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mathematics
acing the new sat math

Acing The New SAT Math 1st Edition Thomas Hyun - Solutions

Working alone, a painter can paint a house in four days. Working alone, his assistant can paint the same house in six days. Working together, they can finish painting the house in x days. The equation above represents the situation described.How many days will it take them to finish painting the
If n ≠ 4, which of the following is equivalent to n² 2 4n - ? -+ n-4 4-n
What is the solution set of the equation? x-1 || x-2 x+1
The function f is defined by a polynomial. If x + 2, x + 1, and x − 1 are factors of f, which of the following table could define f? A) ) X -2 -1 1 2 X -2 -1 1 2 4 0 0 0 f(x) 0 0 4 0 B) D) X -2 -1 1 2 X -2 -1 1 2 f(x) 0 4 0 0 0 0 0 4
Working alone, a painter can paint a house in four days. Working alone, his assistant can paint the same house in six days. Working together, they can finish painting the house in x days. The equation above represents the situation described.Which of the following describes what 1/x represents in
If a ≠ b, which of the following is equivalent to a Ь a-b b-a ?
If y ≠ −1 and y ≠ 0, which of the following is equivalent to 2 1+ -1 ? 1 |- y
What is the solution set of the equation? (k+ 1)² k = 4k
If x ≠ ±1, which of the following is equivalent to 1- 1 x+1 ? 1 1+- 2 1². - 1
Which of the following tables shows a relationship in which y is directly proportional to x? A) X -202 y -1 1 3 C) x -20 y -3 B) 1 5 -20 2 y 5 0-5 8 2 D) X A -20 2 3 1 -1
What is the solution set of the equation?A) −2B) 0C) 2D) There is no solution to the equation. 1 2 X X-2 -4 1² - 2x 2 X
What is the solution set of the equation? 3 x X || 2 | x+ 2 x+2
If x > 3, which of the following is equivalent to x-3 1 x+2 - ? 1 2x-1
What is the solution set of the equation? A) {- 월 B) {3} C) D) 글 3} - 3}
The formula shows the brightness of the light of an object, which varies inversely as the square of the distance. L, measured in lumens, is the brightness of the light and d, measured in meters, is the distance from the object to the light source.The brightness of an object was measured d meters
The formula shows the brightness of the light of an object, which varies inversely as the square of the distance. L, measured in lumens, is the brightness of the light and d, measured in meters, is the distance from the object to the light source.At distance 2 meters from a light source, the
If x ≠ ±1, which of the following is equivalent to 1+ 1- 1 x-1? 1 x +1
Three printers A,B, and C, working together at their respective constant rates, can finish a job in 4.5 hours. Printers A and B, working together, can finish the same job in 6 hours. How many hours will it take printer C, working alone, to finish the job?A) 12.5B) 14C) 16.5D) 18
The distance it takes an automobile to stop varies directly as the square of its speed. If the stopping distance of a car traveling at 40 mph is 320 feet, what is the stopping distance of a car traveling at 50mph?A) 360 ftB) 420 ftC) 500 ftD) 580 ft
Ifis undefined when x = 6, what is the value of a? 1 2 (x-a)²-4(x-a) + 4 f(x) = -
For what value of x is function g above undefined? g(x)= 1 (x+3)²-24(x+3)+144 2
If x > 0, what is the solution to the equation -| + 3 1 2x 10x 10x² || 5 ?
If a ≠ b andwhat is the value of b? 9 1 D-9 9-D b-a 720 ·|· ab
What is one possible value of x, if function f is undefined? f(x)= 5 2(x-2)²-3(x-2)-2
Mike can do a job in 48 minutes. If his brother helps him, it takes them 32 minutes. How many minutes does it take Mike’s brother to do the job alone?A) 72B) 80C) 96D) 102
Working alone, Gary can load an empty truck in 3 hours. Working alone, his brother can load the same truck in x hours. If Gary and his brother worked together for t hours to load the empty truck, which of the following equations can be used to find out how much work was done during t hours?
James can do a job in 8 hours and Peter can do the same job in 5 hours. If they finished 13/25 of the job by working together, how long did they work together?A) 1 hour 24 minutesB) 1 hour 36 minutesC) 1 hour 48 minutesD) 2 hours 8 minutes
If x2 - xy/2x ÷ x - y/3x2 = ax2,what is the value of a?
Ifwhat is the value of a? 1 a + a 2 1 2 = 2.
