40 Arithmetic Reasoning (AR) Practice Questions & Answers

1. 1. A pump moves 84 gallons of water in 6 minutes. At that same rate, how many gallons will it move in 20 minutes?

   • A.252 gallons
   • B.336 gallons
   • C.240 gallons
   • D.280 gallons✓ Answer

   Rate problems are solved by finding the unit rate first, then multiplying by the new amount of time. Here the unit rate is 84 ÷ 6 = 14 gallons per minute, so in 20 minutes the pump moves 14 × 20 = 280 gallons. Multiplying 84 by a whole number of 6-minute blocks fails because 20 is not a multiple of 6, which is why the unit-rate step matters.

   Ref QB-HVTKMMSource: officialasvab.com — Arithmetic Reasoning subtest ("ability to solve arithmetic word problems"); unit-rate principle: rate = quantity ÷ time, then quantity = rate × timeReport a problem with this question

2. 2. One store sells a 4-pound bag of rice for $9.60. Another store sells a 6-pound bag of the same rice for $13.50. How much less per pound does the cheaper bag cost?

   • A.$0.15✓ Answer
   • B.$1.15
   • C.$0.25
   • D.$3.90

   A "better buy" comparison requires reducing both packages to the same unit before comparing: $9.60 ÷ 4 = $2.40 per pound and $13.50 ÷ 6 = $2.25 per pound. The 6-pound bag is cheaper by $2.40 − $2.25 = $0.15 per pound. Comparing the sticker prices ($13.50 − $9.60 = $3.90) is meaningless because the bags hold different amounts.

   Ref QB-ZCNE2MSource: officialasvab.com — Arithmetic Reasoning subtest; unit-price rule: unit price = total price ÷ number of unitsReport a problem with this question

3. 3. A truck travels 350 miles on 25 gallons of fuel. At the same rate of fuel use, how many gallons are needed to travel 476 miles?

   • A.28 gallons
   • B.34 gallons✓ Answer
   • C.36 gallons
   • D.19 gallons

   Set up the fuel-use rate as miles per gallon: 350 ÷ 25 = 14 miles per gallon. Gallons needed is then distance ÷ rate, so 476 ÷ 14 = 34 gallons. Dividing 476 by 25 instead (giving about 19) inverts the relationship — 25 is a quantity of gallons, not a rate.

   Ref QB-GVF9FKSource: officialasvab.com — Arithmetic Reasoning subtest; proportional reasoning with rates (a/b = c/d solved by cross-multiplication)Report a problem with this question

4. 4. A group of 187 people must be transported by bus. Each bus seats 45 people. What is the smallest number of buses needed so that everyone gets a seat?

   • A.3
   • B.5✓ Answer
   • C.6
   • D.4

   Dividing gives 187 ÷ 45 = 4 with a remainder of 7, and a remainder of people still needs transportation, so the quotient must be rounded UP. Four buses seat only 180 people, leaving 7 without a seat, so 5 buses are required. "How many containers are needed" problems always round up; "how many complete items can be made" problems round down.

   Ref QB-4DQEJQSource: officialasvab.com — Arithmetic Reasoning subtest; remainder-interpretation rule for capacity problems (round the quotient up)Report a problem with this question

5. 5. In a training company of 480 recruits, 1 out of every 6 recruits is assigned to the motor pool. How many recruits are NOT assigned to the motor pool?

   • A.80
   • B.384
   • C.400✓ Answer
   • D.96

   "One out of every 6" means the motor pool group is 1/6 of the total: 480 ÷ 6 = 80 recruits. The question asks for the complement, so subtract: 480 − 80 = 400 recruits are not assigned there. The classic trap is answering 80, which is the part that was given rather than the part that was asked for.

   Ref QB-KVH9YPSource: officialasvab.com — Arithmetic Reasoning subtest; part-to-whole ratio rule and complement (whole − part)Report a problem with this question

6. 6. A construction crew mixes gravel and sand in a 3 to 5 ratio by weight to produce 400 pounds of mix. How many pounds of sand are in the mix?

