Practice Test 4: Arithmetic Reasoning

Questions 1–50 are five-option items. For each question, select the option that is most nearly correct.

1.	If a car uses gallons of gas every 30 miles, how many miles can be driven with 6 gallons of gas?

(A)	100
(B)	110
(C)	120
(D)	130
(E)	140

2.	A car has a gasoline tank that holds 20 gallons. When the gauge reads full, how many gallons are needed to fill the tank?

(A)	16
(B)	15
(C)	10
(D)	5
(E)	4

3.	An airplane flying a distance of 875 miles used 70 gallons of gasoline. How many gallons will it need to travel 3000 miles?

(A)	108
(B)	120
(C)	144
(D)	240
(E)	280

4.	The Mayflower sailed from Plymouth, England, to Plymouth Rock, a distance of approximately 2800 miles, in 63 days. The average speed in miles per hour was closest to which one of the following?

(A)
(B)	1
(C)	2
(D)	3
(E)	4

5.	A man drives 60 miles to his destination at an average speed of 40 miles per hour and makes the return trip at an average rate of 30 miles per hour. His average speed in miles per hour for the entire trip is most nearly

(A)	34
(B)	36
(C)	38
(D)	40
(E)	42

6.	A plane flies over Cleveland at 10:20 A.M. It passes over a community 120 miles away at 10:32 A.M. Find the plane’s flight rate in miles per hour.

(A)	600
(B)	540
(C)	480
(D)	420
(E)	360

7.	Two trains start from the same station at 10:00 A.M., one traveling east at 60 mph and the other traveling west at 70 mph. At what time will these trains be 455 miles apart?

(A)	12:30 P.M.
(B)	1:00 P.M.
(C)	1:30 P.M.
(D)	2:00 P.M.
(E)	2:30 P.M.

8.	Two trains running on the same track travel at the rates of 25 and 30 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)
(B)	4 hours
(C)
(D)	5 hours
(E)

9.	On a map, inch = 10 miles. How many miles apart are two towns that are inches apart on the map?

(A)	33
(B)	36
(C)	39
(D)	42
(E)	45

10.	The total savings in purchasing 30 13-cent candies for a class party at a reduced rate of $1.38 per dozen is

(A)	$0.35
(B)	$0.40
(C)	$0.45
(D)	$0.50
(E)	$0.55

11.	Mr. Jackson takes his wife and two children to the circus. If the price of a child’s ticket is half the price of an adult ticket and Mr. Jackson pays a total of $12.60, the price of a child’s ticket is

(A)	$2.10
(B)	$2.60
(C)	$3.10
(D)	$3.60
(E)	$4.10

12.	What part of a day is 5 hours 15 minutes?

(A)
(B)
(C)
(D)
(E)

13.	A team lost 10 games in a 35-game season. Find the ratio of games won to games lost.

(A)	2 : 5
(B)	5 : 2
(C)	5 : 7
(D)	7 : 2
(E)	7 : 5

14.	In a 3-hour examination of 350 questions, there are 50 mathematics problems. If twice as much time should be allowed for each mathematics problem as for each of the other questions, how many minutes should be spent on the mathematics problems?

(A)	45 minutes
(B)	52 minutes
(C)	60 minutes
(D)	72 minutes
(E)	80 minutes

15.	The parts department’s profit is 12 percent on a new magneto. How much did the magneto cost if the selling price is $145.60?

(A)	$120.00
(B)	$125.60
(C)	$130.00
(D)	$133.60
(E)	$136.00

16.	A typewriter was listed at $120.00 and was bought for $96.00. What was the rate of discount?

(A)	16%
(B)	20%
(C)	24%
(D)	28%
(E)	32%

17.	A class of 198 recruits consists of three racial and ethnic groups. If are black and of the remainder are Hispanic, how many of the recruits in the class are white?

(A)	198
(B)	165
(C)	132
(D)	99
(E)	66

18.	One third of the students at Central High are seniors. Three fourths of the seniors will go to college next year. What percentage of the students at Central High will go to college next year?

(A)	25%
(B)
(C)	45%
(D)	50%
(E)	75%

19.	If 2.5 centimeters = 1 inch, and 36 inches = 1 yard, how many centimeters are in 1 yard?

(A)	14
(B)	25
(C)	70
(D)	80
(E)	90

20.	A rectangular fuel tank measures 60 inches in length, 30 inches in width, and 12 inches in depth. How many cubic feet are within the tank?

