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Ready4	If two positive integers $x$ and $y$ are not both even, then which of the following must be odd?
Ready4	If the average (arithmetic mean) of four numbers is 150, how many of the numbers are equal to 150? (1) None of the four numbers is less than 150. (2) None of the four numbers is greater than 150.
Ready4	If $u < v < w$ and $x < y < z$ , is $v < y$ ? $u < x$ $w < x$
Ready4	A right triangle has two legs of equal length. What is the perimeter, in centimeters, of the triangle? The area of the triangle is 4 square centimeters. The hypotenuse of the triangle measures 4 cm.
Ready4	In a school, 180 students study finance or accounting or both. If 60 of these students do not study finance, how many of these students study both finance and accounting? Of the 180 students, 36 do not study accounting. A total of 144 students study accounting.
Ready4	What is the tenths digit in the decimal representation of a certain number? The number is less than $\frac{5}{8}$ The number is greater than $\frac{5}{9}$
Ready4	In the xy-coordinate plane, is point Q equidistant from points (4, 4) and (-2, 4)? The x-coordinate of point Q is 1. Point Q lies on the line $y = 4$ .
Ready4	What is the value of x in the triangle above? $y + z = 130$ $x + z = 100$
Ready4	In a group of 60 integers, how many are divisible (with a remainder of 0) by neither 7 nor 13? Of the 60 numbers, 20 are divisible by 7 but not by 13. Of the 60 numbers, 30 are divisible by both 7 and 13.
Ready4	If p and q are positive integers, can the fraction $\frac{p}{q}$ be expressed as a decimal with only a finite number of nonzero digits? q is a factor of 12. p is a factor of 12.
Ready4	An exam was taken by a group of undergraduate students and graduate students. If the average (arithmetic mean) score for the entire group was 90, was the average score of the undergraduates greater than 95? The average score for the graduate students was less than 85. The group consisted of more graduate students than undergraduate students.
Ready4	During a particular period, water enters a partially filled reservoir at a constant rate through a mountain stream. At the same time, water is pumped out of the reservoir at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the reservoir increasing? (1) The amount of water initially in the reservoir is 1800 gallons. (2) Water enters the reservoir at a rate of 8 gallons per minute and is pumped out at a rate of 20 gallons every 3 minutes.
Ready4 OG2022	In the figure above, points A, B, C, D, E, and F lie on a line perpendicular to the square's sides. If point A lies on the square, point B lies on the circle, point C bisects AF, point D is the center of the circle, point E bisects DF, and point F lies on the circle and on the square, what is the difference in area between the square and the circle? $A B = 6$ and $B C = 4$ . $A B = 6$ and $E F = 3.5$ .
Ready4	Pam has unopened packages of corn and of rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have? (1) Pam has $282 worth of packages of corn and of rice. (2) Pam has twice as many packages of corn as she has of rice.
Ready4	If Chris saved $400 of his earnings last month, how much did Chris earn last month? (1) Chris spent $\tfrac{1}{3}$ of his earnings last month on rent and saved $\tfrac{1}{4}$ of the remainder. (2) Last month, Chris paid three times as much in loan payments as he saved.
Ready4	l, 17.2, 12.2, 7.2, 22.2 What is the value of l in the list above? $l > 7.2$ The median of the numbers in the list is 14.7.
Ready4	Three robots, Q, R, and L, which eject water independently and simultaneously, each at a characteristic, constant rate, can fill a pool in 10 minutes. How long does it take Robot Q, working alone at its constant rate, to fill that pool with water? Machines R and L can fill the pool in 20 minutes. Machines Q and L can fill the pool in 15 minutes.
Ready4	The average (arithmetic mean) of the ages of three people, expressed as integers, is 60. What is the median age? One of the ages is 55. One of the ages is 60.
Ready4	For any integers n and m, $\ddot{m} (n, m)$ and $\dot{m} (n, m)$ denote the minimum and the maximum of n and m, respectively. For example, $\ddot{m} (4, 3) = 3$ and $\dot{m} (4, 3) = 4$ . For the integer m, what is the value of $\ddot{m} (100, m)$ ? $m = \dot{m} (100, n)$ for some integer n. $m = \dot{m} (100, m)$
Ready4	Is n an integer? $3 n^{2}$ is an integer. $\frac{\sqrt{n}}{3}$ is an integer.