ASVAB - Arithmetic Reasoning/Mathematics Knowledge
Study
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
(c) $128
This question asks you to determine the sale price of a camera that normally sells at $160 and is
discounted 20%. To solve, determine what 20% of $160 equals. Rewrite 20% as a decimal.
PR
20% = 0.20. So 20% of $160 = 0.20 x $160 = $32.
The sale price of the camera would be $160 - $32 = $128, choice (c)
A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in one
hour?
O
(a) 15
(b) 18
FD
(c) 20
(d) 30
(b) 18
O
First, set up the rate as a proportion, where (x) is the number of stations.
3 stations/10 minutes = (x) stations/1 hour
C
Then, convert the units.
3 stations/10 minutes = (x) stations/60 minutes
Cross multiply and solve for (x).
180 = 10(x)
18 = (x)
On a certain map, 3/4 inch represents one mile. What distance, in miles, is presented by 1 3/4 inches?
(a) 1 1/2
,(b) 2 1/3
(c) 2 1/2
(d) 5 1/4
(b) 2 1/3
In this question, the ratio is implied: for every 3/4 inch of map there is 1 real mile, so the ratio of inches
to the miles they represent is always 3/4 to 1. Therefore, you can set up the proportion:
number of inches/ number of miles = 3/ = 3/4
Now 1 3/4 inches = 7/4 inches.
Set up a proportion:
PR
7/4 inches
7/4 inches / number of miles = 3/4
Cross-multiply:
O
7/4(4) = 3 (number of miles)
FD
7= 3(number of miles)
7/3 = number of miles or 2 1/3 = number of miles
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?
O
(a) 18
(b) 20
C
(c) 36
(d) 45
(d) 45
You can express the ratio of baseballs to golf balls as 2/3. Since you know the number of baseballs, you
can set up a proportion: 2/3 = 30/ (x) where (x) is the number of golf balls. To solve, cross-multiply to get
2(x) = 90, or x = 45.
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
(d) $11.25
The total cost of the taxi ride equals $36 + (25% of $36), or $36 + (.25 x $36) = $36 + $9 = $45. If four
people split the cost equally, then each person paid $45/4, or $11.25 each.
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
(a) 36
PR
Find the number of seconds in an hour and then multiply this by the distance the car is traveling each
second. There are 60 seconds in a minute and 60 minute in one hour; therefore, there are 60 x 60, or
3,600, seconds in an hour. In one second the car travels 1/100 kilometers; in one hour the car will travel
3,600 x 1/100 or 36 kilometers.
O
20 - (-5) = __.
(a) -25
FD
(b) 25
(c) 15
(d) -15
(b) 25
O
Subtracting a negative number is the same as addition, so 20 - (-5) is really 20 + 5 = 25.
Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon of
C
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
(c) $25.00
If Ms. Smith's car average 35 miles per gallon, she can go 35 miles on 1 gallon. To go 700 miles she will
need 700/35, or 20 gallons of gasoline. The price of gasoline was $1.25 per gallon, so she spent 20 x
$1.25, or $25, for her trip.
, 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
(d) 96
Be careful with a question like this one. You're given the percent decrease (25%) and the new number
(72), and you're asked to reconstruct the original number. Don't just take 25% of 72 and add it on. That
25% is based not on the new number, 72, but on the original number - the number you're looking for.
The best way to do a problem like this is to set up an equation:
(original number) - (25% of original number) = new number
PR
(x) - 0.25(x) = 72
0.75x = 72
x = 96
O
Alternatively, you can use the answer choices to determine the correct answer. The original number of
jelly beans has to be reducible by 25%, or 1/4. That means the original number of jelly beans has to be a
multiple of 4 (or else you'd be reducing by pieces of jelly beans). Only the correct answer, 96, is a
FD
multiple of 4.
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
O
(b) s4
(c) 27
(d) 36
C
(b) 24
The time it takes to complete the entire exam is the sum of the time spent on the first half of the exam
and the time spent on the second half. The time spent on the first half is 2/3 of the time spent on he
second half. If (S) represents the time spent on the second half, then the total time spent is 2/3(S) + (S)
or 5/3 (S). You know this total time is one hour, or 60 minutes. Set up a simple equation and solve for (S).
5/3(S) = 60
3/5 x 5/3(S) = 3/5 x 60
(S) = 36
So the second half takes 36 minutes. The first half takes 2/3 of this, or 24 minutes. You could also find
the first half by subtracting 36 minutes from the total time, 60 minutes.
