ASTB math practice Exam with
Complete Solutions
Two trains running in the same direction on the same track travel at the rates of 40 and
45 mph, respectively. If the slower train starts out an hour earlier, how long will it take
the faster train to catch up with it?
a. 5 hours
b. 6 hours
c. 7 hours
d. 8 hours - ANSWER-d. 8 hours
The slower train is 40 miles ahead in one hour. The difference in rate is 5 mph, and
40/5=8
A naval detachment has enough rations to feed fifteen people for 8 days. If five more
people join the detachment, for how many fewer days will the rations last?
a. 1
b. 2
c. 3
d. 4 - ANSWER-b. 2
Let x = the number of ration days for 20 persons.
15×8=20xx
20x=120
x=120/20
x=6 ration days for 20 persons.
, Therefore 8 days - 6 days = 2 days fewer.
A field can be plowed by 12 machines in 7 hours. If 4 machines are broken and cannot
be used, how many hours will it take to plow the field?
a. 7 1/2 hours
b. 8 1/2 hours
c. 9 1/2 hours
d. 10 1/2 hours - ANSWER-d. 10 1/2 hours
Let x equal the number of hours to plow with 8 machines. So,
12×7=8xx
8x=84
x=84/8
x=10 1/2 hours
What is the square root of 4 raised to the fifth power?
a. 8
b. 16
c. 32
d. 64 - ANSWER-c. 32
√4=2
2⁵=2×2×2×2×2
=32
If 3n - 2 = 27, what does n equal?
a. 5
b. 7
Complete Solutions
Two trains running in the same direction on the same track travel at the rates of 40 and
45 mph, respectively. If the slower train starts out an hour earlier, how long will it take
the faster train to catch up with it?
a. 5 hours
b. 6 hours
c. 7 hours
d. 8 hours - ANSWER-d. 8 hours
The slower train is 40 miles ahead in one hour. The difference in rate is 5 mph, and
40/5=8
A naval detachment has enough rations to feed fifteen people for 8 days. If five more
people join the detachment, for how many fewer days will the rations last?
a. 1
b. 2
c. 3
d. 4 - ANSWER-b. 2
Let x = the number of ration days for 20 persons.
15×8=20xx
20x=120
x=120/20
x=6 ration days for 20 persons.
, Therefore 8 days - 6 days = 2 days fewer.
A field can be plowed by 12 machines in 7 hours. If 4 machines are broken and cannot
be used, how many hours will it take to plow the field?
a. 7 1/2 hours
b. 8 1/2 hours
c. 9 1/2 hours
d. 10 1/2 hours - ANSWER-d. 10 1/2 hours
Let x equal the number of hours to plow with 8 machines. So,
12×7=8xx
8x=84
x=84/8
x=10 1/2 hours
What is the square root of 4 raised to the fifth power?
a. 8
b. 16
c. 32
d. 64 - ANSWER-c. 32
√4=2
2⁵=2×2×2×2×2
=32
If 3n - 2 = 27, what does n equal?
a. 5
b. 7
