GRE - Comprehensive Quantitative Section (420 Questions )

Solve a 1998 data interpretation question about towels, identifying not imported from China. Multiply 22 million by 12 to get 264 million, confirming option B.

Learn to interpret data on rescue squad calls by category, determine the not-listed category by subtracting the sum of listed categories from the total 1000, yielding 90.

Analyze data interpretation by calculating percentage relationships; determine that 32 percent of 50000 equals 16000, illustrating how percentages compare income contributions.

Use the data interpretation chart to identify the combination of activities with the fewest total calories per hour, noting that typing and crocket burn fewer calories, as per choice e.

Calculate the percentage of days in San Luis in July with a maximum temperature of 94 or more, using 44 total days and 15 qualifying days, yielding about 34 percent.

Learn to differentiate actual revenue numbers from percentage changes and apply per customer revenue analysis across stores to determine which statement must be true in data interpretation questions.

Analyze data interpretation in the gre comprehensive quantitative section by comparing 1976 private versus public health expenditures, showing a near 90 to 60 billion ratio, simplified to 3:2.

Compute the percentage of African countries with a GDP between 10 billion and 20 billion that also have a population between 10 million and 20 million, yielding about 23 percent.

practice data interpretation by converting percentages to actual amounts, using yearly incomes of 50,000 and 45,000 to find increases from 1,500 to 4,500, a 3,000 gain.

This data interpretation question derives the 2001 to 2015 ratio by 18 percent of 150 million and 24 percent of 175 million, yielding 9:14.

Analyze data interpretation by comparing per-student expenditure to student population across years to identify the year with the highest per-student expenditure.

Assess data interpretation of profits and division contributions: interpret 17% of 20 million and 11% of 30 million into dollars, yielding about 3.4 million and 3.3 million.

Analyze a data interpretation question by comparing division contributions, noting division P at 30% and division Q at 3%, then compute the percent relationship to conclude 1000%.

Determine which divisions added more dollars to profits in 1980 by comparing percent contributions against rising total profits, revealing four divisions increased their dollar contributions.

Convert the relative frequencies to counts for 100 trials, then apply the even-N median rule. The 50th and 51st observations fall in 1, so the median is 1.

Explore data interpretation using a box and whisker plot to determine the range by identifying the minimum value of 105 and the maximum of 146, yielding a range of 41.

Identify the category with the greatest percent increase from 2003 to 2004: miscellaneous expenses rose from 3% to about 9%, the largest increase among seven categories.

Compute the percent of total expenditures represented by private school expenditures in 2001 by forming and simplifying the fraction to 18.75%, rounded to 19%.

Analyze the data interpretation graph of health expenditures to infer dollar amounts and percentages for 1950 and 1979, focusing on construction, physician, and dental services.

Identify the category with the least share of total health expenditures in 1979, as the caption states that research is the least.

Analyze 1979 health expenditure data to determine how many categories fall below 21 billion dollars or below 10 percent of total expenditures, using approximate percentages from the graph.

Calculate the ratio of hospital care expenditures in 1979 versus 1950, convert percentages to totals, and approximate to identify the correct multiple-choice answer.

Explore prime factorization of numbers like 12 and 54, apply base exponent rules to combine terms, use square roots, and arrive at a final result of 944.

Learn to determine the median of 24 consecutive odd integers when their average arithmetic mean is 48 by averaging the two central terms.

Reveal the prime factorization of 462 as 2, 3, 7, and 11, and show that 22 is a valid divisor, illustrating divisibility and factor-based problem solving.

Apply exponent rules to combine powers of ten and coefficients, showing the result equals two point four times ten to the power fifty one.

Apply exponent rules to relate x and y by taking reciprocal sixteenth powers on both sides, use (a^b)^c = a^{bc} to simplify, cancel the exponents, and conclude y = x^4.

Apply the laws of exponents for like bases to combine powers via multiplication and division, simplify the problem, and reach the solution 1.

