AMCAT Math

Question 1

John Clark and Mae begin their journeys at the same time, traveling at speeds of 40 and 50 kilometers per hour, respectively.
If John takes 15 minutes longer to complete the route than Mae, then the total distance traveled is:

Accepted Answer

50 km

Answer

45 km

Answer

33 km

Answer

24 km

Question 2

The total of the two integers equals 184. If one-third of one surpasses one-seventh of another by 8, identify the smaller number.

Accepted Answer

72

Answer

70

Answer

73

Answer

78

Question 3

The ratio between the two integers is 4:5, and their L.C.M is 200. Then what is the sum of the two numbers?

Accepted Answer

90

Answer

86

Answer

78

Answer

74

Question 4

Find the area of the triangle with sides of 10 cm, 24 cm, and 26 cm.

Accepted Answer

120

Answer

60

Answer

316

Answer

133

Question 5

Ken borrowed $20,000 from his buddy Richard at 15% yearly simple interest and lent it to Mike at the same rate compounded annually. Find Ken's gain after two years.

Accepted Answer

$450

Answer

$755

Answer

$890

Answer

$442

Question 6

A nine-member family has an average age of 22 years. Carlo is the youngest, and he is six years old. What was the family's average age soon before Carlo was born?

Accepted Answer

18

Answer

17

Answer

15

Answer

20

Question 7

The average of 7 numbers is 60. The average of the first three numbers is 50, while the average of the final three is 70. What is the remaining number?

Accepted Answer

60

Answer

58

Answer

75

Answer

63

Question 8

When a specific sum is invested for ten years, the simple interest gained doubles. What rate of interest is being offered?

Accepted Answer

20%

Answer

15%

Answer

45%

Answer

13%

Question 9

A guy rows a boat at 15 mph on calm water. Determine the speed of the river if it takes him 4 hours and 30 minutes to paddle a boat to a location 30 miles distant and back.

Accepted Answer

5 mph

Answer

12 mph

Answer

10 mph

Answer

15 mph

Question 10

If 13x = 371293, find the value of 22x-1.

Accepted Answer

512

Answer

128

Answer

620

Answer

64

John Clark and Mae begin their journeys at the same time, traveling at speeds of 40 and 50 kilometers per hour, respectively.If John takes 15 minutes longer to complete the route than Mae, then the total distance traveled is:

John Clark and Mae begin their journeys at the same time, traveling at speeds of 40 and 50 kilometers per hour, respectively.
If John takes 15 minutes longer to complete the route than Mae, then the total distance traveled is: