufficient.

Learn data sufficiency strategies by moving things around within a statement to resemble the question, proving sufficiency through algebraic rearrangement.

Apply a Venn diagram approach to a GMAT data sufficiency problem, determining how many of 50 people have neither a fax machine nor a laser printer.

This data sufficiency lecture analyzes solving for w from w to the minus one equals one half, shows both statements are sufficient, and concludes the answer is d.

master data sufficiency questions on annual 4 percent compound interest over five years, using year-by-year investments and statements to determine the third-year interest.

Learn data sufficiency strategies for circle problems by identifying when the radius alone yields the circumference using 2πr, and why a circle's center alone is insufficient.

Solve data sufficiency problems by verifying statements, simplifying equations by canceling common terms, and determining t from the cube root of 216; both statements suffice, yielding answer d.

Explains data sufficiency for a GMAT problem on total charge, factoring parts, labor, and 6 percent sales tax, and evaluates whether each statement alone or together provides sufficiency.

Learn to distinguish sufficient from insufficient data in GMAT data-sufficiency questions and practice to recognize when information is not enough.

Analyze how the w component determines positivity in data sufficiency questions, while the h component remains positive, making w the more powerful factor and guiding the answer.

Analyze a GMAT data sufficiency problem about two three-digit numbers; show how the units digits determine the product's units digit, and why both digits are needed.

Use area = 1/2×base×height; base is y and height is vertical, not x. Statements prove data are insufficient to determine the base and height, so the area cannot be found.

Analyze GMAT data sufficiency with midpoint geometry to determine if DB exceeds five; statement 1 is not sufficient, statement 2 is sufficient, giving answer B.

Model a queue with x, y, z for people in front of Adam, between, and behind Beth; use total 32 and x+z=18 to solve for z.

Analyze data sufficiency for a circle and its inscribed square by linking circle area and circumference to the square's side through radius, diameter, and a right triangle.

This data sufficiency question shows that a single point on line k cannot determine a positive slope, even with parallel lines; two points on the same line are needed.

Determine data-sufficiency for a semicircular tunnel problem by analyzing truck width and height with radius 4.2; use geometry and Pythagoras to conclude whether the truck can pass.

Analyze a 50-person data-sufficiency scenario with doctors and lawyers using a Venn diagram to show the intersection cannot be determined from totals alone.

This lesson explains data sufficiency problems with exclusive or for cats and dogs, applying the inclusion-exclusion formula p(a) + p(b) − p(a ∩ b) and using no-cat no-dog counts.

Identify how to allocate 12000 between investments x and y when x earns 3% and y earns 6% simple interest, with both yielding equal interest, using data sufficiency reasoning.

Demonstrates data sufficiency reasoning with a two-statement probability problem about female employees, showing why neither alone nor combined data yield a definite answer.

Tackle data sufficiency questions by cross-multiplying inequalities and applying a bottom-up technique. Determine that statement 1 is sufficient, while statement 2 cannot be substantiated.

Assess data sufficiency by comparing two statements about walking to school; the second shows two of three students walk, which suffices, while the first does not.

Master a data sufficiency problem using a plumber's fee rule: $92 for up to four hours, $23 per hour after. Determine the total for seven hours across two jobs, 230.

Explore data-sufficiency reasoning for the ratio (x+1)/(y+1); test scenarios with numbers, analyze x versus y relationships, and conclude that the correct choice is B.

Analyze data sufficiency using long division to compare fractions and decimals, show statement 1 alone is sufficient, and derive the final answer D.

evaluate a data sufficiency question about red and green cubes in a box; with six cubes, neither statement alone nor combined yields a conclusive count.

Master GMAT data sufficiency techniques by testing positive integers x and y, analyzing divisibility of x^2+y^2-1 by 4 and parity to determine sufficiency and the correct answer.

learn data sufficiency techniques for even and odd number scenarios by plugging in values, testing statements, and using parity reasoning to determine sufficiency.

Analyze data sufficiency for a GMAT problem with x and y, show that each statement alone is insufficient, but together determine the sum and yield the correct choice C.

Explore a GMAT data-sufficiency problem on finding speed v from fuel per mile f and constant k. The lecture analyzes statements 1 and 2 for sufficiency.

Assess data sufficiency for whether R plus S is even, showing statement one is insufficient alone and that R even with S even makes the sum even, yielding answer C.

Determine X<Y in a data-sufficiency question by deducing X=58 and Y=64 from the given diagram. Show that both statements are sufficient, confirming X<Y and selecting option D.

Apply data-sufficiency reasoning on a set of odd numbers to decide if -15 belongs to S; alone statements fail, but together they prove -15 is in S.

Analyze two statements to decide if X is a three-digit number. Between 90 and 150, the only squares are 100, 121, and 144, so the data are sufficient (C).