   • A.250 pounds✓ Answer
   • B.240 pounds
   • C.150 pounds
   • D.200 pounds

   A ratio of 3 to 5 means the mix is divided into 3 + 5 = 8 equal parts, so one part weighs 400 ÷ 8 = 50 pounds. Sand is 5 parts, giving 5 × 50 = 250 pounds (gravel is 3 × 50 = 150 pounds, and the two correctly total 400). Splitting the total in half would only be correct if the ratio were 1 to 1.

   Ref QB-3DC4DPSource: officialasvab.com — Arithmetic Reasoning subtest; ratio rule: each part = total ÷ (sum of ratio terms)Report a problem with this question

7. 7. On a map, 1 inch represents 25 miles. Two supply depots are 3.5 inches apart on the map. What is the actual distance between them?

   • A.87.5 miles✓ Answer
   • B.75 miles
   • C.92.5 miles
   • D.62.5 miles

   A map scale is a proportion: 1 inch / 25 miles = 3.5 inches / d miles. Cross-multiplying gives d = 3.5 × 25 = 87.5 miles. A useful check is that 3 inches would be 75 miles and 4 inches would be 100 miles, so the answer must fall between those two values.

   Ref QB-JV6XSNSource: officialasvab.com — Arithmetic Reasoning subtest; map-scale proportion solved by cross-multiplication (a/b = c/d → ad = bc)Report a problem with this question

8. 8. A machine purchased for $8,000 loses 10% of its value each year. What is the machine worth at the end of 2 years?

   • A.$6,500
   • B.$6,400
   • C.$7,200
   • D.$6,480✓ Answer

   Losing 10% leaves 90% of the value, so each year the value is multiplied by 0.90 rather than having a fixed dollar amount subtracted. After one year: $8,000 × 0.90 = $7,200; after two years: $7,200 × 0.90 = $6,480. Subtracting 10% of the ORIGINAL price twice gives $6,400, which is wrong because the second year's loss is based on the reduced value.

   Ref QB-WCKEHGSource: officialasvab.com — Arithmetic Reasoning subtest; depreciation rule: new value = original × (1 − rate), applied once per periodReport a problem with this question

9. 9. A jacket regularly priced at $240 is marked down 25%. A clerk then takes an additional 10% off the sale price. What is the final price?

   • A.$162✓ Answer
   • B.$156
   • C.$180
   • D.$168

   Successive discounts multiply; they do not add. The first markdown leaves 75%: $240 × 0.75 = $180, and the second leaves 90% of that: $180 × 0.90 = $162. Adding the percents to get a single 35% discount would give $156, which is too low because the 10% is taken on $180, not on $240.

   Ref QB-DVD9XFSource: officialasvab.com — Arithmetic Reasoning subtest; successive-discount rule: final = original × (1 − r1) × (1 − r2)Report a problem with this question

10. 10. A tool is on sale for $63 after a 30% discount. What was the price before the discount?

    • A.$81.90
    • B.$93
    • C.$70
    • D.$90✓ Answer

    After a 30% discount the sale price represents 70% of the original, so original × 0.70 = $63 and the original is found by DIVIDING: $63 ÷ 0.70 = $90. Checking confirms it: 30% of $90 is $27, and $90 − $27 = $63. Multiplying $63 by 1.30 instead gives $81.90, a common error because the 30% would then be taken on the smaller sale price.

    Ref QB-XTVPFKSource: officialasvab.com — Arithmetic Reasoning subtest; working backward from a discounted price: original = sale price ÷ (1 − rate)Report a problem with this question

11. 11. A salesperson earns a 4% commission on everything sold. If total sales for the month were $18,500, how much commission was earned?

    • A.$460
    • B.$740✓ Answer
    • C.$700
    • D.$1,850

    Commission equals the commission rate written as a decimal times total sales: 0.04 × $18,500 = $740. A quick mental check is that 1% of $18,500 is $185, and 4 × $185 = $740. The choice $1,850 is 10% of sales, the error made by shifting the decimal point one place instead of two.

    Ref QB-FB3V2MSource: officialasvab.com — Arithmetic Reasoning subtest; commission rule: commission = rate (as a decimal) × total salesReport a problem with this question

12. 12. A driver travels 120 miles to a job site at an average speed of 60 mph and returns over the same 120 miles at an average speed of 40 mph. What was the average speed for the entire round trip?

