ASVAB Arithmetic Reasoning & Mathematics
Knowledge 2027 | 200 Practice Questions &
Correct Answers | Complete Math Study Guide
1. John bought a camera on sale that normally costs $160. If the price was reduced 20% during the
sale, what was the sale price of the camera?
A) $120
B) $124
C) *$128
D) $140
Answer: C
Rationale: 20% of $160 = 0.20 × $160 = $32. Sale price = $160 − $32 = $128.
2. A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in
one hour?
A) 15
B) *18
C) 20
D) 30
Answer: B
Rationale: 3 stations/10 min = x stations/60 min. Cross multiply: 10x = 180, x = 18.
3. On a certain map, 3/4 inch represents one mile. What distance, in miles, is represented by 1 3/4
inches?
A) 1 1/2
,B) *2 1/3
C) 2 1/2
D) 5 1/4
Answer: B
Rationale: (7/4) / x = (3/4) / 1. Cross multiply: 7/4 = 3x/4 → 7 = 3x → x = 7/3 = 2 1/3.
4. A certain box contains baseballs and golf balls. If the ratio of baseballs to golf balls is 2:3 and
there are 30 baseballs in the box, how many golf balls are in the box?
A) 18
B) 20
C) 36
D) *45
Answer: D
Rationale: 2/3 = 30/x. Cross multiply: 2x = 90, x = 45.
5. Four people shared a taxi to the airport. The fare was $36.00, and they gave the driver a tip
equal to 25% of the fare. If they equally shared the cost of the fare and tip, how much did each
person pay?
A) $9.75
B) $10.25
C) $10.75
D) *$11.25
Answer: D
Rationale: Total cost = $36 + (0.25 × $36) = $36 + $9 = $45. Each paid $45/4 = $11.25.
6. If a car travels 1/100 of a kilometer each second, how many kilometers does it travel in an hour?
A) *36
B) 60
,C) 72
D) 100
Answer: A
Rationale: 60 × 60 = 3,600 seconds in an hour. 3,600 × 1/100 = 36 km.
7. 20 − (−5) = ?
A) −25
B) *25
C) 15
D) −15
Answer: B
Rationale: Subtracting a negative is the same as addition: 20 + 5 = 25.
8. Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon
of gasoline and gasoline cost $1.25 per gallon, what was the cost in dollars of the gasoline for the
trip?
A) $20.00
B) $24.00
C) *$25.00
D) $40.00
Answer: C
Rationale: 700/35 = 20 gallons. 20 × $1.25 = $25.00.
9. After eating 25% of the jelly beans, Brett had 72 left. How many jelly beans did Brett have
originally?
A) 90
B) 94
C) 95
, D) *96
Answer: D
Rationale: x − 0.25x = 72 → 0.75x = 72 → x = 96.
10. A student finishes the first half of an exam in 2/3 the time it takes him to finish the second
half. If the entire exam takes him an hour, how many minutes does he spend on the first half of
the exam?
A) 20
B) *24
C) 27
D) 36
Answer: B
Rationale: Let S = second half. 2/3 S + S = 60 → 5/3 S = 60 → S = 36. First half = 2/3 × 36 = 24.
11. A 25 ounce solution is 20% alcohol. If 50 ounces of water are added to it, what percent of the
new solution is alcohol?
A) *6 2/3%
B) 7 1/2%
C) 10%
D) 13 1/3%
Answer: A
Rationale: Alcohol = 0.20 × 25 = 5 oz. New total = 75 oz. 5/75 × 100% = 6 2/3%.
12. Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his backpack. If he pulls out one
pen at random from his backpack, what is the probability that the pen is either red or black?
A) *2/3
B) 3/5
C) 2/5
Knowledge 2027 | 200 Practice Questions &
Correct Answers | Complete Math Study Guide
1. John bought a camera on sale that normally costs $160. If the price was reduced 20% during the
sale, what was the sale price of the camera?
A) $120
B) $124
C) *$128
D) $140
Answer: C
Rationale: 20% of $160 = 0.20 × $160 = $32. Sale price = $160 − $32 = $128.
2. A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in
one hour?
A) 15
B) *18
C) 20
D) 30
Answer: B
Rationale: 3 stations/10 min = x stations/60 min. Cross multiply: 10x = 180, x = 18.
3. On a certain map, 3/4 inch represents one mile. What distance, in miles, is represented by 1 3/4
inches?
A) 1 1/2
,B) *2 1/3
C) 2 1/2
D) 5 1/4
Answer: B
Rationale: (7/4) / x = (3/4) / 1. Cross multiply: 7/4 = 3x/4 → 7 = 3x → x = 7/3 = 2 1/3.
4. A certain box contains baseballs and golf balls. If the ratio of baseballs to golf balls is 2:3 and
there are 30 baseballs in the box, how many golf balls are in the box?
A) 18
B) 20
C) 36
D) *45
Answer: D
Rationale: 2/3 = 30/x. Cross multiply: 2x = 90, x = 45.
5. Four people shared a taxi to the airport. The fare was $36.00, and they gave the driver a tip
equal to 25% of the fare. If they equally shared the cost of the fare and tip, how much did each
person pay?
A) $9.75
B) $10.25
C) $10.75
D) *$11.25
Answer: D
Rationale: Total cost = $36 + (0.25 × $36) = $36 + $9 = $45. Each paid $45/4 = $11.25.
6. If a car travels 1/100 of a kilometer each second, how many kilometers does it travel in an hour?
A) *36
B) 60
,C) 72
D) 100
Answer: A
Rationale: 60 × 60 = 3,600 seconds in an hour. 3,600 × 1/100 = 36 km.
7. 20 − (−5) = ?
A) −25
B) *25
C) 15
D) −15
Answer: B
Rationale: Subtracting a negative is the same as addition: 20 + 5 = 25.
8. Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon
of gasoline and gasoline cost $1.25 per gallon, what was the cost in dollars of the gasoline for the
trip?
A) $20.00
B) $24.00
C) *$25.00
D) $40.00
Answer: C
Rationale: 700/35 = 20 gallons. 20 × $1.25 = $25.00.
9. After eating 25% of the jelly beans, Brett had 72 left. How many jelly beans did Brett have
originally?
A) 90
B) 94
C) 95
, D) *96
Answer: D
Rationale: x − 0.25x = 72 → 0.75x = 72 → x = 96.
10. A student finishes the first half of an exam in 2/3 the time it takes him to finish the second
half. If the entire exam takes him an hour, how many minutes does he spend on the first half of
the exam?
A) 20
B) *24
C) 27
D) 36
Answer: B
Rationale: Let S = second half. 2/3 S + S = 60 → 5/3 S = 60 → S = 36. First half = 2/3 × 36 = 24.
11. A 25 ounce solution is 20% alcohol. If 50 ounces of water are added to it, what percent of the
new solution is alcohol?
A) *6 2/3%
B) 7 1/2%
C) 10%
D) 13 1/3%
Answer: A
Rationale: Alcohol = 0.20 × 25 = 5 oz. New total = 75 oz. 5/75 × 100% = 6 2/3%.
12. Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his backpack. If he pulls out one
pen at random from his backpack, what is the probability that the pen is either red or black?
A) *2/3
B) 3/5
C) 2/5