In a data sufficiency problem, this lecture analyzes a sequence's fifth term using odd-term and third-term statements; combined, the data remains inconclusive, so the answer is E.

lecture analyzes a 2020 edition data sufficiency problem, showing two odd and two even integers yield an even sum, and that an integer average confirms this, making both statements sufficient.

Solve a GMAT data sufficiency problem: determine total spent on desks and chairs using price per desk, and the relation between amounts spent on X and Y.

Demonstrate GMAT data sufficiency approach with three siblings, using oldest = youngest + 7000, youngest = middle - 9000, and youngest + middle = 45000 to show either statement suffices.

Explore a GMAT data sufficiency problem by analyzing x, y, and z in squared form; show that statements 1 and 2 yield x=2 and y=4, making the values sufficient.

Use value testing to analyze data sufficiency; testing with B=7, E=3 and B=-4, E=4 shows statement two is sufficient, leading to answer B.

Solve a data sufficiency problem on an arithmetic sequence with a common difference of two. With the first term equal to two, the fourth term is eight.

Explore data sufficiency by assessing if P is divisible by five given P is divisible by ten, and conclude statement 1 is not sufficient while statement 2 is, so answer A.

Analyze a data sufficiency puzzle on a grid with zeros and X's; show that while each statement alone is insufficient, their combination proves there are exactly four X's.

This lecture shows that one even and one multiple of five are not enough to decide if sum of two integers is divisible by ten, so the answer is e.

Determine whether x is an integer using data-sufficiency logic, showing that x^3 = 8 gives x = 2 and x^2 = 4 gives x = ±2, making both statements sufficient.

Analyze a data sufficiency problem with 6000 square feet and 20 executive offices, where each office is three times the average of the rest, yet the data is insufficient.

Analyzes three consecutive descending integers p, r, s with x as their average, showing p+r+s=3x; concludes x must be zero and evaluates the two data-sufficiency statements.

Explore GMAT data sufficiency strategies for a 2020 edition problem, analyzing when statement 1 alone suffices and why statement 2 alone fails, with integers and algebraic reasoning.

this lecture covers a 2020 edition data sufficiency problem (#306), analyzing x, y, s, t, and r, showing statement 1 is sufficient and statement 2 is not.

analyze a GMAT data sufficiency problem about distances among s, r, and t, highlighting left-right uncertainty. conclude that s and t are seven apart and select d.

apply data-sufficiency reasoning to a GMAT problem where n times a nonzero x equals zero, forcing n to be zero. conclude that n+0 equals zero, and the option is d.

Apply the map scale—half inch equals 100 miles—to relate X to Y. Conclude that statement 1 is sufficient, statement 2 is not; the answer is E.

This data sufficiency lesson uses remainders; with n divided by 3 yielding quotient 4 and remainder 1, n=13 and remainder 3 mod 5, so the first statement is sufficient.

analyze data sufficiency in a data sufficiency problem, showing that statement 1 is sufficient while statement 2 alone is not, exploring subtraction and division possibilities.

Explore data sufficiency with sign changes in a sequence, showing that odd ending n and combined statements 1 and 2 yield a definite count, making the answer C.

Analyze a data-sufficiency problem about apples sold to Nina and Silvia; show that statement one is not sufficient, statement two is not sufficient, but together they yield the answer C.

Solve data sufficiency questions by analyzing two-variable equations and statements, determine when single or combined statements are sufficient, and derive x and y from linked equations.

the lecture analyzes a data-sufficiency problem using two equations: 5r+3d=21.50 and 5(0.9)r+3(0.8)d=18.45, solving for r and d; both statements are sufficient, answer d.

Demonstrate a GMAT data sufficiency problem by deducing e = -3 from e^3 = -27 and noting the left side is negative; statement 1 sufficient, statement 2 not.

Analyzes a data sufficiency question about a unit-side parallelogram with a 45-degree angle, using a 45-45-90 triangle to determine the height and compute the area.

Solve a GMAT data sufficiency remainder problem by splitting X and applying remainder properties when divided by four. Statement one is sufficient, while statement two is not.

Solve a GMAT data sufficiency problem on painting colors, where green to yellow plus white equals 1 to 3 with a total of 12 quarts, yielding green = 3.

Analyze data-sufficiency for a GMAT problem on the average of x, y, and c versus z, showing how x+y relates to 2z and whether the statements are sufficient.

Analyze data sufficiency in circle geometry when the diagram is missing for question 321, making the statements insufficient and yielding answer E, unlike question 322 that provides a diagram.

Explore data sufficiency strategies using a two-circle Venn diagram problem to determine whether b+c is fixed, showing that statement 1 alone and statement 2 alone are sufficient.

Examine a two-size, two-color toy set with equal red and green counts; use two-thirds small and one-third large to prove large green is 1/6 of all green toys.