    • A.50 mph
    • B.45 mph
    • C.52 mph
    • D.48 mph✓ Answer

    Average speed is always total distance divided by total time, never the average of the two speeds. The outbound leg takes 120 ÷ 60 = 2 hours and the return takes 120 ÷ 40 = 3 hours, for 240 miles in 5 hours: 240 ÷ 5 = 48 mph. The answer is below 50 mph because more time is spent traveling at the slower speed.

    Ref QB-WTHCAJSource: officialasvab.com — Arithmetic Reasoning subtest; average-speed rule: average speed = total distance ÷ total time (d = r × t)Report a problem with this question

13. 13. A truck leaves a depot traveling at a steady 45 mph. One hour later a car leaves the same depot on the same road traveling at a steady 60 mph. How long after the car leaves will it catch up to the truck?

    • A.1.5 hours
    • B.2 hours
    • C.4 hours
    • D.3 hours✓ Answer

    In the hour of head start the truck covers 45 × 1 = 45 miles, so the car begins 45 miles behind. Because both move in the same direction, the gap closes at the DIFFERENCE of the speeds, 60 − 45 = 15 mph, so the catch-up time is 45 ÷ 15 = 3 hours. Using the sum of the speeds would be correct only if the two vehicles were approaching each other.

    Ref QB-EBQHVJSource: officialasvab.com — Arithmetic Reasoning subtest; same-direction overtake rule: time = head-start distance ÷ (faster rate − slower rate)Report a problem with this question

14. 14. Working alone, one worker can unload a truck in 6 hours. A second worker can unload the same truck alone in 12 hours. Working together at those rates, how long will it take them to unload one truck?

    • A.3 hours
    • B.9 hours
    • C.4 hours✓ Answer
    • D.5 hours

    Work problems are solved by adding rates, not times: the first worker does 1/6 of the truck per hour and the second does 1/12, so together they do 1/6 + 1/12 = 3/12 = 1/4 of the truck per hour. Completing 1 truck therefore takes 4 hours. Averaging the two times to get 9 hours is wrong because two workers must always finish faster than the faster one alone.

    Ref QB-VT625HSource: officialasvab.com — Arithmetic Reasoning subtest; combined-work rule: 1/t = 1/a + 1/b, so t = ab ÷ (a + b)Report a problem with this question

15. 15. Four identical machines running together complete an order in 90 minutes. If only 3 of those machines are available and they run at the same rate, how long will the same order take?

    • A.120 minutes✓ Answer
    • B.67.5 minutes
    • C.90 minutes
    • D.135 minutes

    Machines and time are INVERSELY proportional: fewer machines means more time, so the total machine-minutes stay constant. The job requires 4 × 90 = 360 machine-minutes, so with 3 machines it takes 360 ÷ 3 = 120 minutes. Scaling directly (90 × 3/4 = 67.5) is the common error, since it would mean removing a machine makes the work go faster.

    Ref QB-DBC7QHSource: officialasvab.com — Arithmetic Reasoning subtest; inverse proportion / man-hours rule: workers × time = constantReport a problem with this question

16. 16. A worker is paid $18 per hour for the first 40 hours in a week and time-and-a-half for every hour beyond 40. If the worker puts in 46 hours, what is the gross pay for the week?

    • A.$828
    • B.$882✓ Answer
    • C.$720
    • D.$1,242

    Overtime pay must be split into two separate calculations because the two blocks of hours are paid at different rates. Regular pay is 40 × $18 = $720, the overtime rate is 1.5 × $18 = $27, and the 6 overtime hours pay 6 × $27 = $162, so the total is $720 + $162 = $882. Multiplying all 46 hours by $18 gives $828 and ignores the overtime premium entirely.

    Ref QB-UTTPXFSource: officialasvab.com — Arithmetic Reasoning subtest; overtime pay rule: gross = (regular hours × rate) + (overtime hours × 1.5 × rate)Report a problem with this question

17. 17. A person deposits $2,400 in an account that pays 5% simple annual interest. How much interest will the deposit earn in 6 months?

