Which one of the following equals the number of multiples of 3 between 102 and 210, inclusive? 102 and 210 inclusive, so 210/3=70, 70(0-210 We also discuss several other topics like 1001010010
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inclusive) -34(0-102 inclusive) +1(102 itself) =37 How many positive integers less than 500 can be formed using the numbers 1, 2, 3 and 5 for the digits? 4(1 digits) + 16(2 digits) +48(3 digits) =64 4+4+4+4=16 How many different ways can 3 cubes be painted if each cube is painted one color and only the 3 colors red, blue, and green are available? (Order is not considered, for example, green, green, blue is considered the same as green, blue, green.) Rrr,bbb,ggg,bbr,brr,bgg,bbg,grr,ggr,brg, so there are 6 possible ways. Suppose five circles, each 4 inches in diameter, are cut from a rectangular strip of paper 12 inches long. If the least amount of paper is to be wasted, what is the width of the paper strip? Never think that through the residues of cut paper anyone can create a circle. X+Y-both+ none= all Find always with calculation the result of any problem if you solved with theoretical method the problem. A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 50 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost? 50 cents Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5: 3 and 1: 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4: 3. What is the ratio of the composition of the two basic elements in alloy X? 1:1Williams has x eggs. He sells 12 of them at a profit of 10 percent and the rest of the eggs at a loss of 10 percent. He made neither a profit nor a loss overall. Which one of the following equals x? 24 The percentage of integers from 1 through 100 whose squares end with the digit 1 is x %, and the percentage of integers from 1 through 200 whose squares end with the digit 1 is y%. Which one of the following is true? X=Y 20/100=40/200 A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 6 members, then what is the exact number of researchers required? 16 Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles. Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon? 4.5 Katrina has a wheat business. She purchases wheat from a local wholesaler at a particular cost per pound. The price of the wheat at her stores is $3 per pound. Her faulty spring balance reads 0.9 pounds for a pound. Also, in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Katrina purchase the wheat from the wholesaler? 2.43 DOZE N = 12 In how many ways can 2 doors be selected from 3 doors? 3 In how many ways can 2 doors be selected from 3 doors for entering and leaving a room? 3 In how many ways can a room be entered and exited from the 3 doors to the room? 9 How many unequal 5-digit numbers can be formed using each digit of the number 11235 only once? 60 How many different six-digit numbers can be formed using all of the following digits: 3, 3, 4, 4, 4, 5. 60 This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print? 9 C6 A company produces 8 different types of candies, and sells the candies in gift packs. How many different gift packs containing exactly 3 different candy types can the company put on the market? 8 C3In how many ways can 3 red marbles, 2 blue marbles, and 5 yellow marbles be placed in a row? 10!/3!2!5! The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that 3 of Sam’s 4 funds grew by at least 10% over last year? 6C3*4 C1/10C4 In how many of ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin? 45 On average, a sharpshooter hits the target once every 3 shots. What is the probability that he will not hit the target until 4th shot? 8/81 In how many of ways can 5 students-Nurlan, Ray, Ronald, Zinedine and Diego-can be admitted to any of these 7 business schools- Harvard, Stanford, Wharton, Columbia, MIT, London and Oxford? 7*7*7*7*7=75 In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end? 5! 7! /3! In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate their positions (that is, boy girl)? 1152 In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate their positions (that is, boy girl)? 12 In how many ways can 5 people from a group of 6 people be seated around a circular table? 144 If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ? -9 Eric and Ortega and their teammates watch a movie. They all sit in a row, and they can sit in n different ways. In how many of the ways can Eric sit to the right of Ortega? N/2