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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. $m = \dot{m} (100, m)$
OG18 OG19 OG20 OG2022	Kim and Sue each bought some roses and some daisies at the prices shown above. If Kim bought the same total number of roses and daisies as Sue, was the price of Kim's purchase of roses and daisies higher than the price of Sue's purchase of roses and daisies?(1) Kim bought twice as many daisies as roses.(2) Kim bought 4 more roses than Sue bought.
OG12 OG15 OG16 OG17	A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?(1)The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
Magoosh	Metropolitan Concert Hall was half full on Tuesday night. How many seats are in the Hall?Statement #1: If the number of people in the Hall increased by 20% from Tuesday night to Wednesday night, then the Hall would be 60% full on Wednesday night.Statement #2: If 20 more people showed up on Tuesday night, that would have increased the number of people in the Hall by 4%.
OG16 OG17 OG18 OG19 OG20 OG2022	A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of the gasoline in the tank?(1) The inside of the tank is exactly 4 feet in diameter.(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.
Ready4	Car X and Car Y competed with 10 other cars in a cross-country race. If Car X and Car Y drove a total of 300 miles, how many miles did Car X drive? Car Y drove $\frac{3}{4}$ as many miles as Car X did. Car X drove 11 percent of all the miles driven by the competitors in the race.
190310 还原机经选题: 数论&代数	The number of people in the tour group is counted as x. The ticket rules of the amusement park are: when x≤10, the total ticket price is $120; when 11≤x≤20, the total ticket price is 80 + 4x dollars; when x > 20, the total ticket price is 8x dollars. How many people are there in group B? 1: Group A has three fewer people than group B. 2: Group B pays $4 more than group A.
Magoosh	In a certain class, the ratio of girls to boys is 5:4. How many girls are there?Statement #1: If four new boys joined the class, the number of boys would increase by 20%.Statement #2: If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be$$\frac {8}{23}$$
Magoosh	In the x-y plane, point (p, q) is a $$\mathbf {lattice}$$ $$\mathbf {point}$$ if both p and q are integers. Circle C has a center at (–2, 1) and a radius of 6. Some points, such as the center (–2, 1), are inside the circle, but a point such as (4, 1) is $$\mathbf {on}$$ the circle but not $$\mathbf {in}$$ the circle. How many lattice points are in circle C?
Ready4	If money is invested at $r$ percent interest, compounded annually, the amount of the investment will double in approximately $\frac{72}{r}$ years. If $6,000 is invested in an account that pays 9 percent interest, compounded annually, approximately how many years will it take for the value of the investment to be 4 times its initial value?
	Working alone at its constant rate, machine K took 3 hours to produce $$\frac{1}{4}$$ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
190321	There are five cylindrical containers, one large cylindrical container and four small cylindrical containers. The large cylindrical container has a diameter of 8 and a height of 16. The volume of the water it contains is 75% of that of the container. The diameter and height of four small cylindrical containers are 4. If the water from the big cylinder is poured into four small containers, how much water is left in the large container?
Ready4	Machines $M_{1}$ and $M_{2}$ purify air at different constant rates. Machine $M_{1}$ , operating alone for 5 hours, purified the air within part of one floor of a building; then Machine $M_{2}$ , operating alone for 4 hours, purified the air within the rest of the floor. How many hours would it have taken Machine $M_{1}$ operating alone to purify the air in the entire floor? $M_{2}$ purified one cubic foot of air per minute. $M_{1}$ purified fifty percent more air in 5 hours than $M_{2}$ purified in 4 hours.
Ready4	If $w$ represents the tens digit in $a=2{,}125{,}4w6$ what is the value of $w$ ? (1) $a$ is divisible by 6 (2) $a$ is divisible by 4
	While on straight, parallel tracks, train A and train B are traveling at different constant rates. If train A is currently 2 miles behind train B, how many minutes from now will train A be 4 miles behind train B?1. Three minutes ago, train A was 1 mile behind train B.2. Train A is traveling at 80 miles per hour, and train B is traveling at 100 miles per hour.
	If a certain factory makes a total of 30,720 wrenches, how many minutes does the factory take to make the wrenches?1. The factory creates the wrenches without interruption at a rate of 32 wrenches per second.2. It takes 4 times as long for the factory to create the wrenches as it does to load them into trucks, and it takes the factory a total of 20 minutes to do both.
	Sue's monthly earnings consist of a monthly salary and a 4 percent commission on the portion of her monthly sales that is in excess of $2,000. If Sue's monthly salary was the same in July as in August, how much greater were her sales in July than in August?(1) Sue's monthly earnings were $3,620 in July and $3,580 in August.(2) Sue's monthly salary was $3,500 in July and in August.
PREP07 Test 2	Of the 4,800 voters who voted for or against Resolution K, 1800 were Democrats and 3,000 were Republicans. What was the total number of female voters who voted for Resolution K ?(1) 3/4 of the Democrats and 2/3 of the Republicans voted for Resolution K.(2)$$\frac{1}{3}$$ of the Democrats who voted for Resolution K and $$\frac{1}{2}$$ of the Republicans who voted for Resolution K were females.
OG12 OG15	During a 6-day local trade show, the least number of people registered in a single day was 80. Was the average (arithmetic mean) number of people registered per day for the 6 days greater than 90 ?(1)For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.(2)For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.
OG18-数学分册	As shown in the diagram above, a lever resting on a fulcrum has weights of $$w_{1} $$ pounds and $$w_{2}$$ pounds, located $$d_{1}$$ feet and $$d_{2}$$ feet from the fulcrum. The lever is balanced and $$w_{1}d_{1} = w_{2}d_{2}$$. Suppose $$w_{1}$$ is 50 pounds and $$w_{2}$$ is 30 pounds. If $$d_{1}$$ is 4 feet less than $$d_{2}$$, what is $$d_{2}$$, in feet?