    • A.$240
    • B.$120
    • C.$60✓ Answer
    • D.$30

    Simple interest is I = P × r × t with the rate as a decimal and the time in YEARS, so 6 months must be entered as 0.5 rather than 6. That gives $2,400 × 0.05 × 0.5 = $60. Forgetting to convert the months leaves the full-year figure of $120, which is exactly twice the correct amount.

    Ref QB-CBZUHGSource: officialasvab.com — Arithmetic Reasoning subtest; simple-interest formula I = P × r × t (t expressed in years)Report a problem with this question

18. 18. A student has an average score of 82 on the first 4 tests of a course. What score is needed on the fifth test to raise the average for all 5 tests to 85?

    • A.91
    • B.88
    • C.97✓ Answer
    • D.94

    Because the mean equals the sum divided by the count, work with sums rather than averages. The 5 tests must total 85 × 5 = 425 points, while the first 4 have already produced 82 × 4 = 328 points, so the fifth score must be 425 − 328 = 97. Simply adding the 3-point gap to 82 gives 85 and ignores that one test has to make up the shortfall on all four earlier tests.

    Ref QB-TTFCSESource: officialasvab.com — Arithmetic Reasoning subtest; mean rule: required sum = mean × count, then subtract the known valuesReport a problem with this question

19. 19. A person starts the month with $720. She spends 1/3 of it on rent, then spends 1/4 of what is left on groceries. How much money does she have left after both expenses?

    • A.$420
    • B.$240
    • C.$480
    • D.$360✓ Answer

    The second fraction applies to the REMAINDER, not to the original amount, so the steps must be done in order. Rent is 720 ÷ 3 = $240, leaving $480; groceries are 1/4 of $480 = $120, leaving $480 − $120 = $360. Stopping at $480 answers the money left after rent only, which is the most common error on "then he spent part of what was left" problems.

    Ref QB-BBNHCFSource: officialasvab.com — Arithmetic Reasoning subtest; sequential fraction-of-remainder rule (each fraction applies to the current remaining amount)Report a problem with this question

20. 20. A room measures 18 feet by 12 feet. Carpet costs $21 per square yard. What is the cost to carpet the entire room?

    • A.$4,536
    • B.$480
    • C.$1,512
    • D.$504✓ Answer

    First find the area in square feet: 18 × 12 = 216 square feet. Because the price is quoted per square YARD, convert using 1 square yard = 3 ft × 3 ft = 9 square feet, so 216 ÷ 9 = 24 square yards, and the cost is 24 × $21 = $504. Dividing by 3 instead of 9 gives $1,512 — area units must be converted with the SQUARE of the linear factor.

    Ref QB-URVHXFSource: officialasvab.com — Arithmetic Reasoning subtest; rectangle area A = l × w with square-unit conversion (1 yd² = 9 ft²)Report a problem with this question

21. 21. A stamping machine produces 45 metal plates per minute. At that same rate, how many plates will it produce in 1 hour 20 minutes?

    • A.5,400
    • B.3,600✓ Answer
    • C.2,700
    • D.4,500

    Convert the time to one unit before multiplying: 1 hour 20 minutes = 80 minutes, so 45 × 80 = 3,600 plates. Using only 60 minutes gives 2,700, and using 120 minutes gives 5,400 — both come from mishandling the mixed time unit.

    Ref QB-B9QCCFSource: officialasvab.com — AR sample-item style (rate extrapolation over a time interval); unit-consistent rate × timeReport a problem with this question

22. 22. A supply convoy must drive 210 miles at a steady 35 miles per hour and will make one 45-minute rest stop along the way. How long will the whole trip take?

    • A.6 hours 45 minutes✓ Answer
    • B.5 hours 15 minutes
    • C.6 hours
    • D.7 hours

    Driving time = distance ÷ rate = 210 ÷ 35 = 6 hours, then add the 45-minute stop for 6 hours 45 minutes. Choosing 6 hours forgets the stop, 5 hours 15 minutes wrongly subtracts it, and 7 hours rounds the stop up to a full hour.

    Ref QB-TRH7SESource: AR distance-rate-time word problems: t = d ÷ r, plus non-driving time added to totalReport a problem with this question

23. 23. A soldier runs 400 meters in 80 seconds. At that same pace, what is her speed in kilometers per hour?

