GRE - GMAT | Advanced Learners | Math Marathon

Analyze number properties and quantitative comparison questions, focusing on primes, remainders, odd/even integers, and distinct prime factors to determine relationships between columns.

Master quick quantitative comparison strategies for number operations on the GRE/GMAT, using practical tricks—factoring, cross-multiplication, LCM, and direct calculation—to decide A, B, C, or D.

Master quantity comparison with operator-defined functions and logic word problems, including rounding decimals to thousandths, static operations, and algebraic concepts like the drop of a square and nonzero integer properties.

Explore algebraic quantitative comparison strategies, decide which quantity is greater, equal, or indeterminate across varied problems, using linear, quadratic, and variable relationships.

Master averages and quantitative comparison through practical examples. Compare arithmetic means across scenarios such as column A versus column B to determine which average is higher.

Advance your math mastery with a 150–200 question marathon for learners who completed basics like percentages, averages, ratios, and basic probability to prepare for the final test.

Discover quick strategies to compare fractions, identify the smallest or largest value by pairwise comparisons, and decide without full denominator conversion or equalization.

Learn two methods to solve a gas tank capacity problem, converting initial and final levels from fractions and comparing gallons added to find the tank capacity.

Analyze a Q-3 problem about a photographic negative with given dimensions, and determine the shorter side when the long side is four inches to maintain proper orientation.

Determine how many newspapers Bobby delivered by applying a 10 percent commission to his earnings and using 20 cents per paper to compute the quantity.

Explore how to compute margins from vote percentages; for example, 84 percent vs 16 percent yields a 68 percent margin and 476 votes in a 700 vote total.

Solve a GRE math problem about two consecutive ages using the difference of squares to identify a pair whose squares differ by 120 and confirm the difference exceeds 20.

Explore angle relationships with parallel lines, using the Z rule and alternate interior angles along with the W rule to find angle B, yielding B = 70.

Identify non-multiples of three by testing divisibility of expressions like six, eighteen, and x, using elimination to reveal the non-multiple.

Solve a ratio problem with 5 to 4; 900 legislators voted in favor, so 720 voted against.

Solve counting problems using fractions in multi-part setups by computing one fifth of twenty and determining the total number of items in the scenario.

Learn to compute the average of three values by adding them and dividing by three, convert values to decimals, and recognize that in sequence the middle value equals the average.

Solve a 28-coin problem using nickels and dimes to find the total value in dollars. The calculation confirms 16 coins totaling 160 cents, or 1.6 dollars.

Solving a quadratic-like equation by moving terms across sides and subtracting X squared from both sides, this exercise uses square properties to determine X, with the solution labeled as B.

Start with 10 liters of a solution that is 20% acid, add 6 liters of pure acid, and obtain a 16-liter mixture that is 50% acid.

Solve a circle geometry problem by noting two equal angles, set X + X + 85 = 180, solve X = 47.5 degrees, and identify the answer as C.

Explain how to determine the largest value in question 16 by testing x negative and y between zero and one, narrowing options to conclude that option B is the largest.

From the gre-gmat math marathon, this segment covers a rent-sharing problem where base rent is B dollars per student and a 100-dollar increase requires each student’s new contribution.

Learn to compute percentage change by dividing price change by the initial value. The lecture shows how decreases and increases require different denominators, with a stock example yielding 16 percent.

Tackle percent increase and decrease tricks in percent problems, showing why 80 percent is the correct answer for a 25 percent change scenario.

explore a two-part investment: split 200 dollars into x and 200 - x with 4% and 5% returns, then equate 4% of x to 5% of 200 - x to compute total income.

This lecture demonstrates solving a diameter-based circle problem by locating the center coordinates as the midway between endpoints, and by solving the same using equations, yielding (0, -4).

Two trains start 287 miles apart at 10 am and meet at 1 pm, with the faster train 6 mph faster, traveling 44 mph and the slower 38 mph.

Solve a quick market puzzle: buy 10 oranges for 25, sell 9 for 25, and determine the percent profit from the one remaining orange, which yields about 11.1%.

Explore how gear teeth and diameter inversely affect revolutions per minute. Apply gear ratio reasoning to solve rpm problems.

Solve a seven-number average problem by summing six known numbers—86, a value in the 80s range, 92, and 81—and solving (sum plus x)/7 = 84 to find x = 77.

