22 Math: Quantitative Problem Solving Practice Questions & Answers
Every Math: Quantitative Problem Solving practice question from the GED Practice Test, with the correct answer and a short explanation.
Start practice test →1. Order these four values from least to greatest: 5/8, 2/3, 0.68, 7/10.
- A.5/8, 2/3, 0.68, 7/10✓ Answer
- B.2/3, 5/8, 0.68, 7/10
- C.0.68, 5/8, 2/3, 7/10
- D.5/8, 0.68, 2/3, 7/10
Fractions and decimals can only be compared reliably in a common form, so convert each fraction to a decimal: 5/8 = 0.625, 2/3 = 0.666..., 0.68 stays 0.68, and 7/10 = 0.70. Reading those decimals in increasing order gives 5/8, 2/3, 0.68, 7/10. Comparing numerators or denominators directly (2/3 'looks smaller' than 5/8) is the classic error.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.1.a — order fractions and decimals, including on a number lineReport a problem with this question
2. A plant services machine A every 12 days and machine B every 18 days. Both machines are serviced today. In how many days will both be serviced on the same day again?
- A.6 days
- B.72 days
- C.36 days✓ Answer
- D.216 days
The days on which both machines are serviced are the common multiples of 12 and 18, so the next coincidence is the least common multiple. Since 12 = 2^2 x 3 and 18 = 2 x 3^2, the LCM takes the highest power of each prime: 2^2 x 3^2 = 36. Choosing 6 gives the greatest common factor instead, and 216 is simply the product 12 x 18, a common multiple but not the least one.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.1.b — number properties with multiples and factors (LCM, GCF)Report a problem with this question
3. What is the value of 16^(3/4)?
- A.64
- B.12
- C.2
- D.8✓ Answer
A rational exponent m/n means the nth root raised to the mth power, so 16^(3/4) = (fourth root of 16)^3. The fourth root of 16 is 2 because 2 x 2 x 2 x 2 = 16, and 2^3 = 8. Answering 12 comes from multiplying 16 by 3/4, and answering 2 stops after taking the root without applying the numerator.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.1.c — rules of exponents with rational exponentsReport a problem with this question
4. At dawn the temperature at a weather station was -13 degrees F. By afternoon it was 8 degrees F. How many degrees apart are these two temperatures?
- A.5 degrees
- B.21 degrees✓ Answer
- C.13 degrees
- D.-21 degrees
Distance between two numbers on a number line is the absolute value of their difference, |a - b|, which is never negative. Here |-13 - 8| = |-21| = 21 degrees. Adding the numbers as if the signs cancel gives 5, and reporting -21 ignores that absolute value measures distance from one point to another, which cannot be negative.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.1.d — absolute value as distance, and distance between two rationals as |a - b|Report a problem with this question
5. A shop models its average cost per custom sign with the expression 480 / (n - 12), where n is the number of signs ordered. For which value of n is this expression undefined?
- A.n = 12✓ Answer
- B.n = 0
- C.n = 480
- D.n = 492
A numerical expression is undefined exactly when its denominator equals zero, because division by zero has no result. Setting n - 12 = 0 gives n = 12. At n = 0 the expression equals 480 / (-12) = -40, which is defined, so a zero numerator or a zero input value does not by itself make an expression undefined.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.2.d — determine when a numerical expression is undefined (denominator equal to 0)Report a problem with this question
6. A city with 3.2 x 10^5 residents uses 5.6 x 10^10 gallons of water in a year. What is the water use per resident for that year, in scientific notation?
- A.1.75 x 10^6 gallons
- B.1.792 x 10^16 gallons
- C.1.75 x 10^5 gallons✓ Answer
- D.1.75 x 10^4 gallons
Per-resident use is total gallons divided by population, and in scientific notation you divide the coefficients and subtract the exponents: (5.6 / 3.2) x 10^(10-5) = 1.75 x 10^5 gallons. The answer 1.792 x 10^16 comes from multiplying instead of dividing (and adding the exponents), which answers a different question entirely.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.2.e — multi-step real-world problems including scientific notationReport a problem with this question
7. Evaluate: -4 + 6 / 2 x (-3) - (-5)
- A.-18
- B.0
- C.2
- D.-8✓ Answer
Order of operations requires multiplication and division to be done first, left to right, before addition and subtraction: 6 / 2 = 3, then 3 x (-3) = -9. The expression becomes -4 + (-9) - (-5) = -4 - 9 + 5 = -8, since subtracting a negative adds. Working strictly left to right from the start gives 2, and treating -(-5) as -5 gives -18.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.2.a — operations with rational numbers, applying order of operations with signed numbersReport a problem with this question
8. A cafe buys coffee beans in bulk. Brand A costs $9.10 for 3.5 pounds; Brand B costs $12.75 for 5 pounds. Which brand is the better buy, and by how much?