Examine parallelogram and square examples to show adjacent-side equalities alone do not prove P Q R S is a parallelogram; only the two statements together may resolve data sufficiency.

Explore data sufficiency for area comparisons by proving equal bases and equal heights in triangles; evaluate statements to confirm which suffices, as shown in ds #325.

Explore a GMAT data sufficiency problem on a sequence where each term is the sum of preceding terms, with the fifth term twelve and statements 1 and 2 yielding D.

Using data sufficiency, Green, Jones, and Smith involve three unknowns with two equations; statement 1 or statement 2 alone suffices, so the answer is D.

Apply the 30-60-90 rule to a GMAT data sufficiency problem, using the geometry formula sheet to deduce side lengths and determine that both statements suffice for ds.

In a 24-triangle mosaic, identify equilateral triangles with side nine cm, apply a 30-60-90 rule to find height, then multiply by 24 to obtain the total area in square centimeters.

This lecture shows how to compare the areas of triangles EDA and EBC by base and height, with equal heights, yielding a 1:2 ratio.

A data sufficiency approach guides a ball through a square opening, showing the radius and fit together determine the opening's perimeter, with both statements required.

Solve data sufficiency questions by analyzing a rectangle with triangles, using the three four five rule, and combining statements to determine area.

Master data sufficiency with a cube volume problem using the 45-45-90 rule and Pythagoras to find x and compute volume.

Use area reasoning to relate the legs x and y in a right triangle, showing xy = 100 from area 50, as part of a data-sufficiency approach.

apply data sufficiency reasoning to a 2020 edition ds 335 problem, deducing xy=30 and y=10 to find x=3, showing statement 2 is sufficient (answer b).

Using data sufficiency, this problem sets x+y+z=100 and blue 1, red 3 gallons to find green. Statement x=y alone shows green equals 1 gallon, with total 5 gallons.

Explore a data sufficiency problem on rent and utilities totaling 360, showing statements about move-out dates fail to determine the refund amount.

Solve data sufficiency problems on x^2 minus y^2 by evaluating statements; deduce that statement 1 is sufficient and statement 2 is sufficient, yielding final answer D.

Explain data sufficiency for a ten-student exam: mean and total do not reveal the maximum score, and with standard deviation, neither alone nor together are sufficient; the answer is no.

Demonstrates a data sufficiency approach to a cultural-performance attendance problem, using the reciprocal ratio (students per performance vs performances per student) to conclude the correct option b.

Evaluate two data statements about wool and cotton jackets to determine if at least a thousand jackets can be produced. Determine sufficiency by considering each statement alone and together.

Learn data sufficiency tricks using gcd problems, analyzing the gcd of 12 and n with the condition 12n = 432, and conclude that both statements suffice for the answer D.

Explore how base salary plus a 10 percent commission combines with car sales to determine total income, and see why incomplete data prevents calculation.

Analyze a data-sufficiency problem where x is a factor of 18 and 24, with values 1, 2, 3, 6; statement 1 alone is sufficient, statement 2 alone is not.

Analyze data-sufficiency strategies for discount pricing: relate the discounted price to the original price via a 25 percent increase and determine which statements suffice to find the discount percent.

Explore data sufficiency through a fixed rug and fixed stains scenario, using circle area to deduce the rug’s radius and determine whether the stains are covered.

Navigate a GMAT data sufficiency problem by analyzing a multiplication table of variables to determine whether C can be found, given nonzero constraints and relationships among A, B, and F.

Examine data sufficiency in GMAT problems by tracking how the sign of n, negative or positive, and 10 to the power values affect conclusions and consistency.

Analyze a GMAT data-sufficiency problem on a monthly plan with a base 20-minute rate and overage charges; determine sufficiency of statements, concluding statement 2 suffices and statement 1 does not.

solve a GMAT data sufficiency puzzle about three book prices to determine if their total is under 40 dollars using constraints on the most expensive price and price gaps.

Analyze data sufficiency with three-digit numbers by examining digit positions and the tens digit, then show that combining both statements yields a conclusive answer (option c).

Learn how divisibility works in data-sufficiency questions, as xy divisible by x+y hinges on using up the denominator; examples show how statements 1 and 2 together yield sufficiency, answer c.

Assess a two-product data sufficiency problem, where unknown quantities of P and Q affect profit; analyze why statements alone or together fail to determine if profit exceeds 2000.

Master data sufficiency reasoning for a GMAT probability scenario. Use P(none)=0.3 and P(one)=0.5 to deduce P(both)=0.2 and confirm the probabilities sum to one.

Explore data sufficiency in a gmat problem on conveyor belt distance, rate, and unit conversion, showing how statement 1 is sufficient while statement 2 is not.

Analyze data-sufficiency techniques for the GMAT by evaluating how X, Y, Z relate through averages and the X minus Y squared equals Z relation.