Solve the linear equation using elimination or substitution, then combine terms and substitute back to confirm x = 3.

solve a q-27 style math problem by simplifying expressions with square roots and fractions, comparing options, and choosing the correct answer from the given choices.

Master age problems by subtracting years to compare Melanie and others, using algebraic steps like minus x and seven years ago to identify when ages align.

Solve a parallelogram angle problem by setting x and five x to sum to 180, yielding x = 30 and determining the target angle.

Learn to solve a combined work-rate problem: a pool fills in three hours and drains in six, so with both pipes open it takes six hours to fill.

solve a geometry area problem for question 31 by breaking the figure into convenient parts and applying rectangle logic, concluding the total area is 99 (option 8).

Discusses question 32, a fraction-based student participation problem, and analyzes how relationships between girls and boys and total participants affect solvability and reveal inadequacy without a defined ratio.

Clarify question 33 with Pete Persad and Ray's number, showing an easy method to infer one hundred and eleven and caution against guessing.

Compute the average salary for nine executives with salaries of 150k, 70k, and 80k. Conclude that the overall average is 160k.

Solve a Q-35 problem where the original fraction has denominator twice the numerator; after adding four to both parts, the value is 5/8.

solve a 140-foot fencing problem for a rectangular field by relating sides X and Y, using a 3-4-5 right triangle to compute the diagonal.

Analyze a large triangle with heights 15 and 20, computing the square as 20^2 minus 15^2 equals 175. Then deduce surrounding square dimensions to select option B.

Solve the quadratic equation 25x^2 = 4 to find x = ±2/5, revealing two possible values.

Determine how many 3-inch cube tanks fill a 10 by 8 by 4 inch tank, when transferring to two ship tanks each 3 inches on a side, using whole tanks.

Explore two strategies for solving a quadratic: check options to verify values, or factor the equation. Factoring yields (x-3)(x-16) = 0, giving x = 3 or x = 16.

solve advanced algebra problems by factoring and simplifying to find the value of x minus one, shown through a quick exercise where the answer is 3.

Compute the overall average speed for a two leg walk by combining 2 miles at 5 mph and 2 miles at 4 mph, using total distance over total time.

Count the outer-edge tiles of an eight-by-eight square floor with black on the edge and white inside, and arrive at twenty-eight, while noting that thirty-two is incorrect.

Solve a two-species mixture problem by finding the fraction of dogs in a shelter with dogs and cats, clarifying the meaning of 'part of' and 'of' for accurate proportion calculations.

Identify pairs x and y on the real number line whose distance is 16.5, using the absolute value relation |x - y| = 16.5.

solve a question from a GRE-GMAT math marathon that uses fractions, reciprocals, and percent calculations to determine the correct option.

Examine percent change in prices by analyzing decreases and increases, using examples like 10%, 20%, and 110% versus 80% to show how price values shift from the original.

Explore percent concepts through a quick example, showing how 45 is a thousand percent of 1.5 and identifying the correct option as 3155.

Analyze a multi-speed trip with 10 miles at 30 mph, 10 miles at 40 mph, and a distance at 50 mph to determine the time share at 50 mph.

In this math marathon problem, determine how many distinct moves exist when moving a piece by the sum of two dice, considering all possible sums.

Analyze how three straight lines crossing a circle maximize non overlapping sectors, revealing seven sectors as the maximum; identify seven as the correct answer.

Solve a senior versus non-senior attendance problem for a school play using percent data, concluding that the attending proportion is 50 percent.

Solve a word problem linking Sally's and Charles's money by forming and solving an equation with 0.6C plus 6, leading to the conclusion that Charles has nine dollars.

Solve the blue-house counting puzzle: determine how many east-side houses numbered 122 to 182 are painted blue, revealing that the answer to question 14 is 31.

Solve question number 15 by testing various expressions for divisibility by three using remainders, and determine how many options satisfy the condition, selecting the correct choice.

Apply inclusion-exclusion to a 27-student problem with 18 in the French club and 15 in the Spanish club to find that 6 students belong to both clubs.

Solve a linear equation for x by isolating x and dividing both sides by two, expressing x in terms of the other variables.

Master approximations by converting fractions to decimals, memorize common decimal equivalents, and apply quick transformation tricks to identify the correct option.

Compute the average of six numbers by summing 15, 18, 14, 13 and X, then dividing by six, given the average is 14, and apply strategies for directed language questions.

