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random_syn_ori_query_syn6w_infer_part_3

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# Question The sum of the squares of two consecutive positive even integers is 52. Find the difference between the two numbers. # Solution

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# Question The sum of the ages of two sisters is 17. If the elder sister is 5 years older than the younger sister, how old are the sisters? # Solution

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# Question In triangle $ABC,$ we have $AC = 5$ and $BC = 10.$ If $\angle C$ is a right angle, what is the area of triangle $ABC$? # Solution

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# Question The sum of three consecutive numbers is 145. If the first number is x, what is the sum of the second and the third numbers? # Solution

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# Question A 10-meter pole, 4 meters high, casts a 10 meter shadow. At the same time, a nearby tree casts a 15 meter shadow. How tall is the tree? # Solution

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# Question The median of a set of 15 distinct integers is 25. If the largest element is 53, what is the maximum possible number of integers that are greater than 25? # Solution

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# Question A boat travels 24 miles upstream and back to the starting point in 6 hours. If the speed of the current is 3 miles per hour, what is the speed of the boat in still water? # Solution

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# Question The sum of three numbers is 30. The first number is 4 less than the second number. The third number is 2 less than the first number. What are the three numbers? # Solution

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# Question Two-thirds of the students in the seventh grade and three-fifths of the students in the eighth grade are in the band. If there are 132 students in the seventh grade and 180 students in the eighth grade, how many students are in the band? # Solution

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# Question If the radius of a circle is tripled, how does the circumference change? # Solution

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# Question Determine the value of $\displaystyle \sum_{n=0}^{2017} (2n^2 - 1)$. # Solution

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# Question What is the value of $\lim_{x \to 2} \frac{x^3 - 2x^2 - 5x + 6}{x - 2}$? # Solution

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# Question If a fair 6-sided die is rolled, what is the probability that the rolled number is a factor of 3? # 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 How many ways are there to put 4 distinguishable balls into 2 indistinguishable boxes? # Solution

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# Question The two diagonals of a regular hexagon have lengths of $4$ and $5.$ What is the area of the hexagon? # Solution

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# Question A 5-foot tall dog casts a 4-foot shadow. How tall is a dog that casts a 10-foot shadow? # Solution

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# Question A cylindrical tank has a diameter of 15 inches and is 10 inches high. How many gallons of paint are needed to paint the exterior of the tank? (1 gallon = 0.1337 cubic feet) # Solution

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# Question Let $f(x) = 2x^3 - 1$ and $g(x) = x^2 + 3x - 5$. What is the value of $f(g(3))$? # Solution

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# Question A rectangular garden has an area of $3600$ square feet. The length of the garden is $40$ feet more than the width. What is the width of the garden, in feet? # Solution

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# Question If a number is randomly selected from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, what is the probability that it is not divisible by 3? # Solution

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# Question A pound of grapes costs $x and a pound of bananas costs $y. If you spend $5.00 on a pound of grapes and a pound of bananas, what is the value of y? If we know the answer to the above question is 1.5, what is the value of unknown variable y? # Solution

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# Question The price of a $2000 computer was reduced by 10% and then by another 20% of the reduced price. What was the final price of the computer? # Solution

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# Question I have a bag with blue marbles and yellow marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 8:5. If I remove 12 blue marbles and add 21 yellow marbles, the ratio will be 1:3. How many blue marbles were in the bag before I removed some? # Solution

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# Question 11 boys took part in a race. How many different ways can the top 3 finishers be chosen? # Solution

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# Question A bank is selling $10000 loans at 4.5% annual interest, compounded monthly. What is the monthly payment on this loan? # Solution

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# Question If a plane flies 250 miles per hour and the distance from New York City to Los Angeles is 2,700 miles, how many hours will it take to fly from New York City to Los Angeles? # Solution

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# Question A cube has a side length of 3 cm. What is the volume of the cube? # Solution

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# Question A restaurant is having a sale on its pasta. The sale is 20% off the price of the pasta and 15% off the price of the pasta sauce. If you have $10 to spend, what is the most you can buy? If we know the answer to the above question is 2, what is the value of unknown variable x? # Solution

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# Question What is the value of $\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+...$? # Solution

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# Question If $x^2 + y^2 = 25$ and $x + y = 5$, what is the value of $(x – y)^2$? # Solution

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# Question 48 is 48% of what? # Solution

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# Question What is the value of $x$ if $x^{2} = 25?$ # Solution