(a + b/2)2 - (a - b/2)2 = A) ab B) -ab 2ab + b² 2 D) ab+b² C)
In how many ways can the letters of the word SUNDAY be arranged using only 3 of the letters at a time?
A system of inequalities and a graph are shown above. Which section or sections of the graph could represent all of the solutions to the system?A) Section PB) Section QC) Section RD) Section S (x-2y≤-2 [y
Which of the following numbers is NOT a solution to the inequalityA) 0B) 1C) 2D) 3 3b+5 -2 -2b-8?
Nine is not more than the sum of a number and 17.Which of the following inequalities represents the statement above? A) 9217n B) 92n+17 C) 9
Which of the following inequalities represents the graph above? A) 2x-y 20 B) 2x-y≤0 C) x-2y 20 D) x-2y ≤0
If -2 < n < -1, what is the value of 7 + 1/2n rounded to the nearest whole number?
A system of inequalities and a graph are shown above. Which section or sections of the graph could represent all of the solutions to the system?A) Section AB) Section BC) Section CD) Section D section 2y-3x≤6 [y>1_x section B section D section A X
In the xy-plane, if (1,0) is a solution to the system of inequalities above, which of the following must be true? I. a> -1 II. a+b=0 III. b < 1 A) I only B) I and II only C) I and III only D) I, II, and III
Which of the following numbers is NOT a solution to the inequality 1 -x- 2 1 7 5 392 +-x?
Which of the following numbers is NOT a solution to the inequality 3-n-2 or 2n + 3 < -1?
If -3+ n ≤ 25, which inequality represents the possible range of values for 4n - 12? A) 4n-12-100 B) 4n-12 ≤ 100 C) 4n-122-100 D) 4n-12 ≥100
Which of the following numbers is a solution to the inequality 5w+7>2 and 6w-15 ≤3(-1+w)?
A system of inequalities and a graph are shown above. Which section or sections of the graph could represent all of the solutions to the system?A) Section AB) Section BC) Section CD) Section D section & [y-x>1 ly≤-2x section B section D section A X
Which of the following inequalities represents the graph above? ש x
Which of the following inequalities represents the graph above? A) x+y -1 C) x+y≤-1 VIN D) x+y2-1
One half of a number decreased by 3 is at most −5.Which of the following inequalities represents the statement above? A ) 2 n _5 -3≤- 5 1 B) 3-▬n < -5 2 1 C) —n−3
The sum of 120k and 215j does not exceed 2,500.Which of the following inequalities represents the statement above? A) 120k +215j < 2,500 B) 120k +215j > 2,500 C) 120k +215j≤ 2,500 D) 120k +215j ≥ 2,500
Which of the following inequalities represents the graph above? (-4,0) (0,3) 0
Which of the following is the compound inequality for the graph above? + H -5-4-3 -2 -1 0 1 2 3 4 5
Ifand n is an integer, what is one possible value of n? -n-2
Ifwhat is the greatest possible value of x? 1 -x-1≤-x+5, 4
In the xy-plane, if (x,y) lies in the solution set of the system of inequalities above, what is the minimum possible value of y? [y≥12x+600 y2-6x+330
The manager of an apartment building needs an electrician to repair the power generator for the building. The table below shows the fixed amount for a time service call and hourly charges for two different companies.For what number of hours,x, will the total cost of repairing the generator for
The manager of an apartment building needs an electrician to repair the power generator for the building. The table below shows the fixed amount for a time service call and hourly charges for two different companies.Which of the following equations gives the total cost, y, of repairing the power
Jason and Mary are running on a 200 meter track. The expressions in the table above show the distance to the finish line t seconds after they started the race. How many meters will Mary have left to finish the race when Jason is on the finish line?A) 10.5 metersB) 11.5 metersC) 12.5 metersD) 13.5
If -6 ≤ 3 -2x ≤ 9, what is the greatest possible value of x - 1?
The manager of an apartment building needs an electrician to repair the power generator for the building. The table below shows the fixed amount for a time service call and hourly charges for two different companies.Company B’s total cost, ,y is the fixed amount for a service call plus the hourly
If the system of inequalities 3 ≥ x and -1 ≤ y is graphed in the -xyplane above, which quadrant contains no solutions to the system?A) Quadrant IIB) Quadrant IIIC) Quadrant IVD) All four quadrants contain solutions.
