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第一期 If n is a positive integer, what is the remainder when the positive integer n is divided by 5?
(1) If n=p+(p+1)+(p+2), and the remainder when p is divided by 5 is 1.
(2) If n=s(s+1)(s+2), and the remainder when s is divided by 5 is 1.
190113 还原机经选题: 文字题&几何 There are three programs in one ceremony: violin performance, piano performance, and trumpet performance. In each performance, two students will respectively perform on the same instrument in order. A and B can only play the violin, C and D can only play the piano, and E and F can only play the trumpet. How many different appearance orders?
190215 There are 30 objects of various colors and shapes in a bag. An object will be taken out randomly from the bag. What is the probability that the object is red or cube? 1: There are 5 cubes and 8 red objects in the bag. 2: There are three red cubes in the bag.
191222 A car has to go from one place to another, the average speed in city road is 15 miles/hour, and the average speed in highway is 60 miles/hour. Then it goes 5 miles in city road and goes 50 miles in highway, what is the total average speed? (results are round to the nearest integer)
OG2022 Political theorist: Even with the best spies, area experts, and satellite surveillance, foreign policy assessments can still lack important information. In such circumstances intuitive judgment is vital. A national leader with such judgment can make good decisions about foreign policy even when current information is incomplete, since_______ . Which of the following, if true, most logically completes the argument?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022 At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 250 miles per hour against the wind. Which of the following is closest to the pilot's average speed, in miles per hour, for the round-trip?
PREP07 Test 1 On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually. The total amount of interest earned by Tim's investment in the first 2 years was how much greater than the total amount of interest earned by Lana's investment in the first 2 years?
A number of eggs dyed various colors were hidden for an egg hunt. How many eggs in total were hidden?(1) The number of red eggs hidden is the square of an integer, while the total number of eggs hidden is 24 times that integer.(2) Exactly 143 of the eggs hidden were not red.
A budget airline charges each customer e I 3 euros for every leg of the flights between London and Ibiza. The only exception is that it charges e euros for the first leg of the first round-trip for the same customer. How much is the total cost of n round-trip tickets for one customer?
OG17 OG18 OG19 OG20 OG2022 Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
Manhattan Gary's Gas Station serves an average of 20 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary's station serve over the course of a typical week?
Manhattan A certain panel is to be composed of exactly three women and exactly two men, chosen from x women and y men. How many different panels can be formed with these constraints?(1) If two more women were available for selection, exactly 56 different groups of three women could be selected.(2) x = y + 1
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That future teachers do not always select the most rigorous preparation programs cannot truly be said that they are at fault: The National Council on Teacher Quality, a think tank that advocates for higher standards for classroom teachers, only began publishing comprehensive program rankings in 2013.
Magoosh In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?
OG18 OG19 OG20 OG2022 Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
OG19-数学分册 A school club plans to package and sell dried fruit to raise money. The club purchased 12 containers of dried fruit, each containing $$16\frac{3}{4}$$ pounds. What is the maximum number of individual bags of dried fruit, each containing $$\frac{1}{4}$$ pounds, that can be sold from the dried fruit the club purchased?
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If P is a real number and list S is defined as {-4, 4, 2, 2, P}, what is the value of x?

(1) x is the mean of list S

(2) x is the median of list S
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Josh and Dan have 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18 apples?
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During the last two minutes before a lecture began, the number of occupied seats in an auditorium increased from 112 to 135. If the number of occupied seats at the beginning of the lecture was 75 percent of total capacity, how many seats in the auditorium were empty two minutes prior to the lecture?