(A)	12.5
(B)	15.0
(C)	18.5
(D)	21.0
(E)	24.5

21.	How many gallons of fuel will be contained in a rectangular tank that measures 2 feet in width, 3 feet in length, and 1 foot 8 inches in depth (7.5 gallons = 1 cubic foot)?

(A)	110
(B)	75
(C)	66.6
(D)	55
(E)	45

22.	A rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 inches by 4 inches by 2 inches. The number of bricks in the bin is

(A)	54
(B)	324
(C)	648
(D)	1072
(E)	1296

23.	A resolution was passed by a ratio of 5:4. If 90 people voted for the resolution, how many voted against it?

(A)	40
(B)	50
(C)	60
(D)	66
(E)	72

24.	If 2.5 centimeters = 1 inch, how many centimeters are in 1 foot?

(A)	5
(B)	10
(C)	15
(D)	30
(E)	60

25.	A gasoline tank is full. After adding 10 gallons of gasoline, the gauge indicates that the tank is full. What is the capacity of the tank in gallons?

(A)	20
(B)	24
(C)	28
(D)	32
(E)	36

26.	The water level of a swimming pool, 75 feet by 42 feet, is to be raised 4 inches. How many gallons of water are needed (7.5 gallons = 1 cubic foot)?

(A)	7875
(B)	15,750
(C)	23,625
(D)	31,500
(E)	63,000

27.	If the outer diameter of a cylindrical oil tank is 54.28 inches and the inner diameter is 48.7 inches, the thickness of the wall of the tank, in inches, is

(A)	2.79
(B)	3.29
(C)	4.58
(D)	5.58
(E)	6.47

28.	A person travels 30 miles at 6 mph, 20 miles at 10 mph, and 15 miles at 5 mph. What is the person’s average rate for the complete distance?

(A)	6 mph
(B)
(C)	7 mph
(D)
(E)	8 mph

29.

Sue and Joe are on opposite sides of a circular lake that is 1260 feet in circumference. They walk around it, starting at the same time and walking in the same direction. Sue walks at the rate of 50 yards a minute, and Joe walks at the rate of 60 yards a minute. In how many minutes will Joe overtake Sue?

(A)	14
(B)	21
(C)	28
(D)	35
(E)	42

30.	Two ships are 1550 miles apart and sailing toward each other. One sails at the rate of 85 miles per day and the other at the rate of 65 miles per day. How far apart will they be at the end of 9 days?

(A)	100 miles
(B)	150 miles
(C)	175 miles
(D)	200 miles
(E)	225 miles

31.	A family drove from New York to San Francisco, a distance of 3000 miles. They covered of the distance the first day and of the remaining distance on the second day. How many miles were left to be driven?

(A)	2000
(B)	2100
(C)	2300
(D)	2400
(E)	2500

32.	Assuming that on a blueprint inch equals 12 inches of actual length, the actual length (in feet) of a steel bar represented on the blueprint by a line inches long is

(A)	30
(B)	45
(C)	75
(D)	160
(E)	360

33.	If pencils are bought at 36 cents per dozen and sold at 3 for 10 cents, the total profit on 5 dozen is

(A)	18¢
(B)	20¢
(C)	22¢
(D)	24¢
(E)	26¢

34.	The tunnel toll is $1.25 for car and driver and $0.75 for each additional passenger. How many people were riding in a car for which the toll was $4.25?

(A)	3
(B)	4
(C)	5
(D)	6
(E)	7

35.	Pren and Wright invested $8000 and $6000, respectively, in a hardware business. At the end of the year, the profits were $3800. Each partner received 6% on his investment and the remainder was shared equally. What was the total that Pren received?

(A)	$1960
(B)	$2040
(C)	$2180
(D)	$2300
(E)	$2380

36.	How much money is saved by buying a car priced at $12,000 with a single discount of 15% rather than buying the same car with discounts of 10% and 5%?

(A)	$60
(B)	$120
(C)	$180
(D)	$360
(E)	$720

37.	The price of an article has been reduced 25%. In order to restore the original price, the price must be increased by

(A)	15.5%
(B)	20%
(C)	25%
(D)
(E)	40%

38.	A stationer buys books at $0.75 per dozen and sells them at 25 cents apiece. The gross profit based on the cost is

(A)	50%
(B)	100%
(C)	150%
(D)	200%
(E)	300%

39.	A, B, and C invested $8000, $7500, and $6500, respectively. Their profits were to be divided according to the ratio of their investment. If B uses his share of the firm’s profit of $825 to pay a personal debt of $230, how much will he have left?