    • A.20 km/h
    • B.18 km/h✓ Answer
    • C.5 km/h
    • D.12.5 km/h

    First find the unit rate: 400 ÷ 80 = 5 meters per second. There are 3,600 seconds in an hour and 1,000 meters in a kilometer, so multiply by 3.6: 5 × 3.6 = 18 km/h. Answering 5 km/h keeps the m/s number without converting units.

    Ref QB-A9C27ESource: AR rate-unit conversion: 1 m/s = 3.6 km/h (3,600 s/h ÷ 1,000 m/km)Report a problem with this question

24. 24. A field kitchen recipe that serves 8 people calls for 3 cups of flour. How many cups of flour are needed to serve 36 people?

    • A.15 cups
    • B.12 cups
    • C.27 cups
    • D.13.5 cups✓ Answer

    Set up the proportion 3/8 = x/36 and cross-multiply: x = (3 × 36) ÷ 8 = 108 ÷ 8 = 13.5 cups. The scaling factor is 36 ÷ 8 = 4.5; rounding it to 4 gives the wrong answer 12, and 27 comes from using a factor of 9 by mis-setting the proportion.

    Ref QB-WRK7AJSource: AR proportions: cross-multiplication with consistent units (servings-to-servings, cups-to-cups)Report a problem with this question

25. 25. In a training platoon, the ratio of men to women is 7 to 3. If there are 21 women in the platoon, how many soldiers are in the platoon altogether?

    • A.91
    • B.63
    • C.70✓ Answer
    • D.49

    The 3 'parts' of women equal 21, so one part is 7 soldiers. The whole platoon is 7 + 3 = 10 parts, or 10 × 7 = 70 soldiers. Answering 49 gives only the men (7 parts), and 63 comes from multiplying 21 by 3, misusing the part-to-part ratio.

    Ref QB-D9E2QHSource: officialasvab.com — AR ratio sample style (share of a total); part-to-part vs part-to-whole ratiosReport a problem with this question

26. 26. A blueprint uses a scale of 1/2 inch = 4 feet. How long should a 30-foot wall be drawn on the blueprint?

    • A.7.5 inches
    • B.2.5 inches
    • C.15 inches
    • D.3.75 inches✓ Answer

    Each 4 feet of wall takes 1/2 inch on paper. The wall contains 30 ÷ 4 = 7.5 of those 4-foot units, so it needs 7.5 × 1/2 = 3.75 inches. Answering 7.5 inches treats the scale as 1 inch = 4 feet, forgetting the half-inch unit.

    Ref QB-VR8V4HSource: AR scale/proportion word problems: scale drawings, consistent scale unitsReport a problem with this question

27. 27. A backpack priced at $60 is discounted 15%. A 5% sales tax is then charged on the sale price. What is the final cost of the backpack?

    • A.$56.70
    • B.$54.00
    • C.$53.55✓ Answer
    • D.$51.00

    Successive percent changes multiply — they never simply add. Sale price: $60 × 0.85 = $51.00; then tax: $51.00 × 1.05 = $53.55. Answering $54.00 nets the percents (−15% + 5% = −10%), and $51.00 forgets the tax entirely.

    Ref QB-C93QHGSource: AR percent problems: successive percent changes (discount then tax) apply multiplicatively to the running priceReport a problem with this question

28. 28. A recruiting station enlisted 480 people in one cycle and 552 people in the next cycle. By what percent did enlistments increase?

    • A.15%✓ Answer
    • B.13%
    • C.72%
    • D.115%

    Percent increase = (change ÷ original amount) × 100. The change is 552 − 480 = 72, so 72 ÷ 480 = 0.15 = 15%. Dividing by the new value 552 gives about 13%, 72% mistakes the raw difference for a percent, and 115% forgets to subtract the original 100%.

    Ref QB-QRF79BSource: AR percent change rule: percent increase = (new − original) ÷ original × 100Report a problem with this question

29. 29. A supplier buys work boots for $48 a pair and marks the price up 35%. What is the selling price of a pair?