Examine a data sufficiency problem: a rectangle with a 1-foot border and inner perimeter 42, two unknowns requiring two equations, yet the statements do not determine the area.

Solve data sufficiency questions by laying out color-card scenarios, evaluating each statement's usefulness, and combining statements to determine if red or white probability is less than half.

Apply data sufficiency tactics by testing each statement and their combination to determine whether the equation can be solved, given the 2x+y and z structure.

Solve a data sufficiency problem on a parallelogram by applying opposite angles equal and adjacent angles sum to 180 to determine x.

Use Venn diagrams to determine the percent of patients who experience both side effects and relief in a data sufficiency context.

Test x values to assess X < 5 in a data sufficiency problem, showing statement 1 alone and statement 2 alone are insufficient, while combined data yield the correct choice.

Identify data sufficiency strategy by counting unknowns and equations, and forming relations from statements. Combining statement 1 and statement 2 yields four equations for four unknowns, enabling solution.

Evaluate how even powers erase the negative sign, making it impossible to determine whether z is negative from z^4 alone, illustrating why data sufficiency fails in this problem.

Explore data sufficiency reasoning in a GMAT problem: how loss and gain points affect a score, and when two equations with an inequality fail to determine the number of games.

Solve a data sufficiency problem about finance and planning committees using a 1 to 6 left-to-beginning ratio. Deduce equal original sizes and reveal 24 financial committee members.

This data sufficiency lesson analyzes whether a rectangular glass sheet can cover a 36 by 60 inch table, given the glass side area is 2400 square inches.

Develop data sufficiency skills by learning to maneuver a GMAT question so it matches statement 1 or 2, and determine whether either statement alone suffices to decide whether x+y>0.

Work through a data-sufficiency problem on whether sales tax exceeds 3% for a $624 guitar by computing 3% of the price and evaluating statements about tax and price.

Analyze a pentagon inscribed in a circle of radius 4, comparing its straight-edge perimeter to the circle’s 8π circumference, and apply triangle inequality to show it’s less than 26.

In this GMAT data sufficiency question 370, we compare 3x and 2y and deduce that x is less than y; each statement alone suffices, so the answer is d.

Analyze a rectangular box with edges L, W, H to compute its volume and surface area, deducing L=W=H=5 for V/A = 5/6, showing sufficiency of statements 1 and 2.

Analyze a data sufficiency problem with two consecutive odd integers that are negative and positive, yielding -1 and 1; together the statements are sufficient, so the answer is c.

Assess a data sufficiency scenario by analyzing two statements about x and y; one leaves two unknowns unresolved, the other yields x equals y, concluding answer B.

Explore data sufficiency by solving a problem with four consecutive odd numbers summing to 64, showing how one unknown and one equation yield the greatest value.

Solve data sufficiency problems by analyzing weekly versus Saturday totals for two bookstores, X and Y, using percentage relationships to determine whether X is greater than Y.

Explains a data-sufficiency GMAT question on a rectangular box, showing how changes to length, width, and height affect total surface area and that combined statements yield the needed increase.

Identify whether 17 is the mode of a list split into two halves, using data-sufficiency reasoning: statement 1 suffices, statement 2 alone does not, so the answer is A.

Solve a GMAT data sufficiency problem on a checking account balance for May 30, showing that statements 1 and 2 together determine the balance.

Analyze data sufficiency for discount problems, showing that without an initial price, percentage calculations are unusable.

Explore data sufficiency concepts with two equations and two unknowns, using consecutive numbers and their squares to determine solvability without solving for the exact value.

Analyze a data sufficiency problem from the 2020 edition to determine the sofa's selling price from its cost price and the profit relation, using one equation and one unknown.

Explore data sufficiency in a GMAT problem with 20 houses, an average of 160k, a median of 150k, and nine houses below the average.

Apply data sufficiency to determine if the library earned a $2,000 bonus by comparing spend against a $15,000 budget, given 50 books at $20 each and a 5,000 checkout threshold.

Analyze data sufficiency in a GMAT gift certificate problem with $10 and $50 items to determine total tickets sold.

Arrange the list in ascending order, locate X’s possible positions, and determine the median as the average of the 3rd and 4th numbers. Conclude the correct answer is a.

This data-sufficiency example uses three dice with x+y+z=12 to test statements about possible values. Combining them reveals that five must appear, making the correct answer C.

Apply a visual approach to a DS question, combine statements 1 and 2, deducing t is negative and the answer is C.

Apply data sufficiency strategies to count triangles from five points using combinations. Conclude there are ten distinct triangles.

Analyze GMAT data sufficiency by comparing discounted prices from two stores using percentages of the original price to form equations. Combining statements yields enough information to determine the correct answer.

Master data sufficiency strategies for GMAT by analyzing rounding behavior to the nearest tenth and nearest integer, evaluating statements for sufficiency, and identifying answer choices.