Explore a math word problem about ingredients and ratios, using equations to balance quantities like eggs, milk, carbs, and reach a target total.

Learn how to translate fraction-based statements into equations and solve for the unknown, using verification and option-check strategies to find the correct value.

Learn to solve a linear inequality by isolating x, applying sign changes when multiplying or dividing by negative numbers, and carefully moving terms to reach the solution set.

Angles on a straight line sum to 180 degrees; apply this rule to determine the answer for AP question 23, option B.

Explore q.24 by guiding learners through algebraic manipulation of squared terms without a calculator, highlighting strategies for solving complex square-based expressions.

Solve a library problem by determining the nonfiction count from a total of 8000 books in fiction and nonfiction categories, yielding 5000 nonfiction (option seven).

Calculate the average cost per mile for a tiered trip: 10c for the first 50 miles, 20c for the next 20, 30c for the last 10, totaling 15c per mile.

Compute the density from the 75-foot piece weighing 9 pounds, then divide the total weight by that density to obtain the original length of 100 feet.

Apply angle-sum rules for triangles and the full circle to determine that three angles sum to 180 degrees. Use this to answer question 28 in the figure.

Analyze consecutive negative integers x, y, z to determine which expression yields a positive value. The last option, x minus y, y minus z, is identified as the correct choice.

Compute Kobe's weekly earnings: base $100 plus 5% of $8,000 equals $500. The ratio of total weekly earnings to commission to total earnings is 5:4:5.

Learn power and exponent rules for complex expressions, including keeping bases intact, choosing when to subtract or divide, and identifying the maximum factor to determine the correct result.

Explore a ratio problem on weight to mix and tank quantities, and learn two methods to solve it and determine the final ratio and answer.

Solve the five consecutive integers problem where the sum relates to three times the largest plus thirty four, and determine their sum.

For a six-player round-robin tournament, compute how many distinct matches occur when each player faces every other once; there are 15 possible games.

Explain the cost structure of a city-to-city phone call: the first three minutes cost one dollar, with additional minutes charged thereafter, yielding the maximum talk time of eleven minutes.

solve a data interpretation problem that asks for the average of the highest and lowest scores given ten test scores, dropping the extremes, with the remaining average 82.

This lecture guides solving a circle geometry problem by applying the 360-degree circle, recognizing opposite angle relationships, and using triangle sums to find the missing angles.

Analyze when X or Y negative makes expressions negative, including X^2 and -5X^2, and determine that only option B must be negative.

Balance and manipulate algebraic expressions to establish equivalence between two sides, using division by three, and conclude that the answer is one.

Explore problems with 1/x, minus 1/x, and x squared, and analyze how the value of x influences these expressions in today’s session.

This lecture presents Q.01 of the GRE-GMAT math marathon, guiding advanced learners through a numeric logic problem that tests even/odd reasoning and option evaluation to determine the correct answer.

examine a 36-candy box with a 5:4 light-to-dark chocolate ratio and determine the counts of each.

In Q.03, the figure is a square with all four sides equal, leading to a side length of seven and a perimeter of twenty-eight.

solve a work rate puzzle: find how long machine y takes to produce W widgets when x makes W in five minutes and together they make W in two minutes.

Solve 111 percent of 70, showing that moving decimal places converts percent, and suggesting quick practice and calculator use if allowed; the caption concludes the answer is option B.

Tackling question 6 in the math marathon, explore parity, squares, and arithmetic expressions across options to identify the correct answer.

Determine how a thousand-dollar bonus is divided among Dean, Robert, and Vangie when Dean's share is twice Robert's and Robert's is twice Vangie's.

Solve a four-package average problem by using an initial total of 64 pounds and a remaining total of 42 pounds after removal, revealing the removed package weighs 22 pounds.

Solve question nine on a quadratic square puzzle by manipulating nested squares and sign changes to determine XY, with the answer identified as b.

Tackle word problems by translating quantities, prices, and relationships into equations using multiplication and subtraction. Solve for variables such as p and x in practical scenarios like residents and purchases.

Solve a percent-change temperature problem: starting at 66 degrees, increase 25% in the afternoon and decrease 25% in the evening to reach about 61.8 degrees.

Work through a word problem about pounds of coffee priced in dollars with an unknown x, referencing Starbucks. Translate pricing scenarios into equations for GRE-GMAT math marathon.