Study
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
(c) $128
This question asks you to determine the sale price of a camera that normally sells at $160 and is
discounted 20%. To solve, determine what 20% of $160 equals. Rewrite 20% as a decimal.
PR
20% = 0.20. So 20% of $160 = 0.20 x $160 = $32.
The sale price of the camera would be $160 - $32 = $128, choice (c)
A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in one
hour?
O
(a) 15
(b) 18
FD
(c) 20
(d) 30
(b) 18
O
First, set up the rate as a proportion, where (x) is the number of stations.
3 stations/10 minutes = (x) stations/1 hour
C
Then, convert the units.
3 stations/10 minutes = (x) stations/60 minutes
Cross multiply and solve for (x).
180 = 10(x)
18 = (x)
On a certain map, 3/4 inch represents one mile. What distance, in miles, is presented by 1 3/4 inches?
(a) 1 1/2
,(b) 2 1/3
(c) 2 1/2
(d) 5 1/4
(b) 2 1/3
In this question, the ratio is implied: for every 3/4 inch of map there is 1 real mile, so the ratio of inches
to the miles they represent is always 3/4 to 1. Therefore, you can set up the proportion:
number of inches/ number of miles = 3/ = 3/4
Now 1 3/4 inches = 7/4 inches.
Set up a proportion:
PR
7/4 inches
7/4 inches / number of miles = 3/4
Cross-multiply:
O
7/4(4) = 3 (number of miles)
FD
7= 3(number of miles)
7/3 = number of miles or 2 1/3 = number of miles
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?
O
(a) 18
(b) 20
C
(c) 36
(d) 45
(d) 45
You can express the ratio of baseballs to golf balls as 2/3. Since you know the number of baseballs, you
can set up a proportion: 2/3 = 30/ (x) where (x) is the number of golf balls. To solve, cross-multiply to get
2(x) = 90, or x = 45.
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
(d) $11.25
The total cost of the taxi ride equals $36 + (25% of $36), or $36 + (.25 x $36) = $36 + $9 = $45. If four
people split the cost equally, then each person paid $45/4, or $11.25 each.
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
(a) 36
PR
Find the number of seconds in an hour and then multiply this by the distance the car is traveling each
second. There are 60 seconds in a minute and 60 minute in one hour; therefore, there are 60 x 60, or
3,600, seconds in an hour. In one second the car travels 1/100 kilometers; in one hour the car will travel
3,600 x 1/100 or 36 kilometers.
O
20 - (-5) = __.
(a) -25
FD
(b) 25
(c) 15
(d) -15
(b) 25
O
Subtracting a negative number is the same as addition, so 20 - (-5) is really 20 + 5 = 25.
Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon of
C
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
(c) $25.00
If Ms. Smith's car average 35 miles per gallon, she can go 35 miles on 1 gallon. To go 700 miles she will
need 700/35, or 20 gallons of gasoline. The price of gasoline was $1.25 per gallon, so she spent 20 x
$1.25, or $25, for her trip.
, 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
(d) 96
Be careful with a question like this one. You're given the percent decrease (25%) and the new number
(72), and you're asked to reconstruct the original number. Don't just take 25% of 72 and add it on. That
25% is based not on the new number, 72, but on the original number - the number you're looking for.
The best way to do a problem like this is to set up an equation:
(original number) - (25% of original number) = new number
PR
(x) - 0.25(x) = 72
0.75x = 72
x = 96
O
Alternatively, you can use the answer choices to determine the correct answer. The original number of
jelly beans has to be reducible by 25%, or 1/4. That means the original number of jelly beans has to be a
multiple of 4 (or else you'd be reducing by pieces of jelly beans). Only the correct answer, 96, is a
FD
multiple of 4.
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
O
(b) s4
(c) 27
(d) 36
C
(b) 24
The time it takes to complete the entire exam is the sum of the time spent on the first half of the exam
and the time spent on the second half. The time spent on the first half is 2/3 of the time spent on he
second half. If (S) represents the time spent on the second half, then the total time spent is 2/3(S) + (S)
or 5/3 (S). You know this total time is one hour, or 60 minutes. Set up a simple equation and solve for (S).
5/3(S) = 60
3/5 x 5/3(S) = 3/5 x 60
(S) = 36
So the second half takes 36 minutes. The first half takes 2/3 of this, or 24 minutes. You could also find
the first half by subtracting 36 minutes from the total time, 60 minutes.