Replace square and triangle with X and Y to form 3X times 2Y = 864 and X+Y = 10, showing equations with unknowns suffice to determine X; answer is D.

In this GMAT data sufficiency lecture, derive ratio of lengths on a line with M and Q, form equations, and show statement 1 is sufficient while statement 2 is not.

Assess a GMAT data sufficiency problem with three shirt prices to decide if their sum exceeds 60; statement 2 suffices, while statement 1 alone does not.

Explore data sufficiency strategies for GMAT questions, solving a quadratic in n and evaluating statement sufficiency to determine whether a unique value exists.

Explore data sufficiency in GMAT by evaluating whether 500 calls can be processed with X processors and per-processor capacity Y, given ranges 100–200 calls.

Solve data sufficiency questions about spending on roses and daisies, where roses cost $1 and daisies $0.50, to determine if Kim spent more than Sue.

Solve a gmat data sufficiency question on jazz and blues revenue from 1998 to 2000, showing statement 1 insufficiency and using statement 2 to compute the 1998 revenue.

learn data sufficiency on average speed using the dst triangle; total distance equals 2x+3y, total time 5, so the average is 80/5 = 16.

This data sufficiency problem shows sqrt(x) is an integer only if x is a perfect square. Neither statement alone nor together determine unique x, so the value cannot be determined.

Solve data sufficiency problems for a right circular cylinder by applying volume formula π r^2 h, using diameter 4 ft (r=2) and height 6 ft, to confirm the volume.

Use a number-line with Q and S to identify which is closest to zero, then apply a test-value approach showing that statement 1 suffices in data-sufficiency problems.

analyze data sufficiency using amusement park prices: 5500 yen for adults and 4800 yen for children, showing that statements about adults or children alone are insufficient, but together determine count.

This lecture demonstrates solving a data sufficiency triangle area problem by identifying base and height and using area = 1/2 base height, with BD times EC = 20.

Analyze a data sufficiency problem about equidistance from two points on a coordinate plane, showing that statement 1 suffices while statement 2 does not, and derive the answer.

Solve a GMAT data sufficiency problem on the ratio of average heights, showing why statement 1 can't determine X or Y without class sizes; the answer is E.

This lecture demonstrates ds techniques for two-digit numbers, testing candidates below 40, comparing n with four times its units digit, and confirming sufficiency through explicit examples such as 39.

Demonstrate solving a GMAT data sufficiency problem by analyzing x^2=81 to show x=±9, simplifying 2x+y=48 to x+y=16, and concluding that statement combination yields the answer B.

Solve a data-sufficiency GMAT problem about a salesman’s pay, showing how $300 plus 5 percent of sales over 1000 equals 10 percent of sales, yielding 5000 in sales and the pay.

this data sufficiency problem explores determining donut and bagel prices for five donuts and three bagels. statement 1 alone suffices, while statement 2 alone is not sufficient.

Explain how to compute the areas of triangles ABC and DHB using the triangle area formula and the 45-45-90 isosceles right-triangle rule, then combine statements to prove equal areas.

Determine if a fraction yields a finite decimal by the denominator's factors of 100, notably 2 and 5; statement one is sufficient and statement two is not; answer is a.

Analyze a data sufficiency problem with r over s and s over r, test each statement using numbers, and show that either alone suffices, yielding answer d.

Explore data sufficiency in GMAT problems by analyzing remainders and divisibility within a 56 to 66 range, determining when statements alone or together identify the key value.

Explore data-sufficiency analysis for GMAT style questions where a positive integer x is prime because 3x+1 or 5x+1 is prime, showing both statements alone and combined may be insufficient.

This lecture demonstrates data-sufficiency strategies for median problems by arranging numbers and comparing statements about k and n, showing that combining statements 1 and 2 yields the median of 10.

Use data sufficiency to determine x plus y, given x and y are integers. Statement 1 yields x plus y equals 7, and statement 2 confirms it.

Analyze data sufficiency for mortgage payments, taxes and insurance, using one third and one fifth relationships to determine the taxes paid; determine when statement 2 alone suffices.

Learn to solve data sufficiency inequalities by cross multiplying and a bottom-up approach, verify statements 1 and 2, and conclude that statement 2 alone suffices, giving answer b.

Use a Venn diagram with X and Y to analyze a data sufficiency question, determine the intersection and X/Y ratio, and show that statements 1 and 2 together suffice.

Analyze how to determine the average of five consecutive even numbers on a number line using their middle value, and test data-sufficiency with sums like Q+S=24 and Q+R=22.

Learn to interpret least integer greater than or equal to x, apply GMAT data sufficiency reasoning to statements 1 and 2, and determine the answer on a number line.

