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random_syn_ori_query_syn6w_infer_part_3

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# Question Solve for x: 4(x + 2) = 12(x – 3) # Solution

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# Question Aria is 3 years older than her brother. If she is 4x years old, her brother is x years old. How many years old is Aria's brother? If we know the answer to the above question is 27, what is the value of unknown variable x? # Solution

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# Question A certain manufacturing company makes 60% of its products on 50% of the work days. If the company makes 1000 products per day on 60% of the days, how many products does the company make per day on 100% of the days? # Solution

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# Question If a baker charges $10 for a pound of flour, how many pounds of flour can a customer buy with$20? # Solution

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# Question A number of eggs is to be distributed evenly among 6 people. If there are 17 eggs left over, then how many eggs were there originally? # Solution

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# Question A baker used 14 tablespoons of flour to make a cake. If he used 4 times as much flour to make the same cake again, how many tablespoons of flour did he use? # Solution

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# Question A student is planning to go on a trip to the city with 7 of his friends. If they all share the cost equally, how much money should each student contribute if the total cost is $810? # Solution

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# Question Find the distance between the two points (1, 5) and (7, 1). # Solution

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# Question What is the least common multiple of 18 and 24? # Solution

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# Question The total number of children in a class is 100. If 30 of them are boys and 40 of them are girls, how many of the girls are older than 12? # Solution

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# Question On a road trip, a car travels at a constant speed for 4 hours, then restarts and travels at a constant speed for 1 hour, and finally restarts again and travels at a constant speed for 5 hours. If the total distance traveled was 336 miles, what was the average speed of the car for the whole trip? # Solution

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# Question A retail store sells 200 sweatshirts per week. If the sweatshirts are on sale for $20 off, and the weekly revenue is $3000, how much is the cost of each sweatshirt? # Solution

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# Question To get free delivery, Alice needs to spend a minimum of $x online at her favorite grocery store. In her cart she has 1.5 pounds of chicken at $6.00 per pound, 1 pack of lettuce for $3.00, cherry tomatoes for $2.50, 4 sweet potatoes at $0.75 each, 2 heads of broccoli for $2.00 each and a pound of Brussel sprouts for $2.50. How much more does she need to spend in order to get free delivery? If we know the answer to the above question is 11, what is the value of unknown variable x? # Solution

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# Question If the ratio of a number x to 4 is equal to the ratio of 36 to 12, what is the value of x? # Solution

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# Question A store owner sold 1000 chairs in 2015. The store owner sold 300 more chairs in 2016 than in 2015. How many chairs did the store owner sell in 2016? # Solution

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# Question If 62% of the 500 students at West High School wear at least one piece of jewelry, how many students do not wear any jewelry? # Solution

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# Question If 25% of the population of a city is 12.5 million people, how many people live in the city? # Solution

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# Question Find $\sec \left( -\frac{5 \pi}{4} \right).$ # Solution

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# Question The mean of a set of numbers is 32, and the standard deviation is 10. If we add 10 to every number in the set, what will be the new standard deviation? # Solution

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# Question The price of a pair of shoes has increased by 20% and now costs $80. What was the price of the pair of shoes before the increase? If we know the answer to the above question is 64, what is the value of unknown variable x? # Solution

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# Question How many different three-digit numbers can be made from the digits 1,2,3,4,5,6,7,8,9, and 0? # Solution

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# Question In a span of six minutes, the hand-crank pencil sharpener can sharpen one pencil every forty-five seconds, while the electric version can sharpen one pencil every twenty seconds. How many additional pencils can the electric sharpener sharpen compared to the hand-crank sharpener? # Solution

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# Question The product of the digits of a two-digit number is 24. If the digits are reversed, the new number is 36 more than the original number. What is the original number? # Solution

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# Question A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn? # Solution

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# Question Find the value of $2011^{2011} + 2012^{2012} + 2013^{2013} + 2014^{2014} + 2015^{2015} + 2016^{2016}.$ # Solution

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# Question A square has an area of 64 square inches. What is the perimeter of the square? # Solution

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# Question A deck of cards is shuffled and one card is selected at random. What is the probability that the card selected is a king or a queen? Express your answer as a common fraction. # Solution

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# Question If 120% of the people in a group of 100 people are men, how many men are there in the group? # Solution

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# Question Given the function $f(x) = 11x^2 - 6x + 3$. What is the value of $f(2)$? # Solution

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# Question What is the value of the expression $x^2+ 5x-6$, when $x =-1$? # Solution

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# Question Katie has 13 pink marbles. She has 9 fewer orange marbles than pink marbles. She has x times as many purple marbles as orange marbles. Katie has 33 marbles in all. What is the value of unknown variable x? # Solution

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# Question The price of a gallon of gasoline is increasing at a rate of 4.5 cents per day. At this rate, what is the price of a gallon of gasoline in 30 days? # Solution

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# Question Peter has 4 more than 3 times as many bottle caps as Sammy. If Janine has 6 less than Peter and Sammy has 4 bottle caps, how many bottle caps does Janine have? # Solution