    • A.$31.20
    • B.$16.80
    • C.$67.20
    • D.$64.80✓ Answer

    Markup is added to cost: selling price = cost × (1 + markup rate) = $48 × 1.35 = $64.80. Answering $16.80 gives only the markup amount (35% of $48), $31.20 subtracts the 35% as if it were a discount, and $67.20 uses 40% instead of 35%.

    Ref QB-79A2PASource: AR financial math: markup, price = cost × (1 + rate)Report a problem with this question

30. 30. A carpenter cuts one piece 2 3/4 feet long and another piece 3 5/8 feet long from a board 10 feet long. How much of the board is left?

    • A.3 3/8 feet
    • B.4 3/8 feet
    • C.2 5/8 feet
    • D.3 5/8 feet✓ Answer

    Rewrite the fractions with the common denominator 8: 2 3/4 = 2 6/8, so the cuts total 2 6/8 + 3 5/8 = 5 11/8 = 6 3/8 feet. Then 10 − 6 3/8 = 3 5/8 feet remain. Adding numerators and denominators straight across without a common denominator leads to the neighboring wrong values.

    Ref QB-PM6ZDXSource: AR fractions: addition/subtraction of mixed numbers with unlike denominators (LCD)Report a problem with this question

31. 31. A generator's fuel tank is 5/6 full. During a field exercise, the generator burns 3/4 of the fuel that is in the tank. What fraction of the tank's total capacity remains?

    • A.5/24✓ Answer
    • B.5/8
    • C.1/12
    • D.1/4

    The fuel remaining is 1 − 3/4 = 1/4 of what was in the tank, and 'of' means multiply: 5/6 × 1/4 = 5/24 of total capacity. Answering 1/12 subtracts 3/4 from 5/6 directly, 5/8 is the amount burned (5/6 × 3/4), and 1/4 is the fraction of the contents, not of the whole tank.

    Ref QB-75C6ZXSource: AR fraction-of-a-quantity problems: 'fraction of a remainder' requires multiplication, not subtractionReport a problem with this question

32. 32. One copier can finish a print job alone in 40 minutes. A newer copier can finish the same job alone in 24 minutes. Running at the same time, how long will the two copiers take to finish the job together?

    • A.16 minutes
    • B.15 minutes✓ Answer
    • C.64 minutes
    • D.32 minutes

    Rates add, times do not: the first copier does 1/40 of the job per minute and the second 1/24, so together 1/40 + 1/24 = 3/120 + 5/120 = 8/120 = 1/15 of the job per minute, which means 15 minutes. Averaging the times gives the wrong 32, and adding them gives the wrong 64.

    Ref QB-QMHBKYSource: AR combined-work rule: 1/a + 1/b = 1/t (rates are additive; times are not)Report a problem with this question

33. 33. A water tank can be filled by its supply pipe in 3 hours. The drain valve, left fully open by mistake, can empty the full tank in 9 hours. With the supply pipe on and the drain open, how long will it take to fill the empty tank?

    • A.6 hours
    • B.2 hours 15 minutes
    • C.12 hours
    • D.4 hours 30 minutes✓ Answer

    Opposing rates subtract: the pipe fills 1/3 of the tank per hour while the drain removes 1/9, for a net rate of 1/3 − 1/9 = 2/9 per hour, so filling takes 9/2 = 4.5 hours. Adding the rates as if both filled gives 2 hours 15 minutes, and averaging the two times gives 6 hours.

    Ref QB-85QG6ZSource: AR work-rate problems with opposing actions: net rate = fill rate − drain rateReport a problem with this question

34. 34. A mechanic needs 12 liters of a 25% antifreeze solution. He will make it by mixing a 10% solution with a 30% solution. How many liters of the 30% solution does he need?

    • A.3 liters
    • B.9 liters✓ Answer
    • C.8 liters
    • D.6 liters

    The antifreeze before mixing must equal the antifreeze after: with x liters of 30%, 0.30x + 0.10(12 − x) = 0.25 × 12 = 3. That gives 0.20x = 1.8, so x = 9 liters. Answering 3 liters gives the amount of the 10% solution instead, and 6 liters assumes an even half-and-half split.

    Ref QB-RMVNRZSource: AR mixture problems: solute before = solute after (weighted-average setup)Report a problem with this question

35. 35. A rectangular kennel measures 16 feet by 11 feet. Fencing is sold only in 12-foot rolls. How many rolls must be bought to enclose the kennel completely?

