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random_syn_ori_query_syn6w_infer_part_1

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# Question What is the sum of all two-digit positive integers that are divisible by 7? # Solution

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# Question 50% of the students in a class of 40 students are boys. The rest are girls. How many students are girls? # Solution

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# Question In a row of 20 people, the first person wonders how many people are taller than the first person. The second person in the row wonders how many people are taller than the second person, and so on. How many people are taller than the 20th person? # Solution

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# Question The number of students who are in the seventh grade and who play football is 30. The number of students who are in the seventh grade and who play basketball is 25. The number of students who are in the eighth grade and who play football is 20. If the number of students who play football is 70, how many students play basketball? # Solution

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# Question A certain zoo has $c cows and $d donkeys. If there are 50 heads and 104 legs, then what are the values of $c and $d? # Solution

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# Question A rectangle has a length of 10 cm and a width of 6 cm. What is the ratio of its length to its width? # Solution

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# Question The price of gasoline is increasing by 10 cents a day. If the price today is $2.25, what will be the price in 4 days? # Solution

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# Question A full tank of gas costs $200 and 30 gallons of gas. A full tank of diesel costs $240 and 40 gallons. What is the cost per gallon of gas? # Solution

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# Question The length of a rectangle is 3 feet more than its width. The perimeter of the rectangle is 10 feet less than 4 times its width. Find the dimensions of the rectangle. # Solution

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# Question Determine the value of $\csc 45^\circ$. # Solution

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# Question If 5 out of 10 people love cookies, what percentage of the people love cookies? # Solution

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# Question A student earned a 90 on a test with 25 questions. He or she missed 3 problems. How many of the questions were problems? # Solution

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# Question A woman has $1000 to invest. She invests $200 at 5.5% and $700 at 4%. How much interest does she earn in one year? # Solution

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# Question If the length of the rectangle is 5.5 units, what is the length of the diagonal? # Solution

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# Question Shelly is ordering a pizza. She has already ordered 1/2 a pizza. She has also ordered 1/4 of a gallon of soda. If she wants to order 1/3 of a pizza, how many more pieces of pizza will she need to order? # Solution

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# Question If 24 students are in a class and 18 students are boys, what is the probability that a student chosen at random from the class is a girl? # Solution

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# Question If x = 4 and y = 2, then what is the value of x + 3y – 5? # Solution

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# Question If $x = 10^{10}$, what is the value of $x^{x}$? # Solution

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# Question If 12 kids each have 4 pencils, how many pencils are in all? # Solution

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# Question What is the sum of the reciprocals of all the positive divisors of 84? # Solution

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# Question A group of 12 students needs to raise $220 to go on a field trip. They decide to sell candles at a school fair. If each candle sells for $5, how many candles must they sell to raise the money? # Solution

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# Question A line segment has two endpoints. How many points are there on this line segment? # Solution

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# Question If a restaurant serves 2000 hot dogs per day and the restaurant has 5 different hot dog buns, 4 different condiments, and 12 different hot dog flavors, how many different hot dogs can the restaurant offer? # Solution

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# Question What is the value of $\sin(60^{\circ})$? # Solution

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# Question In how many ways can I choose X people from a group of 50 people if any of the 50 people can be chosen? If we know the answer to the above question is 50, what is the value of unknown variable X? # Solution

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# Question A rectangular field is 300 feet long and 100 feet wide. A paddock is built around the field. The paddock is 50 feet wide and 50 feet long. How many square feet are there in the paddock? # Solution

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# Question The sum of the digits in the year 2012 is 3. What is the next year in which the sum of the digits is 3? # Solution

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# Question What is the remainder when $7^{2021}$ is divided by 100? # Solution

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# Question Find the length of the side of a square with an area of 49 square inches. # Solution

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# Question How many squares are there in a 12-by-12 grid of dots? # Solution

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# Question In a 100-mile trip, a car travels 30 miles at 60 miles per hour and 70 miles at 40 miles per hour. What is the average speed of the car for the entire trip? # Solution

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# Question A whale eats 2.75 tons of fish in 1 day. How many days does it take for the whale to eat 12 tons of fish? # Solution

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# Question Simplify $\frac{x^2y^3z^4}{x^4y^2z^3}$. # Solution

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# Question There are 300 students in a school. If the number of girls is 25% more than the number of boys, how many boys are in the school? # Solution

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# Question The volume of a cube is $486\text{ cm}^3$. What is the surface area of the cube, in square centimeters? # Solution