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# Question What is the value of $1000^{1000} \bmod 1001$? # Solution

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# Question In a sequence of numbers, the first number is 1, the second number is 3, and each subsequent number is equal to the sum of the two previous numbers. What is the 20th number in the sequence? # Solution

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# Question Find the greatest value of $b$ such that $4b^2-16b+16 \le 1$. If we know the answer to the above question is 4, what is the value of unknown variable X? # Solution

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# Question If 24,000 miles is 2,400 kilometers, and 1 inch is 2.54 centimeters, how many kilometers is 1 inch? # Solution

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# Question What is the smallest prime number greater than 1000? # Solution

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# Question If 120 students are in the math club, 100 are in the science club, and 80 are in the English club, how many students are in all three clubs? # Solution

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# Question A carpenter is building a house. He needs 400 nails. The store has 10 boxes of nails and each box contains 20 nails. How many boxes of nails does the carpenter need? # Solution

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# Question For the following system of equations, find the values of $a$ and $b$ so that the system has: (a) no solution, (b) a unique solution, and (c) infinitely many solutions. \begin{align} & 2x - 3y = 1\\ & ax + by = 5\\ & 3x + 5y = 15 \end{align} # Solution

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# Question What is the smallest positive integer greater than 2,000 that leaves a remainder of 2 when divided by 3, 5, 6, 7, and 11? # Solution

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# Question The sum of three numbers is $17.$ The first is $4$ less than the second and $5$ less than the third. What is the sum of the squares of these three numbers? # Solution

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# Question The notation $[x]$ stands for the greatest integer that is less than or equal to $x$. Calculate $[-1.2]$. # Solution

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# Question The time it takes for a car to travel 300 miles is directly proportional to the speed of the car. If it takes 3 hours to travel 300 miles, how long will it take to travel 360 miles at the same speed? # Solution

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# Question The sum of two numbers is 40. If the larger number is 3 more than twice the smaller number, what is the value of the smaller number? # Solution

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# Question In a school of 300 students, 55% of the students are female. If 110 students are boys, what is the percentage of the girls in the school? # Solution

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# Question The sum of three numbers is 13. One of the numbers is 10. If the sum of the other two numbers is 11, what are the numbers? # Solution

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# Question 12.8% of 120 is what number? # Solution

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# Question How many different arrangements can be made with the letters of the word STATES? # Solution

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# Question What is the value of 4(2+3)+8? # Solution

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# Question In a group of 10 people, 6 people know each other. 4 people do not know each other. How many people know both of the people that the other 2 people do not know? # Solution

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# Question The first three terms of a geometric sequence are 4, 24, and 144. What is the seventh term in the sequence? # Solution

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# Question Let $n \in \mathbb{Z}^+$. Prove that $\gcd(n^2, (n + 1)^2) = 1.$ # Solution

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# Question If a candy bar costs 75 cents, how much would 16 candy bars cost? # Solution

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# Question A square is inscribed in a circle with radius r. What is the area of the square? # Solution

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# Question If Derek runs 12 miles, and he runs 3 times as many miles as Emily, who in turn runs 2 times as many miles as Cindy, how many miles does Cindy run? # Solution

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# Question What is the solution to the following system of equations? # Solution

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# Question If you are in a room where the temperature is 4 degrees Celsius, and the air conditioner's temperature setting is 18 degrees Celsius, what is the temperature difference between you and the air conditioner? # Solution

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# Question A turtle crawls 2.5 meters in 1 minute. If it continues at this rate, how long will it take for the turtle to crawl 21 meters? # Solution

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# Question If a certain number is divided by 3, the remainder is 2. If the same number is divided by 7, the remainder is 5. What is the remainder if the number is divided by 21? # Solution

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# Question If 6 is added to a number and this sum is then multiplied by 4, the result is 52. What is the number? # Solution

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# Question Sally buys 400 kg of rice. She uses 20 kg in the first week, 25 kg in the second week, and 20 kg in the third week. How many kilograms of rice does she have left? # Solution

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# Question Find the value of $x$ in the following equation: $x^2 + 10x + 21 = 0$. # Solution

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# Question If a couple pays $1500 for 15 hours of babysitting, what is the hourly rate of the babysitter? # Solution

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# Question What is the sum of $1$, $2$, $3$, $4$, and $5$? # Solution

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# Question The sum of two numbers is $10$ and their product is $21$. What is the difference between the two numbers? # Solution

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# Question In a classroom, there are 15 chairs in a row and 20 students are seated in the chairs. If 10 students stand up from their chairs and move to the back of the classroom, how many students will be standing? # Solution

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# Question A 1000-foot rope is cut into two pieces, and the two pieces are then cut into two pieces each, and each of these four pieces are then cut into two pieces each, and so on, forever. How many feet of rope will have been cut in total? # Solution

