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random_syn_ori_query_syn6w_infer_part_3

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# Question What is the value of $a$ in the equation $10^a \cdot 10^b = 10^{a+b}$? # Solution

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# Question John is running a race. John is 200 meters from the finish line and he is running at 150 meters per minute. How many minutes will it take him to finish the race? # Solution

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# Question Determine the coordinates of the midpoint of the line segment with endpoints (4, -1) and (-3, 6). # Solution

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# Question A group of 6 people are going to play a game of pool. What is the probability that 4 people are going to be women? # Solution

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# Question If $a=4, b=2$, and $c=5$, then what is the value of the expression $a^2(b+c)$? # Solution

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# Question A plane flies at an average speed of 420 miles per hour. If the plane flew 20 miles less per hour, what is the new speed of the plane? # Solution

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# Question There are 3 blue marbles, 5 red marbles, and 2 green marbles in a box. The marbles are numbered 1, 2, 3, 4, 5, and 6. Two marbles are drawn randomly and without replacement. What is the probability that the first marble is red and the second is green? # Solution

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# Question Mary spent 2/5 of her money and bought a dress for 300$. If the dress cost 3/4 as much as she spent, what was the amount of money she had left? # Solution

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# Question A shopkeeper has 50 apples. He sells 10 apples for $1 each. How much money will he make? If we know the answer to the above question is $5, how many apples did he sell for $1 each? # Solution

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# Question A number, when divided by 10, has a remainder of 3. When the same number is divided by 6, it has a remainder of 2. What will be the remainder when the number is divided by 5? # Solution

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# Question A and B are two numbers with the same digits, but in reverse order. Which of the following must be true? # Solution

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# Question Irene's phone plan charges her $25.00 a month plus 3 cents per minute she talks. If Irene talks for 10 minutes every month, how much does her phone plan cost? # Solution

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# Question Rita is a cook. She has 24 pounds of flour. She uses 10 pounds to make pizza, 10 pounds to make bread and 4 pounds to make pancakes. How many pounds of flour is left? # Solution

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# Question If a car tire is 70% treaded, how many miles can a car travel before its tires need to be replaced? # Solution

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# Question The following table lists the number of students in a school's band and orchestra. If the total number of students in the school is 119, what is the probability that a randomly selected student is in the orchestra? # Solution

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# Question Let $P$ be a point in the interior of a square $S$. Consider a family of squares with side length $1$ and lower left corner at $P$. Let $F$ be the union of the upper right corners of these squares. Find the area of $F$. # Solution

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# Question How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 such that each digit is used exactly once in each number? # Solution

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# Question What is the simplified form of the expression $\frac{\frac{1}{x} + \frac{1}{x^2}}{\frac{1}{x^2}}$? # Solution

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# Question The side of a square is X inches. The perimeter of a square is 12 inches. What is the value of unknown variable X? What is the value of unknown variable X? # Solution

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# Question 1500 mL of water is added to 360 mL of a 12% solution of acid. What is the concentration of the new solution? # Solution

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# Question If a person walks 3/4 of the way to work on Monday, 1/3 of the way to work on Tuesday, and 1/2 of the way to work on Wednesday, how many miles does he have to walk to get to work? # Solution

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# Question In a certain city, 60% of the registered voters are democrats, and the rest are republicans. If there are in that city 20,000 registered voters, how many of them are democrats? # Solution

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# Question The average of four numbers is 60. If the third number is 100, what is the average of the other three numbers? # Solution

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# Question There are 36 students in a classroom. If 12 of them are boys and 18 of them are girls, then the average age of the girls is 1 year more than the average age of the boys. The average age of the girls is 13 years. How old is the average age of the boys? # Solution

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# Question If x is a positive integer, what is the value of x? # Solution

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# Question There are 600 students in a school. On the first day, 100 students were absent. On the second day, 20 students were absent. On the third day, 50 students were absent. How many students were absent on the 3 days? # Solution

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# Question A bus leaves the terminal at 8:45 am, traveling in a straight line at 15 miles per hour. What time will the bus reach the destination? # Solution

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# Question The manager of a small store charges $\$2$ for each item sold, but reduces the price of every item sold by 10%. If the manager's new price is $\$1.60$ for an item, how much was the original price of the item? # Solution