(A)	$51.25
(B)	$51.20
(C)	$51.10
(D)	$51.05
(E)	$51.00

40.	A merchant who has debts totaling $43,250 has gone bankrupt and can pay off only 15¢ on the dollar. How much will his creditors receive?

(A)	$6287.00
(B)	$6387.00
(C)	$6387.50
(D)	$6487.50
(E)	$6587.00

41.	If 15 cans of food are needed for 6 adults for 2 days, the number of cans needed for 4 adults for 5 days is

(A)	10
(B)	15
(C)	20
(D)	25
(E)	30

42.	The school enrollment is 1700. Eighteen percent of the students study French, 25% study Spanish, 12% study Italian, 15% study German, and the rest study no foreign language. Assuming that each student may study only one foreign language, how many students do not study any foreign language?

(A)	510
(B)	520
(C)	530
(D)	540
(E)	550

43.	Four men working together can dig a ditch in 42 days. They begin the job, but one man works only half days. How long will it take to complete the job?

(A)	46 days
(B)	48 days
(C)	50 days
(D)	52 days
(E)	54 days

44.	What part of an hour elapses between 6:45 P.M. and 7:09 P.M.?

(A)
(B)
(C)
(D)
(E)

45.	What part of an hour elapses between 6:45 P.M. and 7:09 P.M.?

(A)
(B)
(C)	8%
(D)	9%
(E)	10%

46.	Jack sells appliances and receives a salary of $150 per week plus 5% commission on all sales over $750. How much does he earn in a week in which his sales amount to $2400?

(A)	$222.50
(B)	$225
(C)	$227.50
(D)	$230
(E)	$232.50

47.	If the average weight of girls of Jane’s age and height is 105 pounds and if Jane weighs 110% of average, then Jane’s weight in pounds is

(A)	110
(B)	112.5
(C)	115.5
(D)	118.5
(E)	126

48.	A man willed his property to his three children. To the youngest he gave $10,000; to the second, 2.5 times as much as to the youngest; and to the eldest, 1.5 times as much as to the second. What was the value of the estate?

(A)	$72,000
(B)	$72,500
(C)	$73,000
(D)	$73,500
(E)	$74,000

49.	A person wishing to borrow a certain sum of money for 4 months goes to a bank offering an interest rate of 12%. If the interest is $720, how much does the person borrow?

(A)	$10,000
(B)	$12,000
(C)	$14,000
(D)	$16,000
(E)	$18,000

50.	What is the ratio of 2 feet 3 inches to 1 yard?

(A)	2:3
(B)	3:4
(C)	1:1
(D)	4:3
(E)	3:2

Questions 51–75 are four-option items. For each question, select the option that is most nearly correct.

51.	A woman’s weekly salary is increased from $350 to $380. The percent of increase is most nearly

(A)	6%
(B)
(C)	10%
(D)

52.	A clerk divided his 35-hour work week as follows: of his time in sorting mail; of his time in filing letters; and of his time in reception work. The rest of his time was devoted to messenger work. The percentage of time spent on messenger work by the clerk during the week was most nearly

(A)	6%
(B)	10%
(C)	14%
(D)	16%

53.	Many American cars feature speedometers that show kilometers per hour. If you are required to drive 500 miles, and you know that 1 kilometer is approximately  of a mile, how many kilometers would you cover in that journey?

(A)	625
(B)	800
(C)	850
(D)	1000

54.	A stock clerk had 600 pads on hand. He then issued of his supply of pads to Division X, to Division Y, and to Division Z. The number of pads remaining in stock is

(A)	48
(B)	125
(C)	240
(D)	475

55.	Two sailors traveled by bus from one point to another. The trip took 15 hours, and they left their point of origin at 8 A.M. What time did they arrive at their destination?

(A)	11 A.M.
(B)	10 P.M.
(C)	11 P.M.
(D)	12 A.M.

56.	A man deposited a check for $1000 to open an account. Shortly after that, he withdrew $400.00 and then $541.20. How much did he have left in his account?

