ASVAB Arithmetic Reasoning Test 3 — Questions and Answers

Question 1: A soldier can march 4.5 miles per hour. How long will it take to march 18 miles?

3 hours
4 hours (Correct answer)
3.5 hours
5 hours

Correct answer: 4 hours

Time = Distance ÷ Speed = 18 ÷ 4.5 = 4 hours.

This problem uses the fundamental distance-rate-time relationship: Distance = Rate × Time, which rearranges to Time = Distance / Rate. Given: Distance = 18 miles, Rate (speed) = 4.5 miles per hour. Time = 18 / 4.5 = 4 hours. You can verify: 4.5 miles/hour × 4 hours = 18 miles. ✓ Alternate approach: 4.5 miles per hour means every 2 hours covers 9 miles (4.5 × 2). Two sets of 9 miles = 18 miles, requiring 2 × 2 = 4 hours. For ASVAB arithmetic reasoning, always identify the three variables in motion problems (distance, rate, time) and determine which two are given so you can solve for the third. Watch for unit consistency — if speed is in miles per hour, make sure distance is in miles and the answer will be in hours. The formula triangle (D = R × T) is the key to all rate problems.

Question 2: A military base has 240 soldiers. If 15% are reassigned to another post, how many soldiers remain?

36
180
204 (Correct answer)
225

Correct answer: 204

15% of 240 = 0.15 × 240 = 36 soldiers reassigned. Remaining: 240 - 36 = 204 soldiers.

To solve percentage reduction problems, first calculate the amount being removed, then subtract from the total. Step 1: Find 15% of 240. Convert 15% to decimal: 15% = 0.15. Multiply: 0.15 × 240 = 36 soldiers reassigned. Step 2: Subtract from original. 240 - 36 = 204 soldiers remain. Alternate (faster) method: If 15% leave, then 100% - 15% = 85% remain. So calculate 85% of 240 directly: 0.85 × 240 = 204. This single-step approach avoids subtraction and is often faster. Verification: 36 + 204 = 240. ✓ Common errors: (A) 36 is just the number reassigned, not remaining. (B) 180 would be 75% of 240. (D) 225 = 240 - 15, which incorrectly subtracts the percentage number (15) instead of the percentage amount (36). Always calculate the actual amount represented by the percentage, not just the percentage number itself.

Question 3: A supply truck can carry 3,000 pounds. If rations weigh 8 pounds per package and ammunition weighs 15 pounds per case, and the truck is loaded with 150 packages of rations and 100 cases of ammunition, how much weight remains available?

300 pounds (Correct answer)
500 pounds
250 pounds
750 pounds

Correct answer: 300 pounds

Rations: 150 × 8 = 1,200 lbs. Ammo: 100 × 15 = 1,500 lbs. Total loaded: 2,700 lbs. Remaining: 3,000 - 2,700 = 300 pounds.

This is a multi-step arithmetic problem requiring you to calculate two separate totals and combine them. Step 1: Weight of rations = 200 packages × 7 lbs/package = 1,400 lbs. Step 2: Weight of ammunition = 100 cases × 12 lbs/case = 1,200 lbs. Step 3: Total loaded weight = 1,400 + 1,200 = 2,600 lbs. Step 4: Remaining capacity = 3,500 - 2,600 = 900 lbs. For ASVAB word problems involving multiple items, organize the information systematically: identify each item type, its quantity, and its unit weight. Calculate each sub-total, sum them, then subtract from the maximum capacity to find remaining capacity. This type of logistics calculation is common in military supply operations — determining load capacity helps plan missions and ensure vehicles aren't overloaded, which can damage equipment or reduce vehicle performance and fuel economy.

Question 4: A vehicle travels at 55 mph for 2 hours, then at 65 mph for 3 hours. What is the total distance traveled?

355 miles
305 miles (Correct answer)
285 miles
400 miles

Correct answer: 305 miles

Distance 1 = 55 × 2 = 110 miles. Distance 2 = 65 × 3 = 195 miles. Total = 110 + 195 = 305 miles.

For problems with multiple legs at different speeds, calculate each segment independently using D = R × T, then add the distances. Segment 1: Speed = 55 mph, Time = 2 hours. Distance = 55 × 2 = 110 miles. Segment 2: Speed = 65 mph, Time = 3 hours. Distance = 65 × 3 = 195 miles. Total Distance = 110 + 195 = 305 miles. A common mistake is trying to average the speeds: (55 + 65)/2 = 60 mph × 5 hours = 300 miles. This gives the wrong answer because the vehicle spends different amounts of time at each speed (2 hours at 55, 3 hours at 65). Averaging speeds only works when equal time is spent at each speed. For the correct weighted average: Total distance / total time = 305/5 = 61 mph average speed. This is weighted toward the 65 mph leg because more time was spent at that speed. On multi-segment distance problems, always calculate each segment separately and sum — never average speeds unless explicitly told equal time was spent at each speed.

Question 5: A barracks room floor measures 12 feet by 15 feet. If carpet costs $3.50 per square foot, what is the total cost to carpet the room?

$472.50
$630.00 (Correct answer)
$378.00
$525.00

Correct answer: $630.00

Area = 12 × 15 = 180 square feet. Cost = 180 × $3.50 = $630.00.

This problem requires two steps: finding the area of a rectangle, then applying a unit cost. Step 1: Calculate area. Area of rectangle = length × width = 12 feet × 15 feet = 180 square feet. Step 2: Calculate cost. Cost = Area × Price per sq ft = 180 sq ft × $3.50/sq ft = $630.00. The multiplication 180 × $3.50: 180 × 3 = $540, plus 180 × 0.50 = $90. Total = $540 + $90 = $630. Area problems on the ASVAB frequently use the formula for rectangles (length × width). For other shapes: triangle = ½ × base × height; circle = π × r²; trapezoid = ½ × (sum of parallel sides) × height. Always make sure your answer is in the right units: area is in square units, and multiplying by a cost per square unit gives a total cost. Check that your answer is reasonable — a 180 sq ft room at $3.50/sq ft should cost in the hundreds of dollars range, and $630 is reasonable.

Question 6: A squad of 8 soldiers must complete 480 sandbags for a fortification. If 3 soldiers have already filled 120 sandbags, how many sandbags does each remaining soldier need to fill to complete the task equally?

45
60
72 (Correct answer)
52

Correct answer: 72

Remaining sandbags: 480 - 120 = 360. Remaining soldiers: 8 - 3 = 5. Each remaining soldier fills: 360 ÷ 5 = 72 sandbags.

This multi-step problem requires finding remaining quantities before dividing. Step 1: How many sandbags are left? 480 total - 120 already filled = 360 sandbags remaining. Step 2: How many soldiers still working? 8 total - 3 who have finished = 5 soldiers remaining. Step 3: Divide the work equally. 360 sandbags ÷ 5 soldiers = 72 sandbags per soldier. Wait — let me recheck the answer options. 360 ÷ 5 = 72, which matches answer choice C (72). The correct answer index should be 2 (0-indexed). The explanation above has an error in the answer label. Common errors in this type of problem: forgetting to subtract the work already completed (using 480/5 = 96 instead of 360/5 = 72), or forgetting to subtract the soldiers who finished (using 360/8 = 45 instead of 360/5 = 72). For work distribution problems: always calculate the remaining work and remaining workers as separate steps before dividing.

ASVAB Arithmetic Reasoning Test 3

A soldier can march 4.5 miles per hour.
How long will it take to march 18 miles?