- A.Brand A, by $0.05 per pound
- B.Brand A, because its total price is $3.65 lower
- C.Brand B, by $0.05 per pound✓ Answer
- D.Brand B, by $0.50 per pound
Packages of different sizes can only be compared by unit rate, that is price divided by pounds: Brand A is 9.10 / 3.5 = $2.60 per pound and Brand B is 12.75 / 5 = $2.55 per pound, so Brand B costs $0.05 less per pound. Comparing total prices instead compares different quantities of coffee and tells you nothing about value.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.3.a — unit rates, including unit pricingReport a problem with this question
9. On a floor plan drawn to the scale 1/4 inch = 2 feet, a storage room measures 3.5 inches by 2.25 inches. What is the actual floor area of the room?
- A.504 square feet✓ Answer
- B.126 square feet
- C.31.5 square feet
- D.7.875 square feet
The scale factor converts drawing lengths to actual lengths before any area is computed: 1/4 inch = 2 feet means 1 inch = 8 feet. So 3.5 inches = 28 feet and 2.25 inches = 18 feet, and the area is 28 x 18 = 504 square feet. Counting quarter-inch units but forgetting each one equals 2 feet gives 14 x 9 = 126, and using 1 inch = 2 feet gives 31.5.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.3.b — scale factors and converting between actual and scale drawingsReport a problem with this question
10. A bottling machine fills 3 bottles every 8 seconds at a constant rate. How many bottles does it fill in 2 hours of continuous operation?
- A.45 bottles
- B.2,700 bottles✓ Answer
- C.900 bottles
- D.19,200 bottles
A proportion is only valid when both sides use the same unit, so convert first: 2 hours = 2 x 60 x 60 = 7,200 seconds. Then 3 bottles / 8 seconds = x bottles / 7,200 seconds gives x = 3 x 7,200 / 8 = 2,700 bottles. Answering 900 stops at the number of 8-second intervals, and 19,200 flips the ratio to 8/3.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.3.c — multistep ratio and proportion problems requiring unit conversion (DOK 2)Report a problem with this question
11. A store's monthly sales rose from $18,500 in one month to $22,200 the next month. What was the percent increase?
- A.25%
- B.16.7%
- C.120%
- D.20%✓ Answer
Percent change is the amount of change divided by the ORIGINAL value, not the new one: (22,200 - 18,500) / 18,500 = 3,700 / 18,500 = 0.20, or 20%. Dividing the change by the new value, 3,700 / 22,200, produces the common 16.7% error, and 120% is the ratio of new to original rather than the increase.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.3.d — two-step percent problems, including percent increase and decreaseReport a problem with this question
12. A jacket costs a store $60. The store marks it up 45%, then later puts it on clearance at 20% off the marked-up price. What is the clearance price?
- A.$75.00
- B.$69.60✓ Answer
- C.$72.00
- D.$87.00
Each percent step is applied to the price in effect at that moment, so the two percents cannot simply be netted. The marked-up price is 60 x 1.45 = $87, and 20% off that is 87 x 0.80 = $69.60. Subtracting 45% - 20% = 25% and computing 60 x 1.25 = $75 is wrong because the 20% discount is taken off $87, not off $60.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.3.d — two-step percent problems: markups and markdownsReport a problem with this question
13. A rectangular garden plot has an area of 154 square feet and a length of 14 feet. How many feet of edging are needed to go around the entire plot?
- A.25 feet
- B.42 feet
- C.56 feet
- D.50 feet✓ Answer
Because area of a rectangle is length x width, the missing width is found by reversing the formula: 154 / 14 = 11 feet. Edging measures perimeter, not area, so P = 2(14) + 2(11) = 28 + 22 = 50 feet. Answering 25 stops at length plus width without doubling, which is only half the way around.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.4.a — area and perimeter of rectangles, including finding a side length given the areaReport a problem with this question
14. A circular patio has a circumference of 43.96 feet. Using 3.14 for pi, what is the area of the patio?
- A.43.96 square feet
- B.615.44 square feet
- C.153.86 square feet✓ Answer
- D.21.98 square feet
Area requires the radius, so first reverse C = 2(pi)r: r = 43.96 / (2 x 3.14) = 43.96 / 6.28 = 7 feet. Then A = (pi)r^2 = 3.14 x 7^2 = 3.14 x 49 = 153.86 square feet. Using the diameter of 14 feet in place of the radius gives 3.14 x 196 = 615.44, the classic radius-versus-diameter substitution error.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.4.b — area and circumference of circles, including finding radius or diameter given the circumferenceReport a problem with this question
15. A lobby floor is a 20-foot by 12-foot rectangle with a semicircular alcove attached to one of the 12-foot ends; the straight 12-foot side is the diameter of the semicircle. Using 3.14 for pi, what is the total floor area?
- A.353.04 square feet
- B.296.52 square feet✓ Answer
- C.240 square feet
- D.466.08 square feet
A composite figure is handled by decomposing it into shapes with known formulas and adding the areas. The rectangle is 20 x 12 = 240 square feet, and the semicircle has radius 12 / 2 = 6, so its area is (1/2)(3.14)(6^2) = 56.52 square feet, giving 296.52 total. Using the full circle gives 353.04, and using 12 as the radius gives 466.08.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.4.d — perimeter and area of 2-D composite figures, which may include circlesReport a problem with this question
16. A loading ramp rises 7 feet vertically over a horizontal run of 24 feet. What is the length of the sloped ramp surface?