    • A.3 rolls
    • B.5 rolls✓ Answer
    • C.6 rolls
    • D.4 rolls

    The perimeter is 2 × (16 + 11) = 54 feet, and 54 ÷ 12 = 4.5 rolls. Since partial rolls cannot be bought and 4 rolls leave a gap, round UP to 5 rolls. Answering 4 rounds down and leaves 6 feet unfenced; 3 comes from adding only one length and one width without doubling.

    Ref QB-953UB2Source: AR division-context rounding: containers/rolls needed round UP; perimeter P = 2(l + w)Report a problem with this question

36. 36. A field mess pours juice into 8-fluid-ounce cups. How many full cups can be poured from 5 gallons of juice?

    • A.160
    • B.40
    • C.80✓ Answer
    • D.64

    One gallon is 128 fluid ounces, so 5 gallons = 5 × 128 = 640 fluid ounces, and 640 ÷ 8 = 80 cups. Answering 40 comes from the common error of treating a gallon as 64 ounces (which is actually a half gallon), and 160 doubles the correct result.

    Ref QB-SM8ZW2Source: US customary capacity conversion: 1 gallon = 128 fl oz (4 qt × 32 fl oz)Report a problem with this question

37. 37. A dispatcher logs five delivery times, in minutes, in this order: 12, 26, 9, 18, 15. What is the median delivery time?

    • A.17 minutes
    • B.15 minutes✓ Answer
    • C.9 minutes
    • D.16 minutes

    The median is the middle value of the ORDERED list. Sorted, the times are 9, 12, 15, 18, 26, so the middle (third) value is 15 minutes. Answering 9 takes the middle of the list as written without sorting, 16 is the mean (80 ÷ 5), and 17 is the range (26 − 9).

    Ref QB-A5E6H3Source: AR statistics: median = middle value of the data set after ordering (odd n)Report a problem with this question

38. 38. A crate holds 4 red flags, 5 blue flags, and 3 green flags. If one flag is pulled out at random, what is the probability that it is NOT blue?

    • A.5/12
    • B.1/3
    • C.5/7
    • D.7/12✓ Answer

    There are 4 + 5 + 3 = 12 flags in all, and 4 + 3 = 7 of them are not blue, so P(not blue) = 7/12 — equivalently 1 − 5/12 by the complement rule. Answering 5/12 gives P(blue) instead, 1/3 counts only the red flags, and 5/7 is a part-to-part ratio, not a probability.

    Ref QB-JMRNQSSource: AR probability: P(not A) = 1 − P(A); probability = favorable ÷ total outcomesReport a problem with this question

39. 39. A quartermaster receives 15 cases of bottled water, each holding 24 bottles, for a 4-day exercise. During the exercise, 8 bottles are found damaged and discarded, and the troops drink 296 bottles. How many bottles remain at the end?

    • A.64
    • B.90
    • C.56✓ Answer
    • D.14

    Start with the total: 15 × 24 = 360 bottles; then subtract everything that left the supply: 360 − 8 − 296 = 56 bottles. The '4 days' is a planted distractor number the problem never needs — 90 (360 ÷ 4) and 14 (56 ÷ 4) both come from using it, and 64 forgets the 8 damaged bottles.

    Ref QB-35XTATSource: officialasvab.com — AR description (multi-step arithmetic word problems); official items include unused distractor numbersReport a problem with this question

40. 40. A sergeant is 3 times as old as his son. In 12 years, the sergeant will be only twice as old as his son. How old is the son now?

    • A.24
    • B.36
    • C.8
    • D.12✓ Answer

    Let the son be s now, so the sergeant is 3s. In 12 years both are 12 years older: 3s + 12 = 2(s + 12), which gives 3s + 12 = 2s + 24, so s = 12. Check: the sergeant is 36 now; in 12 years, 48 is exactly twice 24. Answering 36 gives the sergeant's age, and 24 gives the son's future age.

    Ref QB-UEYVA5Source: AR algebraic-translation word problems (age relationships), single-variable linear equation; both people age equallyReport a problem with this question

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