(A)	$56.72
(B)	$58.80
(C)	$59.09
(D)	$60.60

57.	After an employer figures out an employee’s weekly salary of $190.57, he deducts $13.05 for Social Security and $5.68 for pension. What is the amount of the check after these deductions?

(A)	$171.84
(B)	$171.92
(C)	$172.84
(D)	$172.99

58.	A pole 12 feet high has a shadow 4 feet long. A nearby pole is 24 feet high. How long is its shadow?

(A)	4 feet
(B)	8 feet
(C)	12 feet
(D)	16 feet

59.	A skier started a fire in the fireplace. Each log she put on burned for a half-hour. If she started with a supply of 10 logs, for how many hours could the fire burn?

(A)	5 hours
(B)	7 hours
(C)	hours
(D)	10 hours

60.	Mrs. Jones wishes to buy 72 ounces of canned beans for the least possible cost. Which of the following should she buy?

(A)	Six 12-ounce cans at 39¢ per can
(B)	Seven 10-ounce cans at 34¢ per can
(C)	Three 24-ounce cans at 79¢ per can
(D)	Two 25-ounce cans at 62¢ per can

61.	A carpenter needs four boards, each 2 feet 9 inches long. If wood is sold only by the foot, how many feet must he buy?

(A)	9
(B)	10
(C)	11
(D)	12

62.	It costs 31¢ a square foot to lay linoleum. To lay 20 square yards of linoleum, it will cost

(A)	$16.20
(B)	$18.60
(C)	$55.80
(D)	$62.00

63.	A piece of wood 35 feet, 6 inches long was used to make 4 shelves of equal length. The length of each shelf was most nearly

(A)
(B)
(C)
(D)

64.	A change purse contained 3 half dollars, 8 quarters, 7 dimes, 6 nickels, and 9 pennies. Express in dollars and cents the total amount of money in the purse.

(A)	$3.78
(B)	$3.95
(C)	$4.32
(D)	$4.59

65.	A champion runner ran the 100-yard dash in three track meets. The first time he ran it in 10.2 seconds; the second in 10.4 seconds; and the third in 10 seconds. What was his average time?

(A)	10.1 seconds
(B)	10.2 seconds
(C)	10.3 seconds
(D)	10.4 seconds

66.	A crate containing a tool weighs 12 pounds. If the tool weighs 9 pounds, 9 ounces, how much does the crate weigh?

(A)	2 pounds, 1 ounce
(B)	2 pounds, 7 ounces
(C)	3 pounds, 1 ounce
(D)	3 pounds, 7 ounces

67.	The daily almanac report for one day during the summer stated that the sun rose at 6:14 A.M. and set at 6:06 P.M. Find the number of hours and minutes in the time between the rising and setting of the sun on that day.

(A)	11 hours, 2 minutes
(B)	11 hours, 52 minutes
(C)	12 hours, 8 minutes
(D)	12 hours, 48 minutes

68.	If cup of spinach contains 80 calories and the same amount of peas contains 300 calories, how many cups of spinach have the same caloric content as cup of peas?

(A)
(B)
(C)	2
(D)

69.	A night watchman must check a certain storage area every 45 minutes. If he first checks the area as he begins a 9-hour tour of duty, how many times will he have checked this storage area?

(A)	13
(B)	12
(C)	11
(D)	10

70.	What is the fifth term in the series:

(A)
(B)
(C)	11
(D)

71.	Three workers assemble 360 switches per hour, but 5% of the switches are defective. How many good (nondefective) switches will these 3 workers assemble in an 8-hour shift?

(A)	2736
(B)	2880
(C)	2944
(D)	3000

72.	The butcher made pounds of beef into hamburger and wrapped it in pound packages. How many packages did he make?

(A)	15
(B)	16
(C)	17
(D)	18

73.	If a car-renting agency charges a fixed rate of $12 per day plus 17¢ per mile, what would the charge be for using a car for 6 days and traveling 421 miles?

(A)	$143.57
(B)	$153.57
(C)	$163.57
(D)	$173.57

74.	If the area of the figure below, which consists of 5 equal squares, is 125, what is the perimeter of this figure?

(A)	125
(B)	100
(C)	80
(D)	60

75.	If the cost of digging a trench is $8.48 a cubic yard, what would be the cost of digging a trench 2 yards by 5 yards by 4 yards?

(A)	$93.28
(B)	$186.56
(C)	$237.44
(D)	$339.20