Determine the seating arrangement for fifty children on seesaws, with two per seesaw, noting that twenty-five seesaws would be occupied.

Examine the equation where nine equals y minus one over t, and verify equality by performing operations on both sides, including multiplying by three, to determine truth.

Calculate the fraction of old price per ounce to new price per ounce when a four-ounce bar shrinks to 3.6 ounces at the same price; result is 9/10.

Solve a two-thirds distribution puzzle about microphone company X with 60 employees, identifying programmers, salespeople, and others to determine how many fall into each role.

Allocate $10,000 between six and five percent investments, with x at six percent and (10,000 - x) at five percent, to express the annual income from the five percent portion.

Solve a classic age-ratio problem from the GRE-GMAT math marathon: with Jim at 20 and Gary at 14, determine how many years ago Jim was three times Gary's age.

explore a GRE/GMAT style coin problem with nickels and dimes for 45 clients, totaling 3.5 dollars, illustrating how to calculate additional coins needed.

Two buses starting 515 miles apart meet after five hours as speeds add to 103 mph when moving toward each other.

Apply rate and proportional reasoning to determine the time to seal 720 cans at 4.5 cans per 2 seconds, converting the result from seconds to minutes.

Analyze a salary problem with percentage raises: a clerk at 256 dollars, a supervisor 50 percent higher, then both gain 64 dollars, ending at 448 dollars.

Solve a mixed-amount problem by adding an ingredient to adjust the final mixture from 32 percent to 12 percent, determining the required amount x through equation setup.

Analyze question 24 on events, outcomes, and their values in a probability context, identifying which options describe valid events and one-time events.

Solve for x in a circle-angle problem by using the fact that the full circle equals 360 degrees, with given angles of 90 and 150 degrees.

Solve a two-speed distance problem by equating the distance for the trip to college: 60 mph for two hours and 50 mph for the return, yielding a 120-mile distance.

Solve an age-riddle using multiple relationships: Harold is twice Jack’s age and other age links, then apply algebra to determine Jack’s exact age.

Combine two hoses delivering 2 gallons per minute to fill a 40-gallon tank from empty, taking 40/7 minutes, about 5.7 minutes.

Solve x^2 - 4x = 21 by factoring or by checking the options, yielding x = 7 or x = -3.

Formulate a stock sale problem by setting up an equation with an average cost per share of 40 and 10,000 and 12,000, then substitute to determine number of shares sold.

Use a Venn diagram to tally two groups: 18 in French, 15 in Spanish, with 27 students total. Compute how many are in both groups to find six students.

This q.32 math marathon lecture analyzes a logic puzzle about what must be an ANA, testing truths like two plus one equals three, two times, and one plus one.

Solve a word problem involving fractions of money, including half, one third, and five dollars, expressed as equations in X to find the total amount.

This lecture practices solving a GRE/GMAT math problem by establishing relationships between quantities, guiding students to identify the correct option (eight) for question q.34.

Explore inverse relationships in work-rate problems: with three printing presses, a job takes 60 minutes, and with five presses it takes 36 minutes, illustrating proportional time reduction.

Compute the average toll per mile for an 80-mile trip with tiered rates of 10, 20, and 30 cents.

Solve question 37 by linking the rectangle’s area to its side lengths, using 54 percent and algebraic expressions to determine which option fits.

Examine number properties in a GRE/GMAT style problem, focusing on ensuring even outcomes through multiplication of specific values for advanced math learners.

Solve question 39 by expressing one over three and evaluate terms about access to trade, export, and world access to determine the correct option.

Explore how a 10 percent increase followed by a 10 percent decrease yields a net 1 percent drop from the original, using the 110 example to show 99 percent effective.

Learn to calculate the net effect of sequential percentage changes by multiplying 1.10 and 0.80 to get 0.88, revealing a 12% decrease from the original price.

learn to compute the average speed for a round trip with equal distances using the formula 2*s1*s2/(s1+s2), illustrated with 30 mph and 40 mph, and avoid dividing by two.

Calculate the discount percentage on a cost price of 400 with a 25% markup to 500, then selling at 450 yields a 10 percent discount.

Solve an averages problem: with three boys averaging 140 pounds (total 420), adding a fourth raises the average to 145; the fourth boy weighs 160 pounds.

Solve a 100-liter juice mix at 20% by adding pure juice to reach 50%, yielding x = 60 liters.