Develop GMAT data sufficiency skills using 2018–2020 edition problems, showing how statements 1 and 2 prove x is greater than minus y when y is negative.

Explore how quadratic equations and factoring reveal roots and signs in GMAT data sufficiency. See why a negative last term makes the signs different, rendering statement 2 sufficient.

Break down the composite figure into four rectangles, formulate area expressions for each region, and use the perimeter to test statement sufficiency in this data sufficiency question.

Solve data-sufficiency problems by applying ratio reasoning to shirts, dresses, and jackets; show that statement one is sufficient to determine exact counts (18, 8, 10) in the closet.

Compute the region's expense by applying the 94-degree angle to the 360-degree circle of a 5.4 million total, and assess whether data about the regions suffices to determine that amount.

analyze a data sufficiency question with negative x, showing that x^2 > 9 implies x < -3; statement 1 is sufficient, statement 2 is not.

Solve a data sufficiency problem on how many cans fit in a carton, showing that carton and can dimensions alone are insufficient and that combining information is required.

Use data sufficiency techniques to find r from statements about v and z with v+z=6 and grid constraints; statement 1 alone yields r=3, and statement 2 also provides sufficiency.

This data sufficiency walkthrough tests x and y grams with a 3x+5y<40 cost constraint and x+y=10, proving x>y and selecting answer B.

Analyze data-sufficiency to determine the train speed halfway through a 450-mile trip. Examine why statements 1 and 2, alone or together, fail to fix the instantaneous speed.

analyze a GMAT data sufficiency problem, using the average of 120,000 to identify Jane’s price as the median and determine which statements suffice.

This data sufficiency lesson tests x in (-2,2) under x^3 < x^2, showing integers give x ∈{-1,0,1}, with only -1 satisfying the inequality, so the answer is B.

Analyze GMAT data sufficiency strategies for a mean problem by evaluating how max and min operations constrain W under statements 1 and 2.

Combine top and bottom shelf data to apply data sufficiency techniques. Identify the 25th book among 49 and conclude the median page count is 400.

apply data sufficiency to determine the shaded area between the big circle and the inner circle, using radii 5 and 3 and pi.

Explains data sufficiency using a ds problem on estimating trip distance and average speed, showing that statements about distance and speed ranges alone or together are insufficient to determine time.

The lecture shows that the average equals the median only for consecutive three numbers, illustrated with two three four, and finds that both statements are sufficient in the ds problem.

Shows that a line not through the origin has a negative slope, since the x-intercept is twice the y-intercept; rise over run yields slope -1, illustrating data sufficiency reasoning.

Explore data sufficiency in GMAT problems by solving two equations in x and y to determine b, and evaluate whether each statement alone suffices.

Analyze a GMAT data-sufficiency perimeter problem, using a six-length configuration and a partial 9 perimeter to decide whether single or combined statements suffice to determine the outside perimeter.

Identify how a range is the difference between the largest and smallest numbers in a set, and why unknown values in S and T stop you from comparing their ranges.

Use x^2 + y^2 = 100 and area 25 to get xy = 50. Then (x+y)^2 = 200, so x+y = 10√2 and perimeter = 10√2 + 10.

Analyze a two-truck data-sufficiency problem: truck one must hold more than half of total shipments, and statement 2 alone is sufficient to prove S3 sits on truck one.

Explore data sufficiency in a GMAT problem with three-digit numbers x, y, z, testing whether x's hundreds digit equals the sum of y and z's digits.

Analyze data sufficiency questions about voter outcomes in a 100-vote scenario, dissecting totals, favorable and unfavorable counts, and the intersection where a voter favors both candidates.

Analyze two statements to determine if n/m is an integer for classroom assignments. Statement 1 is not sufficient; statement 2 is sufficient, so the answer is B.

Walks through a data sufficiency question by plugging in numbers to test statements; shows statement 1 is sufficient, statement 2 is not, yielding the answer A.

Explore GMAT data sufficiency by determining the median number of employees per project using a high-end percent table, concluding about three and selecting option C.

Analyze profitability by comparing $100,000 plus 5% of revenue to revenue from unit sales, showing data-sufficiency that statement 1 is insufficient and statement 2 is sufficient.

Solve a data sufficiency problem with monthly deposits of 120 and later withdrawals of 50, using April and June balances to bound the high and low, and determine the range.

This data sufficiency lesson analyzes a 15-number list, showing any three numbers sum to 12 only if all numbers are 4; statement 1 fails, statement 2 suffices, answer B.

this lecture explains a GMAT data sufficiency problem: with an average of six numbers equal to 75 and none below 75, all must be 75, via statements 1 and 2.

Demystify data sufficiency questions on commissions by analyzing first-half vs second-half sales, percentages, and averages to determine what information is enough to compute Jane's commission.

