AMC Practice exam 1

• A) 3

• B) 5

• C) 8

• D) 13

• E) 16

• A) 10

• B) 11

• C) 12

• D) 13

• E) 14

A restaurant offers four appetizers, five entrées, and three desserts. Leah will order one entrée, at most one appetizer, and at most one dessert. How many different meal combinations can Leah order?

• A) 12

• B) 60

• C) 75

• D) 90

• E) 100

How many of the following five shapes could be the shape of the region where two triangles overlap?

• A) 1

• B) 2

• C) 3

• D) 4

• E) 5

Five students stand in line from shortest to tallest. The average height of the three shortest students is 58 inches, and the average height of the three tallest students is 70 inches. The average height of all five students is 63 inches. What is the median height of the five students, in inches?

• A) 59

• B) 64

• C) 67

• D) 68

• E) 69

For how many integers n is |n^2 - 6n + 5| prime?

• A) 1

• B) 2

• C) 3

• D) 4

• E) 5

Maria flips six fair coins. What is the probability that at least half of the coins land heads?

• A)10/32

• B) 1/2

• C) 41/64

• D) 21/32

• E) None of the preceding

A rectangular box has integer edge lengths in the ratio 1 : 3/2 : 2. Which of the following could be the volume of the box?

• A) 120

• B) 144

• C) 168

• D) 192

• E) 216

The sum of the first 20 terms of an arithmetic sequence which has first term 1 is equal to the sum of the first 10 terms of an arithmetic sequence which has first term 10. If positive integers x and y are the respective common differences of the sequences, what is the minimum possible value of x + y?

• A) 35

• B) 38

• C) 40

• D) 43

• E) None of the preceding

The number N = 11111...111 is formed by writing 105 ones in a row. What is the sum of the digits of the product 105 × N?

• A) 504

• B) 555

• C) 630

• D) 945

• E) 1105