ASVAB Arithmetic Reasoning, the word-problem subtest

A mess hall serves 300 soldiers. 45% choose beef, 1/3 choose chicken, and the rest choose the vegetarian meal. How many vegetarian meals are needed?

1. 100
   100 is the number choosing chicken.
2. 135
   135 is the number choosing beef.
3. 165
   165 subtracts only the beef (300 − 135) and forgets the chicken.
4. 65
   Beef is 0.45 × 300 = 135 and chicken is 1/3 × 300 = 100, so vegetarian is 300 − 135 − 100 = 65.

ID 716345 · Report a problem

A supply officer plans to split 840 rounds of ammunition equally among 24 soldiers. If 4 soldiers are absent and the rounds are split equally among the soldiers present, how many more rounds does each present soldier get than planned?

1. 7
   As planned each soldier gets 840 ÷ 24 = 35 rounds; with 20 present each gets 840 ÷ 20 = 42, which is 7 more.
2. 35
   35 is the planned share per soldier, not the increase.
3. 42
   42 is the new share per soldier; the question asks how many more than the planned 35.
4. 6
   6 spreads the absent soldiers' 140 rounds over all 24 soldiers (about 5.8); those rounds go only to the 20 present.

ID 716139 · Report a problem

A training course lasts 9 weeks, with classes 5 days a week for 6 hours a day. Classes are not held on 3 holidays during the course. How many hours of training are given?

1. 255 hours
   255 hours subtracts 3 days of 5 hours (15 hours); each lost day is 6 hours.
2. 267 hours
   267 hours subtracts 3 hours instead of 3 days of 6 hours.
3. 252 hours
   There are 9 × 5 = 45 class days minus 3 holidays = 42 days, and 42 × 6 = 252 hours.
4. 270 hours
   270 hours is 45 × 6 with the 3 holidays left in.

ID 716143 · Report a problem

A cook must prepare meals for 120 people, with 1/4 pound of meat per person. Meat comes in 5-pound packages that cost $18.50 each. How much will the meat cost?

1. $2,220.00
   $2,220.00 multiplies the 120 people by $18.50, skipping pounds and packages.
2. $111.00
   The cook needs 120 × 1/4 = 30 pounds, which is 30 ÷ 5 = 6 packages, and 6 × $18.50 = $111.00.
3. $129.50
   $129.50 buys 7 packages; 30 pounds fills exactly 6 five-pound packages, so no extra package is needed.
4. $555.00
   $555.00 treats $18.50 as a price per pound (30 × $18.50); it is the price of a 5-pound package.

ID 716146 · Report a problem

A unit buys 42 signal relays at $350 each and gets a 15% bulk discount. What is the total cost after the discount?

1. $12,495
   The regular cost is 42 × $350 = $14,700; the discount is 0.15 × $14,700 = $2,205, leaving $12,495 (that is, 85% of $14,700).
2. $2,205
   $2,205 is the discount itself, not the cost after the discount.
3. $14,685
   $14,685 subtracts $15 instead of 15%.
4. $16,905
   $16,905 adds the 15% to the price instead of taking it off.

ID 716158 · Report a problem

A platoon of 30 soldiers must cross a river in one trip using rafts. Each raft holds 8 people, and one of the 8 on every raft must be an engineer who rows (engineers are not part of the platoon). What is the fewest rafts needed?

1. 3
   3 divides 30 by 8 and rounds 3.75 down; it forgets the engineer's seat and leaves soldiers on the bank.
2. 4
   4 is 30 ÷ 8 rounded up, which forgets that one seat on every raft belongs to the engineer.
3. 5
   Each raft carries 8 − 1 = 7 platoon members, and 30 ÷ 7 = 4 2/7, so 4 rafts leave 2 soldiers behind and 5 are needed.
4. 7
   7 is the number of soldiers each raft can carry, not the number of rafts.

ID 716160 · Report a problem

Soldiers are posted every 15 meters around a closed defensive perimeter 720 meters long, with one soldier at the starting point. How many soldiers are needed?

1. 49
   49 adds one for a straight line with a soldier at each end; on a closed loop the end post is the starting soldier.
2. 48
   720 ÷ 15 = 48 gaps, and on a closed loop the last gap ends at the first soldier, so 48 soldiers.
3. 47
   47 subtracts one, the rule for posts strictly between two fixed ends; a closed loop has no ends.
4. 24
   24 divides by 30, as if each soldier covered 15 m on each side; the posts are 15 m apart, so there are 720 ÷ 15 posts.

ID 716327 · Report a problem

A training program runs 12 weeks, 5 days a week, 6 hours a day. A recruit must attend at least 90% of the hours. What is the greatest number of hours the recruit can miss?

1. 60
   60 is the number of class days (12 × 5), not hours that can be missed.
2. 324
   324 is 90% of 360, the fewest hours the recruit must attend.
3. 36
   The program has 12 × 5 × 6 = 360 hours; attending 90% allows missing 10%, which is 36 hours.
4. 6
   6 is 10% of the 60 class days, not of the 360 hours.

ID 716328 · Report a problem

A repair team can fix 5 vehicles in 4 hours. At that rate, how many vehicles can it completely fix in a 10-hour workday?

1. 50
   50 multiplies 5 vehicles by 10 hours without dividing by the 4 hours.
2. 12
   The team fixes 5 ÷ 4 = 1.25 vehicles an hour, so 1.25 × 10 = 12.5: 12 vehicles are fully fixed.
3. 8
   8 inverts the rate, 4 × 10 ÷ 5, as if it took 5 hours for every 4 vehicles.
4. 13
   13 rounds 12.5 up, counting a vehicle that is only half repaired.

ID 716348 · Report a problem

A ship steams at 24 knots for 3 hours and then at 18 knots for 2 hours. What is its average speed for the whole run?

1. 21 knots
   21 knots averages the two speeds, but the ship spends more time at 24 knots, so the speeds are not weighted equally.
2. 20.4 knots
   20.4 knots swaps the times, (24 × 2 + 18 × 3) ÷ 5.
3. 21.6 knots
   Average speed is total distance over total time: (24 × 3 + 18 × 2) ÷ 5 = 108 ÷ 5 = 21.6 knots.
4. 18 knots
   18 knots divides the 108 nautical miles by 6, multiplying the 3 and 2 hours instead of adding them.

ID 813323 · Report a problem

A spinner has 8 equal sections numbered 1 to 8. What is the probability of spinning a number that is greater than 5 or even?

1. 5/8
   The numbers greater than 5 or even are 2, 4, 6, 7, 8, five of the eight, so 5/8.
2. 3/8
   3/8 counts only the numbers greater than 5 (6, 7, 8).
3. 1/4
   1/4 counts only the numbers that are both greater than 5 and even (6 and 8).
4. 7/8
   7/8 adds 3/8 + 4/8 and counts 6 and 8 twice; the overlap has to be subtracted once.

ID 857649 · Report a problem

In a squadron, 60% of the members are pilots, and 25% of the pilots are women. What percent of the squadron are women pilots?

1. 85%
   85% adds the percents (60% + 25%).
2. 25%
   25% is the share of the pilots who are women, not the share of the whole squadron.
3. 35%
   35% subtracts the percents (60% − 25%).
4. 15%
   A part of a part multiplies: 25% of 60% is 0.25 × 0.60 = 0.15, or 15% of the squadron.

ID 858508 · Report a problem

A student pilot must choose 3 different aircraft types to practice on from 5 available types. The order of choice does not matter. How many different selections are possible?

1. 60
   60 = 5 × 4 × 3 counts ordered choices; each trio is counted 6 times.
2. 15
   15 multiplies 5 × 3, which is not a counting rule for choosing 3 of 5.
3. 125
   125 = 5³ allows the same type to be picked again, but the three types must be different.
4. 10
   Order does not matter, so this is a combination: C(5,3) = (5 × 4 × 3) ÷ (3 × 2 × 1) = 10.

ID 970236 · Report a problem

An aircraft can fly 2,100 miles on a full tank of fuel. It has already flown 840 miles. What percent of its fuel is left?

1. 6%
   6% misplaces the decimal point: 1,260 ÷ 2,100 = 0.6, which is 60%, not 6%.
2. 60%
   Fuel for 2,100 − 840 = 1,260 miles is left, and 1,260 ÷ 2,100 = 0.6, so 60% remains.
3. 67%
   67% compares the used fuel with the fuel left (840 ÷ 1,260); both must be shares of the full tank.
4. 40%
   40% = 840 ÷ 2,100 is the fuel already used, not what is left.

ID 716337 · Report a problem

An aircraft descends from 9,000 feet to sea level at 1,500 feet per minute with a ground speed of 180 knots. How many nautical miles does it cover during the descent?

1. 18 nautical miles
   The descent takes 9,000 ÷ 1,500 = 6 minutes, which is 0.1 hour, so the distance is 180 × 0.1 = 18 nautical miles.
2. 6 nautical miles
   6 is the descent time in minutes, not a distance.
3. 1,080 nautical miles
   1,080 nautical miles multiplies 180 by 6 as if the descent took 6 hours.
4. 30 nautical miles
   30 nautical miles divides 180 by 6 instead of multiplying by 6/60 hour.

ID 813475 · Report a problem