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# Question A team of 5 people can paint 3 houses in 6 hours. How many people are needed to paint 5 houses in 8 hours? # Solution

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# Question If 60% of 200 is 120, then what is 150% of 400? # Solution

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# Question Let $a,$ $b,$ $c$ be distinct integers, and let $\omega$ be a complex number such that $\omega^3 = X and $\omega \neq 1.$ Find the smallest possible value of \[|a + b \omega + c \omega^2|.\] If we know the answer to the above question is \sqrt{3}, what is the value of unknown variable X? # Solution

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# Question Each year, the amount of fish in the lake is 15% less than the year before. In 2000, the lake contained 3000 fish. How many fish were in the lake in 2007? # Solution

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# Question A group of students are selling tickets for a school play. Student tickets are $4 each and adult tickets are $7 each. If 120 tickets were sold and the total receipts were $780, how many student tickets were sold? # Solution

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# Question A 20-gallon tank is 3/4 full of water. How much more water should be added to fill the tank? # Solution

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# Question How many values of $x$ with $0^\circ \le x < 360^\circ$ satisfy $\cos x = 0.5$? # Solution

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# Question A box contains 25 pencils, of which 15 are red, 9 are blue, and 1 is yellow. If a person selects a pencil at random, what is the probability that it will be either a red or a yellow pencil? # Solution

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# Question Find the smallest positive integer $k$ such that $k^2 - 2k + 1$ is a perfect square. # Solution

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# Question Marlene's house is 600 square feet larger than 4 times Benedict's house. If Kennedy's house is 10000 square feet, how many square feet is Benedict's house? # Solution

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# Question On a certain day, a total of 420 tickets were sold to the first 100 people who entered a movie theater. Each of the next 250 people who entered the theater received a free ticket. What was the ratio of the number of people who received a free ticket to the total number of people who entered the theater that day? # Solution

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# Question What is the largest integer that divides all the numbers $1, 2, 3, ..., 100$? # Solution

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# Question If 20% of a number is 4, what is 80% of the number? # Solution

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# Question If the probability of snow is 10%, what is the probability of snow? # Solution

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# Question The area of the base of a right circular cone is 40 $cm^2$ and its height is 6 $cm.$ What is the volume of the cone, in cubic centimeters? # Solution

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# Question The sum of two numbers is 10. If the smaller number is subtracted from the larger number, the result is 15. What are the numbers? # Solution

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# Question Compute $\sin 180^\circ$. # Solution

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# Question What is the smallest possible value of $y$ that satisfies the equation $x^2 + 2x + y = 0$? # Solution

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# Question Compute $\frac{4 + 3i}{1 - 2i}.$ (Note that $i^2 = -1$.) # Solution

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# Question The population of a certain city is 150000. It grows at a rate of 10% each year. How many years will it take for the population to reach 192000? # Solution

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# Question A town's population increased by 120 people, and now the population is 8,240. What was the town's population 2 years ago? # Solution

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# Question 1800 is the sum of x and 3 times x. What is the value of x? # Solution

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# Question What is the value of $x$ in the equation $2\cos^2 x = \sqrt{3}\cos x + 1$? # Solution

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# Question The cost of a pair of shoes is 1000$dollars. If the price is increased by 10% what is the new price? # Solution

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# Question The sum of three consecutive integers is 27. What is the middle number? # Solution

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# Question The sum of the two angles of a triangle is 120 degrees. What is the value of the third angle? # Solution

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# Question Tom is working on his taxes. He has a refund of \$1500. If he paid \$340 in federal income taxes, how much did he earn last year? # Solution

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# Question What is the decimal representation of the binary number 10010? # Solution

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# Question If the probability of picking a blue ball from a box containing 10 blue balls is 2/7, what is the probability of picking a blue ball from a box containing 10 blue and 5 red balls? # Solution

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# Question Daisy's Flower Shop sold 45 daisies on its first day. On their second day, they sold 20 more flowers than they did on their first day. On the third day, they sold 10 less than twice the flowers that were sold than on the second day. If the flower shop sold a total of 350 daisies for 4 days, how many daisies were sold on the 4th day? # Solution