Solve a ratio puzzle with male to female 5:3 and married to unmarried 1:3; given 20% of males are married, compute the female unmarried percentage, which is 66.66%.

Explore a mixture problem with costs of 20 and 12 per kilogram, targeting an 18 per kilogram mix. Use the difference method to obtain a 3:1 ratio of the expensive to cheaper component.

Solve an upstream downstream wind problem: with still-air speed of 500 mph, two hours downstream and three hours upstream give wind speed of 100 mph.

Apply inverse work-rate to a four-man problem: ten hours with four men means twenty hours with two men; eight hours cover two-fifths of the job, confirming two methods agree.

Compare 30 wpm and 40 wpm to derive hourly words and pages from a 600-word page. Compute Frost's and Omar's errors per hour to obtain a 3:10 ratio.

Apply basic combinations by multiplying choices, selecting one from five shirts, one from six options, and one from three ties, yielding 90 possible outfits to wear to work.

Compare simple interest and compound interest on a 20000 principal at 10% over two years, highlighting a 200-dollar advantage of compounding.

Apply inverse proportional reasoning to a survival problem: twenty people use food for 100 days; after twenty days four die, leaving sixteen, yet the supply lasts 100 days in total.

Five teams play each other six times, yielding sixty games in total. The lecture compares two counting methods: using combinations (five choose two equals ten matchups) and direct round counting.

The lecture explains transferring water between two cylindrical containers with different base areas using volume equals base area times height. The water rises to 3.8 inches.

Compute the pool area of 60 by 30 feet and the overall area of 70 by 40 feet, then subtract to reveal a 1,000 square-foot walkway around the pool.

Set Carol's win probability as x and Bob's as 3x, sum to 1 to yield x = 1/10, so Bob's probability is 3/10 (0.3).

Solve a batting average problem: with a current 80 over five innings, scoring 200 runs in the sixth inning raises the average to 100, a 25% increase.

Solve a common-sense train length problem: with carriages of 25 feet and 2 feet between carriages, a 268-foot train has 10 carriages.

Determine, from a 100-question test where correct earns 1 point and wrong loses 0.25, the number correct given a 62.5 total; conclude 70 correct and 30 wrong.

Use combined rates of 1/5 and 1/4 per hour to fill the tank; after one hour, the total time is 3.2 hours from start.

Analyze a work rate problem using inverse relationships among workers, hours, walls, and days to determine that 21 days are needed.

solve a linear equation word problem about burgers and fries using substitution and elimination to determine individual item costs, as part of the gre-gmat math marathon.

Solve the one-million-dollar division where the widow receives twice a son's share and the three sons share equally, resulting in 400,000 for the widow and 200,000 for each son.

Solve a remainder-type fraction problem: determine the initial amount when one sixth is spent, leaving five sixths totaling 250,000 rupees; result is 500,000 rupees.

Examine how a bankruptcy pays creditors 60 percent of the debt in dollars or cents. Use the asset total to calculate liabilities by solving the 60 percent relation.

The lecture shows how fixed costs of 100,000 and a 50 price with 20 unit profit yield a break-even of 5,000 units. 7,500 units achieve a 50,000 profit.

solve a tiered cost problem where the first kilometer costs six dollars and each additional kilometer costs eight dollars, with a forty four dollar budget to determine travel distance.

Convert the floor dimensions from feet to inches, compute the total floor area, and divide by the four-by-four inch tile area to determine that 2,880 tiles are needed.

Solve for five consecutive even integers whose sum is 1570 by dividing by five to find the middle term, then form the sequence; two approaches yield the same numbers.

Solve a two-variable age problem using simultaneous equations to find Ann's and Ben's ages today and their sum of 25.

Calculate the remaining work after two days of joint effort by John (1/5 per day) and Ann (1/8 per day). Ann finishes the rest in 14/5 days (2.8 days).

Solve a system of equations to find that 800 adult tickets and 200 child tickets were sold, given 500 and 200 rupees, with 1000 tickets and 440,000 revenue.

Analyze a grandfather clock’s hourly strikes and gaps to find the time between the first and last stroke. Derive 46 seconds at 12 p.m. from 22 seconds at 6 p.m.

On a number line, find one fourth of the distance from 5.1 to 5.3, which is 0.05, and add it to 5.1 to obtain 5.15.