For what integer value of x is 4x - 2 > 17 and 3x + 5 < 24?
Adam and Betty purchased a printer together for $258. If Adam paid $18 less than twice Betty, how much money did Adam pay for the printer?A) 172B) 166C) 158D) 146
Tom wants to rent a truck for two days and pay no more than $300. How far can he drive the truck if the truck rental cost $49 a day plus $0.40 a mile?A) 490B) 505C) 520D) 535
At the beginning of a trip, the tank of Chloe’s car was filled with 12 gallons of gas. When she travels constantly on the highway 60 miles per hour, the car consumes 1 gallon of gas per 35 miles. If she traveled 5 hours and 15 minutes on the highway with a constant speed of 60 miles per hour, how
There are 28 tables for customers at Mesa Grill Restaurant. The tables are either two-seat tables or four-seat tables. When all the tables are full, there will be 90 customers in the restaurant. How many two-seat tables are at the restaurant?A) 11B) 13C) 15D) 17
Manny bought c candies at a price of 70 cents each. He sold all but k candies at a price of $1.25, and made a profit of p dollars. Which of the following represents p in terms of c and k? 1.25(c-k)-0.7c A) p= B) p = 1.25c-0.7k C) p = 1.25c-0.7(c-k) D) p = 1.25(c-k)-0.7k
Carl drove from his home to the beach at an average speed of 50 mph and returned home along the same route at an average speed of 30 mph. His total driving time for the trip was 2 hours. Solving which of the following systems of equations yields, x, the time it took for Carl to drive to the beach
A rock climber is climbing up a 450 feet high cliff. By 9:30 AM. the climber reached 90 feet up the cliff and by 11:00 AM he has reached 210 feet up the cliff. If he climbs with a constant speed, by what time will he reach the top of the cliff?A) 1:45 PMB) 2:00 PMC) 2:15 PMD) 2:30 PM
The number of students in a geometry class is four fifths the number of students in a Spanish class. The total number of students in both classes does not exceed 54. What is the greatest possible number of students in the Spanish class?A) 30B) 32C) 34D) 36
At a bagel shop the first 6 bagels purchased cost 55 cents apiece, and additional bagels cost c cents apiece. If a customer paid $5.70 for 12 bagels, what is the value of c?A) 25B) 30C) 35D) 40
Tim has 140 paperback and hard cover copies in his book shelf. If the hard cover copies do not exceed one sixth the number of paperback copies, what is the minimum number of paperback copies in Tim’s book shelf?A) 114B) 116C) 118D) 120
To join Eastlake Country Club one must pay d dollars for a one time membership fee and pay wdollars for a monthly fee. If the first month is free for the club, what is the total amount, y, x months after a person joined the club, in terms of d, w, and x? A) y=x-1+d B) y (x-1) + d C) y=d(x-1)+w D)
In 2005 a house was purchased for $280,000 and in 2013 it was sold at $334,000. Assuming that the value of the house increased at a constant annual rate what will be the price of the house in the year 2018?A) $354,250B) $361,000C) $367,750D) $374,500
At a coffee shop, a 16 ounce bag of coffee is on sale at $5.25 less than the regular price. The cost of 4 bags of coffee at regular price is the same as the cost of 6 bags of coffee at sale price. Let r be the regular price of coffee and s be the sale price of coffee. Which of the following systems
In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament, Jim made 73 more 2-point field goals than 3-point field goals. If he scored a total of 216 goals in the tournament how many 3-point field goals did he make?A) 12B) 14C) 16D) 18
In a car dealership, all of the vehicles are either a sedan or a SUV. If 36 sedans are sold and 36 SUVs are added, there will be an equal number of sedans and SUVs. If 8 SUVs are sold and 8 sedans are added, there will be twice as many sedans as SUVs. How many sedans were at the dealership before
One section of a grocery store display only water bottles. The water bottles are in either 6-bottle packages or 8-bottle packages. Let x represent the number of 6-bottle packages and y represent the number of 8-bottle packages. The total number of packages displayed are 270 and the total number of
At a sporting goods store, Jay paid $172 for a pair of shoes and a pair of pants. The pants cost less than two thirds of what the shoes cost. What is the minimum price of the shoes to the nearest dollar?