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# Question A shopkeeper bought 300 pounds of cheese for $1800. He sold 25% of the cheese at a profit of 20% and the rest at a loss of 20%. What was the average profit or loss per pound of cheese? # Solution

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# Question A circle is circumscribed around a square, what is the ratio of the area of the square to the area of the circle? # Solution

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# Question The quadratic equation $x^2-4x-14=3x+16$ has two solutions. What is the sum of these solutions? # Solution

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# Question What is the simplified form of $\frac{x^2 + 3x - 4}{x^2 - 9} \div \frac{x + 4}{x - 3}$? # Solution

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# Question How many 10-foot long sections of 2x4 boards do you need to cover 1,200 square feet of floor? # Solution

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# Question What is the smallest number that can be divided by 2, 3, 4, 5, 6, 7, 8, 9, and 10? # Solution

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# Question A pizza company charges a fixed fee of $2.50 plus$2.50 per pizza. If I order 3 pizzas, how much will I pay? # Solution

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# Question If $x$ and $y$ are integers and $x^2 + 3x + 4 = 2y + 1,$ what is the greatest possible value of $x$? # Solution

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# Question An elevator is being built. It will be 10 stories high. The elevator will be divided into four compartments. The elevator will have a total of 32 windows. How many windows will each compartment have? # Solution

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# Question The sum of three consecutive odd integers is 57. What is the largest of these integers? # Solution

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# Question If $x$ is an odd integer, which of the following is an even integer? # Solution

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# Question The sum of two numbers is 31, and their product is 231. What are the two numbers? # Solution

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# Question The sum of two numbers is 30, and their difference is 18. What are the numbers? If we know the answer to the above question is 12 and 18, what is the value of unknown variable x? # Solution

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# Question If a pentagon has an area of 36 square units, what is its perimeter? # Solution

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# Question If 1/3 of a number is 6, what is 1/4 of the number? # Solution

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# Question Three brothers share $1500 equally. One brother is sick and misses 1/2 of his share. How much does the sick brother miss out on? # Solution

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# Question In a city, 20% of the people who received an MBA degree in 2016 were women. If 1000 people received an MBA degree in 2016, how many women received an MBA degree in 2016? # Solution

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# Question A store is selling 120 apples for $2.50. The store has 100 apples left. Calculate the cost per apple. # Solution

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# Question A 36-foot-tall tree casts a shadow that is 18 feet long. How long is the shadow of a 13-foot-tall flagpole? # Solution

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# Question If you have 227 ounces of peanuts and 136 ounces of cashews, what is the maximum number of ounces of a mixture that contains 20% cashews and 80% peanuts? # Solution

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# Question There are 16 boys in a class. If 12 boys like basketball, 11 boys like football, and 6 boys like both sports, how many boys do not like either sport? # Solution

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# Question An airplane travels 1,320 miles in 2 hours. What is its average speed, in miles per hour? # Solution

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# Question If Raine's house is within walking distance from her school and it takes her 150 steps to walk to the school, how many steps does she take in total when walking to and from school over a span of five days? # Solution

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# Question If a ball is thrown straight up into the air with an initial velocity of $40$ feet per second, it height in feet after $t$ seconds is given by $h=-16t^2+40t$. What is the maximum height the ball will reach? # Solution

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# Question A taxi costs $1.50 for the first $\frac{1}{10}$ mile, and $0.25 for each additional $\frac{1}{10}$ mile. How far can you travel in a taxi for$2.00? # Solution

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# Question If a house has 24 square feet of floor space, and each room is 6 feet long, and 4 feet wide, how many rooms are in the house? # Solution

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# Question The number of miles traveled by a car is equal to the number of miles traveled by a truck, plus twice the number of miles traveled by a bike. If the bike traveled 18 miles, and the truck traveled 150 miles, how many miles did the car travel? # Solution

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# Question If the price of a pair of shoes is $200 and the discount is 10%, what is the sale price? # Solution

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# Question A carpenter is cutting a piece of wood into 16 equal sections. He will then glue 10 of those sections to make a rectangular frame. What is the length, in inches, of the side of the rectangular frame? # Solution

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# Question The average of 2 numbers is 14. If one of the numbers is 4, what is the other number? # Solution

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# Question What is the smallest integer x such that 1000 can be evenly divided by 15, 20, 30, 40, and x? # Solution

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# Question We have that $a^2+b^2+c^2+d^2=25000.$ If $a \leq b \leq c \leq d$, what is the minimum value of $a$? # Solution