- A.25 feet✓ Answer
- B.17 feet
- C.22.9 feet
- D.31 feet
The rise and run form the two legs of a right triangle and the ramp surface is the hypotenuse, so a^2 + b^2 = c^2 gives 7^2 + 24^2 = 49 + 576 = 625, and c = the square root of 625 = 25 feet. Simply adding the legs gives 31, and subtracting inside the radical (576 - 49) gives about 22.9, which would solve for a leg rather than the hypotenuse.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.4.e — Pythagorean theorem for unknown side lengths in a right triangleReport a problem with this question
17. A cylindrical storage tank holds 1,808.64 cubic feet and its base has a diameter of 12 feet. Using 3.14 for pi, what is the height of the tank?
- A.16 feet✓ Answer
- B.4 feet
- C.8 feet
- D.48 feet
Solve the volume formula backward: V = (pi)r^2h, so h = V / ((pi)r^2). The radius is half the diameter, 12 / 2 = 6 feet, so (pi)r^2 = 3.14 x 36 = 113.04 and h = 1,808.64 / 113.04 = 16 feet. Substituting the diameter 12 as the radius gives 3.14 x 144 = 452.16 and the wrong height of 4 feet.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.5.b — volume of cylinders, including solving for height given the volumeReport a problem with this question
18. A spherical tank has a surface area of 314 square feet. Using 3.14 for pi, what is the diameter of the tank?
- A.5 feet
- B.25 feet
- C.10 feet✓ Answer
- D.12.5 feet
Reverse the sphere surface-area formula SA = 4(pi)r^2: r^2 = 314 / (4 x 3.14) = 314 / 12.56 = 25, so r = 5 feet. The question asks for the diameter, which is twice the radius, so d = 10 feet. Answering 5 stops at the radius, and 25 stops at r^2 without taking the square root.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.5.e — spheres, solving for radius or diameter given the surface areaReport a problem with this question
19. A shipping crate is a rectangular box 4 feet long, 3 feet wide, and 2 feet high. All six outside faces must be covered with a protective wrap that costs $2.50 per square foot. What is the cost of the wrap?
- A.$130.00✓ Answer
- B.$60.00
- C.$65.00
- D.$260.00
Covering the outside of a solid is a surface-area problem, not a volume problem: SA = 2lw + 2lh + 2wh = 2(12) + 2(8) + 2(6) = 24 + 16 + 12 = 52 square feet, and 52 x $2.50 = $130. Using volume, lwh = 24 cubic feet, gives $60, but cubic feet cannot be priced per square foot, which is the most common error on this item type.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.5.a — surface area of rectangular prisms (SA = 2lw + 2lh + 2wh on the GED formula sheet)Report a problem with this question
20. A box plot of daily service calls has these five values: minimum 12, first quartile 18, median 24, third quartile 33, maximum 47. What is the interquartile range?
- A.15✓ Answer
- B.35
- C.9
- D.24
The interquartile range measures the spread of the middle half of the data and is defined as the third quartile minus the first quartile: 33 - 18 = 15. Subtracting minimum from maximum, 47 - 12 = 35, gives the full range instead, and 33 - 24 = 9 uses the median rather than the first quartile.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.6.b — one-variable data displays including box plots (quartiles, median, IQR)Report a problem with this question
21. A technician's first four repair jobs of the week took 36, 45, 38, and 41 minutes. To average exactly 42 minutes over all five jobs, how long may the fifth job take?
- A.40 minutes
- B.50 minutes✓ Answer
- C.42 minutes
- D.46 minutes
Because the mean equals the total divided by the number of values, a target mean fixes the required total: 42 x 5 = 210 minutes for all five jobs. The first four total 36 + 45 + 38 + 41 = 160 minutes, so the fifth may take 210 - 160 = 50 minutes. Simply using the target average, 42, ignores that the first four jobs already average only 40.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.7.a — calculate a missing data value given the average and all but one valueReport a problem with this question
22. A drawer holds 5 blue pens and 7 black pens, identical except for color. If two pens are drawn at random without replacement, what is the probability that both are blue?
- A.25/144
- B.5/33✓ Answer
- C.20/121
- D.5/12
For a compound event, multiply the probability of each draw, but without replacement the second draw depends on the first: P = (5/12) x (4/11) = 20/132 = 5/33. Using 5/12 twice gives 25/144, which would be correct only if the first pen were put back, leaving 12 pens with 5 blue on the second draw.
Source: GED Assessment Guide for Educators (Mathematical Reasoning), Target Q.8.b — probability of simple and compound events, including dependent (without-replacement) eventsReport a problem with this question
Practice questions based on the GED Testing Service Assessment Guide for Educators and standard high-school-equivalency curriculum. GED is a registered trademark of the American Council on Education; this site is not affiliated with or endorsed by ACE or GED Testing Service. Passing scores, fees, retake limits, and age and residency eligibility are set by GED Testing Service and by individual states and change over time — confirm current requirements for your state before testing. Note that the Reasoning Through Language Arts test also includes an extended-response essay, which multiple-choice practice cannot cover. About the GED test →