Apex Car Rental company charges a flat fee of $40.00 per day plus $0.75 per mile to rent a car. Jason Car Rental company charges a flat fee of $64.00 per day plus $0.60 per mile to rent a car. If a car is rented for three days, at how many miles would the rental charges of the two companies be the
On a map, 1 inch represents 5 miles. If a certain state is represented on a map by a rectangle 10 inches by 7.2 inches, what is the area of the state in square miles? 2 A) 360 m² B) 720 m² C) 1.080 mi² D) 1,800 mi²
David used 1/10 of his monthly salary for groceries and 3/18 of his remaining money for his car payment. He also paid twice as much money for rent as for his car payment. If David has $1,620 left after paying for groceries, car payment, and rent, how much is his monthly salary?A) $3,240B) $3,320C)
In a school election, 680 students voted for one of two candidates for president. If the winner received 120 more votes than the loser, how many votes did the winner receive?
Ty earns $14 an hour working on weekdays and $21 an hour working on weekends. If he wants to make at least $600 by working a total of 36 hours in a week, to the nearest hour, at least how many hours does he need work on the weekends?
From 1990 to 2000 The population of cityArose from 12,000 to 28,000 and the population of cityB rose from 18,000 to 24,000. If the population of the two cities increased at a constant rate, in what year was the population of both cities the same?
It took Sara a total of 42 minutes to jog from home to the park and back again, by the same path. If she averaged 8 miles per hour going to the park and 6 miles per hour coming back, what is the distance from her home to the park?A) 2.4 milesB) 2.8 milesC) 3.2 milesD) 3.6 miles
If a gas tank contains 15 liters of gas and is 3/8 full, how many additional liters of gas are needed to fill up the tank?
If 3/4 quart of lemonade concentrate is mixed with 6(2/3) quarts of water to make lemonade for 40 people, how many quarts of lemonade concentrate are needed to make the lemonade for 24 people? A) B) C) D) 날 10 20 S|N 20
To join Ace Gym, one must pay a $180 membership fee plus dues of $35 per month. To join Best Gym, one must pay a $300 membership fee plus dues of $23 per month. At how many months would the total cost of either gym be the same?A) 7B) 8C) 9D) 10
An empty 1,200 gallon tank is filled with water at a rate of 6 gallons of water per minute. At the same time, another 1,200 gallon tank full of water is being drained at a rate of 9 gallons per minute. How many minutes will it take for the amount of water in both tanks to become the same?
At a county fair the admission is $8.00 and each ride costs $1.25. If you go to the fair with $20.00, what is the maximum number of rides you can go on?A) 8B) 9C) 10D) 11
A car averages 18 miles per gallon of gas for city driving and 27 miles per gallon of gas for highway driving. What is the total number of gallons of gas needed to drive 6x miles in the city and 18x miles on the highway?A) xB) 2xC) 3.5xD) 4.5x
The ratio of 1(3/4) to 2(1/2) is equal to the ratio of 14 to what number?A) 18B) 20C) 22D) 24
If 20 machines produce 1,240 printers in a day, how many more machines are needed to produce 1,984 printers in a day?A) 12B) 20C) 24D) 32
Jason and Donny painted a house and received $1,200. To complete the painting job Jason painted 4 hours 25 minutes and Donny spent 2 hours and 15 minutes. If they split the $1,200 in proportion to the amount of time each spent painting, how much did Donny receive?A) $405.00B) $443.00C) $472.00D)
A car is traveling at a constant rate of x miles per hour. How many miles will the car travel in yminutes? A) 60xy 60x y B) C) D) xy 60 60x
The length of a rectangle is 8 inches longer than the width. If the ratio of the length to perimeter is 5:16, what is the area of the rectangle? A) 160 in² B) 180 in² C) 240 in ² D) 280 in ² 2
Aaron reads x pages of a science fiction book in m minutes. If he continues reading at this rate, what will be the number of pages he reads in 20m seconds? A) B) -im 3 - | 2 2 X C) D) 2x
If 12 grams of coffee costs x dollars and each gram makes y cups of coffee, what is the cost of one cup of coffee in terms of x and y? A) B) C) D) 12y y 12x 12x y X 12y
Ifwhat is the value of x? 5xx+14 2 3
If x/y = 1, what is the value of x−y−1? A) -1 B) 0 C) 1 D) The value cannot be determined from the information given.
A 32-acre field yields 768 bushels of corn each year. How many more acres are needed to yield 960 bushels of corn each year?A) 6B) 8C) 10D) 12
A car travels 218.5 miles on 9.5 gallons of gas. What is the car’s gas mileage?

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