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# Question Determine the greatest value of x that satisfies the equation $3x^2 + 2x - 4 = 0$. # Solution

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# Question If $\sqrt{x^2-1} = 7$, then $\sqrt{x^2+1}$ = ? # Solution

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# Question The population of a town is 10,000 and is growing at a rate of 2% each year. What will the population be in 3 years? # Solution

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# Question A group of three girls had a total of 160 books. Lydia had 12 books more than the sum of the other two girls combined. How many books did Lydia have? # Solution

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# Question A mixture of 30 liters of water and orange juice contains 12% of orange juice. How many liters of orange juice should be added to the mixture to increase the percentage of orange juice to 20%? # Solution

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# Question Martha bought a 3-pound bag of potatoes. Her son eats 1/3 pound per day. How many days will the potatoes last? # Solution

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# Question If $f(x) = x^2 - 2$ and $g(x) = 5x + 1$, what is the smallest possible value of $f(x) - g(x)$? # Solution

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# Question Which of the following numbers is divisible by 11? # Solution

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# Question What is the volume of a box with a square base and height of 10 cm, if the area of one of its sides is 200 cm$?^2$? # Solution

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# Question Compute $\frac{20!}{17!}$. # Solution

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# Question Find the area of the shaded region. # Solution

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# Question The sum of two numbers is 35. Their difference is X$. The larger of the two numbers is 21. What is the value of unknown variable X? # Solution

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# Question What is the value of x if x^2 - 11x + 30 = 0? # Solution

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# Question A factory produces 500 toys per day, 300 of which are defective. If 130 toys are chosen at random, what is the probability that all 130 toys will be defective? # Solution

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# Question A square has sides of length $a$. What is its area in terms of $a$? # Solution

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# Question In a certain state, license plates consist of two letters followed by three digits. How many different license plates are possible if no letter or digit can be repeated? # Solution

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# Question If we know that the number of questions in the first test was 50 and the number of questions in the second test was 50, what is the value of the unknown variable x? # Solution

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# Question If the total number of boxes in the two warehouses is 1000, how many boxes are in the second warehouse? # Solution

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# Question If $\frac{a}{b} = 2$, what is the value of $\frac{a+5b}{a-b}$? # Solution

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# Question Which of the following is equivalent to the expression $$\frac{1}{2} + \frac{1}{2} \cdot \frac{1}{2} + \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} + \ldots$$? # Solution

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# Question If the ratio of the area of a square to the area of a circle is 16: 25, what is the ratio of the perimeter of the square to the circumference of the circle? # Solution

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# Question The price of a book has been increased by 25%. The price of the book is now $50. What was the original price of the book? # Solution

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# Question The following are the length, width, and height, in inches, of a box. Which box has the greatest volume? # Solution

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# Question Jack has 50 apples and he is going to give 1/3 of them to his brother, 1/4 to his sister, and 1/5 to his mom. How many apples will he have left over? # Solution

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# Question An infinite geometric series has a first term of X and a second term of $4.$ A second infinite geometric series has the same first term of $12,$ a second term of $4+n,$ and a sum of four times that of the first series. Find the value of $n.$ If we know the answer to the above question is 6, what is the value of unknown variable X? # Solution

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# Question Two brothers have 100 pennies. They decide to share them equally. After the first brother gets his share, they are left with 12 pennies. How many pennies does the second brother get? # Solution

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# Question The following is a list of numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. How many 10-digit numbers can be formed from the above numbers such that no digit is repeated? # Solution

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# Question The number 2015 can be written as the sum of 2 consecutive integers. What is the difference between these 2 integers? # Solution

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# Question If a car travels 45 miles per hour, how many miles will it travel in 8 hours? # Solution

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# Question If $a, b$ and $c$ are integers such that $a \mid b$ and $b \mid c$, which of the following statements must be true? # Solution

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# Question What is the maximum possible value of $x$ such that $2x + 3y = 10$ and $5x - 4y = 7$? # Solution

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# Question There are 13 different books in a library, and at least 4 of them are novels. If there are 16 more novels than nonfiction books, how many novels are there? # Solution

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# Question The ratio of boys to girls at Camp Wonka is 2 to 3. The ratio of girls to boys who want to toast marshmallows is 3 to 5. If 96 boys want to toast marshmallows, how many girls are there at Camp Wonka? # Solution

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# Question What is the value of $f(-1)$ if $f(x)=x^{2}-2x$? # Solution

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# Question If the sum of the ages of a father and son is 50 and their difference is 30, what are their ages? # Solution