AMC 10A
What is the hundred digit of (20! - 15!)?
(A)0 (B)1 (C)2 (D)4 (E)5
What is (A) 0?
Carl has 5 cubes each having side length 1, and Kate has 5 cubes each having side length 2. What is the total volume of these 10 cubes?
(A)24 (B)25 (C)28 (D)40 (E)45
What is (E)45?
The area of a pizza with radius 4 inches is N percent larger than the area of a pizza with radius 3 inches. What is the integer closest to N?
(A) 25 (B) 33 (C) 44 (D) 66 (E) 78
What is (E) 78?
Portia's high school has 3 time as many students as Lara's high school. The two high schools have a total of 2600 students. How many students does Portia's high school have?
(A)600 (B)650 (C)1950 (D)2000 (E)2050
(C)1950
Kate bakes a 20-inch by 18-inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches. How many pieces of cornbread does the pan contain?
(A)90 (B)100 (C)180 (D)200 (E)360
What is (A)90?
Suppose a is 150% of b. What percent of a is 3b?
(A) 50 (B) 66+2/3 (C) 150 (D) 200 (E) 450
What is (D) 200?
What is the sum of all real number x for which |x2-12x+34| = 2?
(A) 12 (B) 15 (C) 18 (D) 21 (E) 25
What is (C) 18?
Consider the statement, "If n is not prime, then n-2 is prime." Which of the following values of n is a counterexample to this statement?
(A)11 (B)15 (C)19 (D)21 (E)27
What is (E)27?
What is the greatest number of consecutive integers whose sum is 45?
(A) 9 (B) 25 (C) 45 (D) 90 (E) 120
What is (D) 90?
What is the value of
1+2+3-4+5+6+7-8+ ... +197+198+199-200?
(A)9800 (B)9900 (C)10,000 (D)10,100 (E)10,200
What is (B)9900?
A 3D rectangular box with dimensions X, Y, and Z has faces whose surface areas are 24, 24, 48, 48, 72, and 72 square units. What is X+Y+Z?
(A) 18 (B) 22 (C) 24 (D) 30 (E) 36
What is (B) 22?
What is the least possible value of (xy-1)2 + (x-y)2 for real numbers x and y?
(A) 0 (B) 1/4 (C) 1/2 (D) 1 (E) 2
What is (D) 1?
Real numbers x and y satisfy x + y = 4 and x * y = -2. What is the value of
x + x2/y2 + y3/x2 + y?
(A)360 (B)400 (C)420 (D)440 (E)480
An inverted cone with base radius 12cm and height 18cm is full of water. The water is poured into a tall cylinder whose horizontal base has a radius of 24cm. What is the height in centimeters of the water in the cylinder?
(A) 1.5 (B) 3 (C) 4.5 (D) 4 (E) 6
What is (A) 1.5?
Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?
(A) 1/4 (B) 1/3 (C) 3/8 (D) 2/5 (E) 1/2
What is (D) 2/5?