Derive base and height from the triangle area and apply the Pythagorean theorem to find a side length. Conclude that statement 1 is sufficient, yielding the DS answer D.

explore data sufficiency questions from GMAT prep, deducing k from a numeric constraint and confirming that both statements are sufficient, yielding the answer d.

Assess data-sufficiency in a GMAT geometry problem by evaluating statements about angles, using 180- and 360-degree sums to show X+Y = 140 when combined.

In this data sufficiency lecture, we simplify a square-root inequality, reformulate the problem, and test statements one and two with sample values to determine sufficiency, concluding option a.

Model direct proportionality with constants to form two equations linking P, E, and I; deduce constants from the statements and assess sufficiency. Statement 2 is sufficient; statement 1 is not.

This lecture analyzes a data sufficiency problem on the tens digit, showing how multiplying by 10 shifts digits and that statement 1 is sufficient while statement 2 is not.

Analyze a GMAT data sufficiency problem, using a mean relation and fraction splitting to test statements. Conclude that statement 1 is sufficient while statement 2 is not, yielding answer A.

Learn to assess data sufficiency questions by testing each statement's sufficiency, using logic over math, and identifying when combined information still leaves totals or neither unknown.

Master data sufficiency by matching unknowns to equations; test each statement alone, then together, using a map of two unknowns and two equations to determine sufficiency.

Explore data sufficiency strategies by modeling income, expenses, and savings where spending half leaves half, saving a third of the remainder equals 600, and evaluate statement sufficiency.

Evaluate data sufficiency for a right triangle problem by checking whether points P and Q share x coordinates and whether PR shares a y coordinate, showing combined statements yield sufficiency.

Compare inflow and outflow rates to determine the tank's gallons-per-minute increase. Statement 1 is insufficient; statement 2 alone is sufficient, so the answer is B.

Analyze data sufficiency with the cube root of w, using statement 1 and statement 2 to determine whether each statement alone is sufficient and identify the correct answer.

Analyze a data sufficiency problem: start at 18 seats, add two per rule to 27 rows, with the last row at 70, to determine total seats; both statements are sufficient.

Apply the distance–speed–time triangle to compute the overall speed for a 50‑mile journey, using statement data (30 miles at 60 mph; 20 miles at 50 mph) to assess data sufficiency.

Explore how data sufficiency resolves a boys-to-girls ratio problem, using statement 1 and statement 2 to show the ratio is 1:3 and conclude the answer is D.

Apply data sufficiency to a 300-term sequence using a known term and common difference, and use ds map to identify statement 1 as sufficient and 2 as not, answer A.

Explore data sufficiency by using two statements about a company's donation percentage of profits to decide if last year's donation exceeded $10,000. Together, statements 1 and 2 are sufficient.

Analyze a data sufficiency scenario in the GMAT prep course, where multiple investments and unknowns show that two equations cannot determine three unknowns.

Explore data sufficiency strategies for non-proportional relationships, learning to follow the 'do not proportionally' rule, interpret profit-by-unit scenarios, and determine when statements suffice in GMAT DS problems.

Explore data sufficiency techniques for GMAT style problems by selecting values that yield an integer square root and an even result, using perfect squares to verify the conditions.

Explore data-sufficiency strategies to determine how many fewer hours Carmen must work after a $1.50 raise (a 20 percent raise) to keep the same weekly pay, using a 30-hour reference.

Explore number system positions from units to thousands and decimal places, and apply rounding to the nearest hundred and thousand to solve data sufficiency questions.

Examine data sufficiency for positive integers A and B by testing parity of the sum and product, using examples, and conclude with a data sufficiency answer described in the lecture.

Access the adaptive GMAT practice test on successprep.com, log in, purchase, and start timed sessions. Analyze analytics for math, data sufficiency versus problem solving, pacing, and school comparisons.

analyze GMAT data sufficiency questions with two dish types, x and y, by forming equations from statements 1 and 2 to determine whether x is less than y.

Evaluate a data sufficiency question about three days of science fair attendance. Compare 30 percent two-or-more days and 10 percent at least one day to illustrate data-insufficiency reasoning.

Apply data sufficiency techniques using the average formula for three items, and analyze 6 percent tax on items over 80, illustrated by a 50 average and 100 maximum.

Explore how standard deviation measures how far data deviate from the mean, using eggs in nests, and show that identical counts yield zero deviation, clarifying data sufficiency for ds questions.

Explore data sufficiency in GMAT pricing by deriving SP = CP + M and evaluating M as a percent of SP, including a 25% markup example.

Analyze statements about two unknowns with two equations in this GMAT data sufficiency lesson; alone they are insufficient, but together they yield the answer C.

Explore data sufficiency in a GMAT ds problem about 900 students attending a science fair over three days, showing that statements alone and together may be insufficient.

Apply data sufficiency to find graduate counts from total 80: statement 1 sets graduates as three times non-graduates, statement 2 says non-graduates exceed graduates by 40; together, answer D.

Analyzes data sufficiency for the tens digit of a decimal using statements about numbers below one third and above one fourth, showing no definitive tens digit.

Analyze a GMAT data-sufficiency question from the 2017 edition, focusing on x, y, z and two statements; combining them shows z is the greatest.

Explain data sufficiency for x and y through two scenarios, showing that statement 2 (b < c) guarantees y > x while statement 1 does not, yielding the answer B.

Apply a two-circle venn diagram to a GMAT data-sufficiency problem about directors in two companies; show that statements 1 and 2 together are sufficient to determine the intersection count.

Explore data sufficiency strategies for a GMAT profit-percent problem, showing how profit as a percent of cost can be determined from x and y in the 2017 edition.

Solve data sufficiency questions by analyzing X and Y with XY = 100, exploring possible factor pairs, and using algebraic manipulation like square root transformations to determine sufficiency.

solve data sufficiency problems on taxi fare pricing with first-mile f cents and m cents for each additional mile, using two equations to determine f and m.

Explore data sufficiency in a GMAT question about net income, where a 4 percent income rise and a 15 percent deduction rise show why starting values matter.

Master GMAT data sufficiency using district ratios of teachers to students. Recognize when one equation is insufficient and combining equations cannot determine district M to district P student ratios.

Analyze a GMAT data sufficiency question about the tens digit, using remainders modulo 100 and 110 to show statement 1 yields a consistent tens digit, while statement 2 can vary.

Analyze a data sufficiency scenario using a Venn diagram of loans and scholarships, with 200 students and statements about those with only loans, only scholarships, and both.

explain a gmats data sufficiency problem with three machines k, m, and p to determine k's solo time, assessing if statements 1 or 2 suffice given 24 minutes total.

Analyze data sufficiency using a seesaw model to balance a global average of 80 with more men and lower male scores, showing women must have much larger values.

Examine a 2017 ds question where the total donated equals 120,000, with one equation and one unknown; statement 2 is sufficient, giving answer D.

Breaks down a sufficiency problem with a 60000 investment split between x and y rates, forming three unknowns and two equations, showing how combining statements tests sufficiency to yield c.

Solve a data-sufficiency problem with 125 dollars in five- and twenty-dollar bills, using divisibility and integer constraints to find the bill counts and show that both statements suffice.

Explores the distance-speed-time triangle and how to form time expressions from distances and speeds; shows that with multiple unknowns, the data may be insufficient to solve.

Analyze a 2017 edition data sufficiency problem on the greatest power of two that divides numbers, using examples to compare the two height concepts. Conclude that statement 2 alone suffices.

GMAT data sufficiency problem requires selecting eight numbers from a ten-number sequence and removing 22 and 4 to achieve a mean of 13 with a standard deviation of 2.

With x and y integers and x = y + 1, the product xy is always even, as demonstrated in examples. Statement 1 alone suffices, so the answer is D.

Analyze a 2017 DS problem on midpoints in triangle ABC, using area fractions to relate a known value to the whole. Conclude statement 1 suffices, statement 2 does not.

Evaluate data sufficiency in a GMAT problem by analyzing ratios and multipliers for pens, pencils, and pads to determine if the total staff and item counts can be deduced.

Apply data sufficiency techniques to a gmat problem about passengers, employees, guests, and managers, using fractions to deduce total passengers and non-managers; conclude P=690 and non-managers=345.

Explore data-sufficiency questions in circle geometry by linking circumference and radius to area, using halves of circumferences to find radii via pi r^2.

explain how to compare ranges by max minus min and evaluate data sufficiency; neither statement alone nor together reveals enough to decide if X's range exceeds Y's.

Analyze rent changes from 1997 to 1999 using a $100 baseline with x and y in data sufficiency; evaluate statements 1 and 2 to decide if 1999 rent exceeds 1997.

Analyze a data-sufficiency triangle problem with hypotenuse 10 and area 25 cm², deriving xy = 50 with Pythagoras. Use the 45-45-90 case x = y to determine the perimeter.

This lecture shows a data sufficiency problem using the region x+3y ≤ 6, evaluating statements about r and s, and demonstrates that neither statement alone nor together yields unique solution.

In this data sufficiency walkthrough, determine the volume of a rectangular solid by deducing its length, width, and height from face areas 15 and 24, with 40 opposite faces.

Analyze a 2017 data sufficiency problem about a 2600-word book now split into 25 paragraphs and conclude the answer is B.

Analyze a 2017 edition data sufficiency problem on absolute values of an integer X, evaluating whether |X| < 2 and how negative values affect the conclusion.

Use a computer-adaptive, timed GMAT practice test with analytics on data sufficiency and problem solving. Track pacing and pinpoint weaknesses in topics like circles, fractions, inequalities, and geometry.