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What is the equation of the graph obtained by shifting the graph of y=x2 horizontally to the left 4 units and vertically down 3 units?
y = (x+4)2 - 3
In how many different ways can five students be seated in three chairs?
5x4x3=60
When the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10. What is the cost of the gift?
120
What is the area of a circle in which a 3 by 4 rectangle is inscribed?
pi*r2
If 1/3 of a number is 4 less than 1/2 of the number, the number is
24. Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
Pete's pies all cost an integer number of pounds. A cherry pie costs the same as two apple pies. A blueberry pie costs the same as two damson pies. A cherry pie and two damson pies cost the same as an apple pie and two blueberry pies. Paul buys one of each type of pie. Which of the following could be the amount he spends?
A. $16 B. $18 C. $20 D. $22 E. $24
B. $18
Suppose you have a regular hexagon, and for every pair of non-adjacent vertices, you draw a line segment connecting them. How many times do the line segments intersect in the interior of the hexagon?
13
For how many integer values of b is b+3>0 and 1>2b-9?
7
For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?
8
A. -2015 B. -1 C. 0 D. 1 E. 2015
D. 1
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32
A. 11 B. 12 C. 13 D. 14 E. 15
C. 13
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?
$8
Andy rides his bike from his house to the store at 6 mph. Upon arriving at the store, he realizes it's closed and immediately heads back, riding his bike back home at a speed of 2 mph. What is Andy's average speed in mph over the entire trip?
3 mph
Eight consecutive three-digit positive integers have the following property: each of them is divisible by its last digit. What is the sum of the digits of the smallest of these eight integers?
A. 9 B. 10 C. 11 D. 12 E. 13
E. 13
The digits from 1 to 9 are randomly arranged to make a 9-digit number. What is the probability that the resulting number is divisible by 18?
A. 1/3 B. 4/9 C. 1/2 D. 5/9 E. 3/4
B. 4/9
Given that one and only one answer is correct, which of the following is true?
A. All of the below
B. None of the below
C. One of the above
D. All of the above
E. None of the above
F. None of the above
F. None of the above
Allen is taller than Brad and shorter than Clara. Diana is shorter than Clara and taller than Allen. Brad is shorter than Sarah. If the first three statements are true, which of the following must be true?
A. Diana is taller than Brad
B. Brad is the same height as Diana
C. Sarah is taller than Allen
A. Diana is taller than Brad
163,000 basketball teams are playing in a single elimination bracket. (For each game, two teams play each other where one team is eliminated and the other team moves on to the next round). How many games are needed to determine a winner?
162,999