The lecture demonstrates simplifying a rational expression by factoring and cross-multiplication to show it equals (x+6)/(x+2) for defined values of x.

Compute the percent decrease from 2105 to 1705, a 400 drop relative to the original 2105, illustrating how to estimate a roughly 19 percent decrease.

Solve a GRE quantitative item using substitution and elimination on a linear system, deriving Y equals four times X from simplified equations.

Solve the linear relation 2x - 3y = 6 by multiplying by -1 and then by 2, using distribution to show that 6y - 4x = -12.

Analyze a recurrence sequence with t1 = -2 and t2 = -1, deriving t3 = 1 and t4 = 5, and note sign rules: opposite signs minus, same signs plus.

Apply the difference of squares and algebraic simplifications to evaluate a GRE quantitative question involving x and y, illustrating how to simplify complex expressions to a final value.

Explore how adding a fifth number changes the average of five numbers, set up the sum relationships, and solve the resulting algebraic equations using cross-multiplication and expansion.

Determine the area of an isosceles right triangle with hypotenuse eight by applying Pythagoras to find equal legs and using the area formula.

Use the difference of squares to relate the shaded area to the rectangle’s dimensions, showing the area equals (Y-X)(Y+X). Determine the rectangle’s width as Y-X via the identity Y^2-X^2=(Y-X)(Y+X).

Apply Pythagoras to a right triangle, form X^2 - X - 6 = 0, and obtain X = 3 using 3-4-5 and 5-12-13 triangles; the answer is B.

Use a 30-60-90 triangle inside a circle to find the diameter as eight, then compute the area as pi r^2 with radius four, yielding 16 pi.

In this geometry problem, solve the perimeter of the ABCDE pentagon using symmetry and a 30-60-90 triangle, finding each side length as 12 to obtain a perimeter of 60.

solve a geometry-based gre question by angle chasing with parallel lines, using the interior angles sum of a triangle, to find x as 75 degrees.

The lecture explains ranking points P, Q, and R by their distance to the origin using d = sqrt(x^2+y^2), comparing x^2+y^2 values to order from smallest to largest.

Compute angle measures in a regular pentagon by applying exterior-angle sums and isosceles properties, concluding X = 36° and A = 54°.

Solve for W in terms of X and Y by applying triangle angle sums and algebra, deriving expressions from interior angles totaling 180 degrees.

This lecture uses a circle with diameter 10 and a 6-length segment to apply Thales' theorem and Pythagoras, showing the angle inside exceeds 90 degrees and BC is under 8.

Apply Pythagoras to a composite figure, using 3-4-5, 5-12-13, and 7-24-25 right triangles to find base, height, and area, then sum triangle and rectangle areas.

Solve a three-kind high school distribution across districts using totals and equal-size constraints to determine the number of private independent schools in district a.

Convert 90 kilometers per hour to meters per second, apply the distance equals velocity times time formula, and determine that 600 meters takes about 24 seconds.

Compute the overall MBA rate by weighting 30% male and 50% female MBA with a 60/40 gender split. The result is that 62% of employees do not have an MBA.

Solve a system of linear equations to find the chocolate bar price from gumball and lollipop costs, using elimination, yielding the chocolate price of 0.71 dollars.

Set up 85 + 5(x - 1) = 365 to model the first kilometer cost plus the remaining distance, solving yields x = 57 kilometers.

A produces 350 widgets per hour and B produces 250, for a combined 600 widgets per hour. To reach 1000 widgets, they need 1 hour 40 minutes.

Use a universal diagram to determine how many of 50 students study both French and Spanish, given 31 French, 17 Spanish, and 10 neither, resulting in eight.

Solve a GRE quantitative problem about a barrel's capacity: from one-fifth full, add liquid to form a linear equation and express volume V in terms of K.

Determine the television advertising expenditure as 50x when 60 percent of total revenue is allocated to advertising and five sixth of that advertising is spent on television.

Applies the distance equals speed times time to a GRE quantitative section problem about a two-part bike trip totaling 120 miles, with speeds of 25 mph and 50 mph.

Compute the three vice presidents' average salary by using 15 executives at 80k, 82 data-entry staff at 25k, and the overall 44.5k across 100 employees, yielding 400k annually.

Convert six minutes to hours and convert kilometers to meters, then multiply velocity by time to determine the bridge length in meters, and the result is 800 meters.

Explore how a price per transaction and the number of transactions change by a percent, and compute the resulting percent increase in revenue from the prior year.

Solve a time-distance problem: determine the usual speed x for a 280 km trip when a 30-minute late departure and a 7/6 times faster speed yield regular arrival.

Apply the distance equals speed times time formula to a GRE comprehensive quantitative section two-leg journey with speeds 115 and 135 km/h. Compute A to B time in minutes.

Rearrange a division with remainder problem to isolate E, showing that E equals Q minus W as the subject of the equation.

Determine the radius of a circle tangent to each other and to the sides of an equilateral triangle of side two, using 30-60-90 relationships; the answer is E.

Fifteen equally spaced points on a circle yield 455 total triangles when choosing any three points. Five equilateral triangles exist, so 455 minus 5 equals 450 non-equilateral triangles.

Solve a ratio-based problem converting eight minutes for 30 potatoes into an hourly rate using cross-multiplication, arrive at 225 potatoes, and memorize square numbers to speed calculations.

Analyze and compare means, medians, standard deviations, and ranges for two data sets A and B, with examples using consecutive numbers, to determine which statements are true.

Solve a GRE quantitative problem by converting divisions to multiplications using reciprocals, simplifying fractions and negatives, and selecting the option pair that yields a sum between 1 and 2.

The lecture explains how multiplying by powers of ten shifts the decimal point, using positive and negative exponents to find equivalent representations of a small number.

Analyze a normal distribution with Jamal at mean plus two standard deviations and Charlie at the fifth percentile, compare their distances to the mean, and identify statements for 500 students.

Show that if A, B, C are multiples of three, then A+B+C and A-B+C are divisible by three, since A=3X, B=3Y, C=3Z with X, Y, Z integers.

Factor X^2−Y^2 as (X−Y)(X+Y) to derive X=0 or X=±Y, and use modulus properties to show X^2/Y^2=1, concluding that statements B and C are true.

Identify when two equations determine X and Y, using examples like X+Y=4 and X-Y=4, and explain why inequalities may not suffice.

Calculate triangle area using base times height over two, with base five and height four yielding area ten; vertex C on the line y=4 preserves height and area.

Master prime factorization and the divisor-counting formula to determine the number of positive divisors, and recognize when that count is odd.

Resolve a GRE quantitative puzzle by converting a ratio into a product, applying reciprocal, cancellation, and inequality reasoning to bound 3x and identify equal choices B and C.

Analyze 200 length measurements with a 17 cm range and a 49.5 cm value to determine cases where 49.5 is max or min, yielding values like 33 or 34 cm.

Solve a GRE quantitative problem using one fourth and one third of gross income to bound x with inequalities, deducing mortgage and expense ranges and identifying valid answer choices.

Apply triangle inequality to sides 1, x, and x^2, determine valid x values, identify isosceles and equilateral cases, and conclude that options b and c form valid triangles.

Apply the triangle inequality to determine possible perimeters for a triangle with sides 12, 18, and x. Determine 6 < x < 30, so the perimeter lies between 36 and 60.

Analyze factor pairs of 14 to find possible arithmetic means of two integers whose product is 14, yielding 7.5, 4.5, -7.5, and -4.5.

Analyze the region in the xy plane bounded by x=0, y=0, and 4x+3y=60 with x>0 and y>0, using point tests to identify inside points, such as B and C.

Use the recurrence a_{n+1} = 2a_n - 3 to deduce earlier terms from a4 = 19, revealing a1 = 5 and values like 5, 7, 11, 19, 35.

Analyze clerks' salary data from 1990 to 2000 to compute percent increases using original values and actual increases, revealing a range from about 27% to 175%.