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# Question A regular polygon has sides of length 5 units and an exterior angle of X degrees. What is the perimeter of the polygon, In units, the answer is 15. What is the value of unknown variable X? # Solution

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# Question The sum of the digits of $x$ is $13$. What is the sum of the digits of $2x^3+5$? # Solution

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# Question Evaluate 20% of 120. # Solution

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# Question A $1.50$ pound bag of nuts cost $2.75$. How many pounds of nuts can you buy for $8.00$? # Solution

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# Question The number of employees in a company is 2100. If 70% of the employees are men and 30% of the employees are women, how many women work in the company? # Solution

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# Question What is the value of $2+4+6+8+10$? # Solution

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# Question Jane has 5 bags of flour, each with a different amount of flour. The bags of flour contain 1 pound, 2 pounds, 3 pounds, 4 pounds, and 5 pounds of flour. If Jane wants to use 20 pounds of flour to make a cake, how many bags of flour does she need to use? # Solution

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# Question The lengths of the sides of a triangle are 6, 7, and 14. What is the perimeter of a similar triangle whose shortest side is 10? # Solution

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# Question The sum of two numbers is $12$ and their difference is $18$. What is the lesser of the two numbers? # Solution

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# Question Kirsten's school bus takes 4 minutes to pick her up from the school. If her bus picks her up every 12 minutes, how many minutes does it take for her to get to school? # Solution

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# Question There are 12 pieces of fruit in a basket. The ratio of apples to bananas is 3:5. How many apples are in the basket? # Solution

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# Question The length of a rectangle is 16% greater than its width. The perimeter of the rectangle is 222. What is the width of the rectangle? # Solution

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# Question How many positive factors does $120$ have? # Solution

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# Question A woman is 30 years older than her son. In 5 years, she will be twice as old as her son. How old is her son now? # Solution

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# Question There are 5 pencils and 4 pens in a box. If a person buys two pencils and two pens, what is the probability that the two pencils are the first two items purchased? # Solution

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# Question If 36 marbles were shared equally among a group of children, with each child getting 4 extra marbles, how many marbles would each child receive? # Solution

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# Question Which of the following is equivalent to $2^5 \cdot 3^2 \cdot 4^3$? # Solution

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# Question At the start of a game, a team had 300 points. During the game, they scored 20 points 3 times and lost 20 points twice. How many points did they have at the end of the game? # Solution

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# Question The point $(3, 4)$ is reflected across the $y$-axis. What are the coordinates of the image point? # Solution

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# Question How many 4-digit positive integers are there such that the product of their digits is 60? # Solution

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# Question What is the remainder when $123456789$ is divided by $99$? # Solution

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# Question The average age of the students in a class is 15. If 7 new students are added, the average age is 15.7 years. How many students are there in the class? # Solution

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# Question Determine the number of positive integers $a$ less than $10$ such that the congruence $ax\equiv 1\pmod{10}$ has a solution in $x$. # Solution

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# Question The ratio of girls to boys in a classroom is 2 to 3. If there are 48 students in the classroom, how many more girls are there than boys? # Solution

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# Question In the town of Wackyville, 40 percent of the children are girls, 40 percent of the girls are 5 years old, and 20 percent of the boys are 5 years old. What is the percent of boys 5 years old? # Solution

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# Question 3.5 # Solution

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# Question The difference of two numbers is 7. The sum of their squares is 207. What are the numbers? # Solution

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# Question A number is multiplied by 2, and the result is increased by 4. The new result is then multiplied by 3. The final result is 54. What was the original number? # Solution

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# Question How much of each of two solutions of water and acid is required to obtain 200 milliliters of an acid solution that is 20% acid? # Solution

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# Question A store has 420 lollipops. There are 3 lollipops in each pack. How many packs of lollipops are there? # Solution

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# Question If a ball is dropped from a height of 16 feet, the height of the ball above the ground is given by the function h(t) = -16t2 + 16, where t is the time in seconds. What is the instantaneous rate of change of the height of the ball at t = 1? # Solution

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# Question If 28 is 30% of a number, what is 20% of the same number? # Solution

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# Question Find the 3rd term in the sequence 2, 6, 10, 14, 18, 22, 26. # Solution

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# Question The number of students in a school is 700. There are 425 students in the sixth grade. There are 362 students in the seventh grade. There are 275 students in the eighth grade. There are 280 students in the ninth grade. How many more students are there in the tenth grade than in the eleventh grade? # 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 boy had a certain number of candies. He gave away 100 candies and ate 24 candies. If he had 48 candies left, what was the original number of candies he had? # Solution