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# Question A caterer ordered 1000 chocolate chip cookies. The caterer accidentally ordered 25 more sugar cookies than chocolate chip cookies. How many sugar cookies were ordered? # Solution

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# Question A farmer has a rectangular field. The length of the field is 5x+4 meters and the width is 11x-11 meters. What is the area of the field? # Solution

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# Question During a fundraiser, a student collected 180 cans. He collected 5 times as many cans as a classmate. How many cans did the classmate collect? # Solution

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# Question A group of 30 people are going to the circus. Children are charged 10 cents for admission and adults are charged 25 cents for admission. If they paid a total of $12.50, how many of the people in the group were adults? If we know the answer to the above question is 20, what is the value of unknown variable x? # Solution

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# Question 40% of a number is 20. What is 20% of that number? # Solution

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# Question The population of a town is 16000. It decreases by 4% per year. What is the population of the town after 2 years? # Solution

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# Question 1/3 of a group of 15 people are girls. 1/4 of the girls are left-handed. What percent of the group are left-handed girls? # Solution

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# Question David is in the 5th grade. He is the 4th-oldest student in his class. There are 19 students in his class. How many students are younger than David? # Solution

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# Question A baseball team has 24 players, 18 of whom are pitchers and 6 of whom are catchers. 2/3 of the non-catchers are right-handed. 1/3 of the pitchers are left-handed. 2/5 of the catchers are left-handed. What fraction of the team is left-handed? # Solution

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# Question A student has a balance of 12 dollars and 15 cents. He spends 17 dollars and 85 cents. How much does he have left? # Solution

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# Question The number of days in 2018 was a perfect square. If the number of months in 2018 was a perfect square, what was the number of months in 2018? # Solution

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# Question If a can of tomatoes costs 60 cents, how much will 10 cans cost? # Solution

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# Question Solve for $x$: $\frac{x}{2}-\frac{x}{3}=6$. # Solution

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# Question In a 24-hour day, there are x hours from 12 noon to 8 pm. What is the value of x? # Solution

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# Question Carson runs a carpool for five of his friends. The five of them cover all the gas expenses to compensate Carson for his time. Their total commute is 21 miles one way, gas costs $2.50/gallon, Carson's car gets 30 miles/gallon, and they commute to work 5 days a week, 4 weeks a month. How much does Carson's car cost to run a month? # Solution

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# Question Let $a$, $b$, and $c$ be positive integers such that $a$ is an odd prime and $b$ is an even nonprime. Which of the following statements must be true? # Solution

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# Question The value of $x$ satisfying the equation \[\left( \sqrt{x} - \frac{1}{\sqrt{x}} \right)^2 = 2 + \sqrt{x} - \frac{1}{\sqrt{x}}\] is equal to? If we know the answer to the above question is 1, what is the value of unknown variable X? # Solution

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# Question A piece of wire is 40cm long. It is cut into two pieces. The longer piece is 9cm longer than the shorter piece. What is the length, in centimeters, of the longer piece? # Solution

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# Question The product of the digits of a two-digit number is 24. If the digits are reversed, the new number is 36 more than the original number. What is the original number? # Solution

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# Question In the xy plane, the graph of y = x^2 + 12x + 46 is a parabola. The parabola intersects the x-axis at points A and B. What is the maximum area of triangle AOB that can be formed, where O is the origin? # Solution

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# Question The teacher gave a math quiz to his class of 20 students. The average (arithmetic mean) score of the class was 80. The average score of the boys was 82 and the average score of the girls was 76. What is the number of boys in the class? # Solution

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# Question In a sequence of numbers, the first number is 1, the second number is 3, and each subsequent number is equal to the sum of the two previous numbers. What is the 20th number in the sequence? # Solution

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# Question What is the value of the floor function applied to the negative square root of 49/4? # Solution

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# Question Which of the following is the correct graph of the function $f(x) = |x - 2| + 1$ on the domain $[0, 5]?$ # Solution

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# Question Compute \[\begin{vmatrix} 4 & 2 \\ 7 & 9 \end{vmatrix}.\] # Solution

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# Question The square of the sum of three positive integers is equal to the sum of their cubes. The three integers have a median of $14$. What is the smallest possible value of their sum? # Solution

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# Question Let $A(4,2),$ $B(-1,0),$ and $C(1,-3)$ be three points. The point $D$ is on the segment $BC$ such that $AD:DB = 2:1.$ What is the area of the quadrilateral $ABCD?$ # Solution

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# Question In a certain store, the price of a pair of shoes is $120. If the price of a new pair is 3 times the price of a pair already in the store, what is the price of the pair in the store? # Solution

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# Question If $f(x) = x^2 + 2$, what is the value of $f(f(f(f(f(f(1))))))$? # Solution

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# Question If $f(x) = x^2 - 4$, what is the value of $f(x - 4)$? # Solution

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# Question The average of 20, 30, 40, and 50 is x. The average of 60, 70, 80, and 90 is y. The average of x, y, and 45 is z. What is the value of z? # Solution