Explores a mpg comparison between highway and city driving, where city mpg is six lower than highway, using 62 miles per tank on the highway and 336 in the city.

Compute the required percentage increase after consecutive 25% and 10% drops on an $80 price to reach $88 for a 10% profit, about 62.9%.

Set up the problem with equal apples and oranges, add 30 oranges, and apply a 6:5 oranges-to-apples ratio to determine x as 150, giving a total of 300 fruits.

Solve a fractions word problem where Mike travels 2/5 of the distance by bus and 1/10 by walking, showing that the combined bus and walk distance equals half the total.

Solve a discount and profit problem by comparing 10% and 20% discounts, where selling price adjustments yield profits of ₹35 and ₹20, and determine the original price as ₹150.

Demonstrates how to compute the yellow fraction in a mixture of green and orange paints using parts and equal quantities, revealing yellow makes up 11/30 of the final mix.

Solve a two-group average problem by equating total scores; with girls averaging 85, boys 90, and a class average of 87 in a 50-student class, determine the number of girls.

Calculate typing time for a 300-page book with 1000 words per page at 40 words per minute, resulting in 125 hours.

The lecture presents a linear equation problem: a fixed monthly charge of 300 plus 5 rupees per minute, capped at 1000, yielding 140 minutes of talk.

Compute the selling price per kilogram to earn 20% profit after 20% of 300 kg tomatoes are unusable, leaving 240 kg to sell at ₹22.50 per kg.

Explore data sufficiency for the GMAT, learning when each statement alone or together is sufficient and applying the SSD and SSP conventions, including the big seven numbers.

Assess data sufficiency for whether yx-3 is even. Show that x odd implies yx-3 is even, and y even implies it is even, so either statement suffices.

Analyze a data sufficiency exercise with p, q, r as consecutive positive integers; show that two odd and one even, and an even average, prove the sum is even.

Analyze a data sufficiency exercise with three candidates and 100 voters; first statement is insufficient, while the second shows A received 32 votes and did not have the most votes.

this data sufficiency exercise analyzes A, B, and C to decide if an expression is not less than zero; neither statement alone suffices, but together they yield option c.

Explore data sufficiency for counting integers between x and y by testing with diverse x values, including positive, negative, zero, and fractional numbers, showing that together statements yield answer C.

Determine how many integers lie between a and b using two statements; assess sufficiency with the difference of four and non-integer endpoints, then combine.

Assess a data-sufficiency unit-digit problem: y is a non-negative multiple of eight; neither statement alone nor together suffices to determine y’s unit digit.

Explore data sufficiency in question 8: determine if 2x is a multiple of y for positive integers x and y. Only the first statement suffices; the second does not.

Solve a data sufficiency exercise on divisors. Determine that a number formed by the product of two distinct primes has four distinct factors, and compare with 9 and 81.

Analyze data sufficiency in prime number problems, evaluating if n plus one is prime under conflicting statements about n and n plus two, showing limits of data.

Assess data sufficiency for distinct integers x and y under prime conditions. Show neither statement alone suffices, but together they establish the prime status of the sum and product.

Solve a data sufficiency problem by factoring a quadratic to find values of a, then test statement one and statement two to identify when a single value satisfies both.

Explore data sufficiency in q13 by testing x with x^2 - x and x^2 - 1, showing both statements alone and together are insufficient, yielding answer e.

Analyze a data sufficiency problem on z less than zero, comparing statement one and statement two. Conclude that statement one determines z's sign and suffices, while statement two is insufficient.

Develop data sufficiency skills by analyzing x and y nonzero integers to compare x/y with y/x, and show that statements 1 and 2, together, remain insufficient to determine the inequality.

Explore data sufficiency for a/b between 0 and 1, given ab is positive and a−b is negative. Both statements fail to determine whether a/b lies between 0 and 1.

Analyze data sufficiency for k using two statements: k^2 > k^3 and k^3 > k^2. Statement one is insufficient; statement two is sufficient for positive integers.

Analyze a data sufficiency exercise on whether PR > 0; individually, statements are insufficient, but together they show PR is negative, yielding a definite no.

Examine data sufficiency for inequality a plus b greater than c plus d, showing that each statement alone and both together can be insufficient due to unknown signs and counterexamples.

Apply the precondition a/b > c/b implies a > c and test the two statements. Determine that neither statement alone suffices, but together they conclude a > c.