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# Question I have a bag of 40 marbles. 20 of them are red, 10 are blue, 5 are green, and 5 are yellow. I draw 4 marbles out at random without replacement. What is the probability that all 4 marbles are yellow? # Solution

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# Question If $\log_{5} x = 3$, find $\log_{125} x$. # Solution

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# Question If $x = 4$, what is the corresponding value of $y$ in the equation $y = 2x + 1$? # Solution

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# Question A car is traveling at 30 miles per hour. It is going uphill at a rate of 0.02 miles per hour, and downhill at a rate of 0.01 miles per hour. How far will the car travel in 1 hour? # Solution

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# Question If the product of the numbers 57, 53, and x is equal to the product of 52, 50, and 65, then what is the value of x? # Solution

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# Question If the first digit of your phone number is 1, what is the last four digits of your phone number? # Solution

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# Question If $n$ is an integer and $n^2$ is divisible by 48, what is the least possible value of $n$? # Solution

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# Question In a company, there are 140 employees. If 100 of them are female, 60 of them are male and the other 40 are mixed gender, what is the number of mixed gender employees? If we know the answer to the above question is 40, what is the number of male employees? # Solution

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# Question In the first week of May, 2019, the temperature was 20 degrees Celsius. It has been rising 2 degrees Celsius per day since then. What is the temperature in Celsius on the 24th day of May, 2019? # Solution

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# Question If $a \text{ Y } b$ is defined as $a \text{ Y } b = a^2 - 2ab + b^2$, what is the value of $2 \text{ Y } 3$? # Solution

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# Question Find the period of the function $f(x) = \frac{1}{2} \cos \left( \frac{x}{3} \right).$ # Solution

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# Question Find the area of a square with side length 1.3 meters. # Solution

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# Question Find the inverse of the matrix \[\begin{pmatrix} 2 & X \\ 2 & 3 \end{pmatrix}.\]If the inverse does not exist, then enter the zero matrix. If we know the answer to the above question is \begin{pmatrix}0&0\0&0\end{pmatrix}, what is the value of unknown variable X? # Solution

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# Question A 1000-watt light bulb is used for 8 hours a day. What is the amount of energy in joules used by the light bulb in a week? # Solution

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# Question If the sum of three integers is 1,000, and the second integer is 500 more than the first integer, what is the sum of the three integers? # Solution

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# Question If the last digit of a two-digit number is deleted, the number is decreased by 18. What is the original number? # Solution

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# Question What is the slope of the line that passes through the points $(-3, 10)$ and $(10, -3)$? # Solution

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# Question In a certain sequence, the term $a_n$ is given by the formula $a_n = a_{n-1} - 2n + 3$ for each integer $n$ where $n \ge 2$. If $a_1 = 11$, then $a_{20}$ = ? # Solution

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# Question The average of 10 consecutive integers is 25. What is the sum of the smallest and largest integers? # Solution

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# Question If the sum of three consecutive numbers is 30, what is the largest number? # Solution

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# Question The side lengths of a triangle are given by $a=5$, $b=5$, and $c=6$. Determine the area of the triangle. # Solution

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# Question If a person walks 15 miles in 2 hours, how many miles can he walk in x hours? # Solution

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# Question A certain type of light bulb has a mean life of 1000 hours. The distribution of life lengths for this type of light bulb is approximately normal with a standard deviation of 250 hours. Find the probability that a randomly selected light bulb of this type will have a life length greater than 1300 hours. # Solution

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# Question The total number of students in a school is 300. If 50 students are in the marching band, 30 are in the chorus, 10 are in both the marching band and the chorus, and 100 students are not in either group, how many students are in the marching band only? # Solution

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# Question A 50-meter by 25-meter rectangle is divided into 250 equal-sized squares. What is the area of the largest square? # Solution

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# Question A set of 12 numbers has a range of 30. What is the least possible median of the set of numbers? # Solution

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# Question If $x = 2$ and $y = 1,$ what is the value of $x \times y - 2?$ # Solution

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# Question The first four terms of a sequence are as follows: 2, 3, 5, 6. Each term after the first is defined as the sum of the three previous terms. What is the $50^{th}$ term of this sequence? # Solution

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# Question If 200 people took the math test, 25 people scored 400. What is the probability that a student who scored 400 was actually an adult? # Solution

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