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mathematics
mcgraw hills conquering sat math
McGraw Hills Conquering SAT Math 2nd Edition Robert Postman, Ryan Postman - Solutions
A = (−3,5) and B = (3,−4). The absolute value of the slope of ĀB̄ is equal to the slope of ĀC̄ What are the coordinates of point C?A. (8,−1)B. (−1,8)C. (−3,2)D. (2,−3)E. (−2,3)
Let mS be the slope of line S and mT be the slope of line T. If ⊥ T which of the following is always true? I. Ms Mr = -1 |ms|mr| II. = III. = 1 Ms mr A. I B. II C. III D. I and II E. I and III
A car travels from Al’s house 10 miles south to Brad’s house and then 6 miles east. What is the distance from Al’s house to Brad’s house? A. 2√34 B. 4 C. 8 D. 2√17 E. 4√17
In the graph below, Mis the midpoint of ĀB̄ X is the midpoint of ĀM̄ and Y is the midpoint of B̄M̄ What is the length of X̄Ȳ. + (-5,-4) = A M B = (11,8) +
For which value of x does f(x) = 4? X4+
What must be done to the graph of f(x) = √x the graph of h(x) = √x + 3 - 7?
If f (x) is a linear function such that f (2) = 5 and f (4) = 13, f(x) = A. f(x) = 3x - 4 B. f(x) = 4x - 3 C. f(x) = 4x + 3 D. f(x) E. f(x)= || 1 -X + 4 1 - X 4 772272 9 9
What are the domain and range of f(x) = −⎟ x + 4⎟ −3?
On the first day of a two-day fishing trip, George caught 9 trout; 33 1/3% of the trout are rainbow trout. By the end of the fishing trip, George caught 6 more trout, but none are rainbow trout. What percent of all the trout that George caught are rainbow trout?
15% of what number is 18?A. 102B. 110C. 112D. 120E. 125
Jack is 30 years old and Alice is 35 years old. What percent of Alice’s age is Jack, rounded to the nearest tenth of a percent?
In a 20-game season a certain basketball player scores at least 15 points in 60% of the first 10 games, 40% of the next 5 games, and 20% in the last 5 games. In what percent of all 20 games did this player score less than 15 points?A. 40%B. 45%C. 50%D. 55%E. 60%
90% of the students in a high school have a cell phone. If there are 750 students in the school, how many of the students have cell phones?
45% of 80 equals what percent of 60?A. 60%B. 55%C. 50%D. 45%E. 40%
What percent of 60 is 14? A. 23% B. 23.3% C. 23-% 3 D. 23.6% E. 23 % 3
Richard’s car cost 70% of Brian’s car. If Richard’s car cost $17,500, what is the price of Brian’s car?
Below is a table showing the classes that Mr. Lipton taught and the number of students in each class. If no student was enrolled in more than one class, what percent of the students in Mr. Lipton’s classes did not take Statistics? Algebra 35 Statistics 55 Calculus 10
A house was appraised at $300,000. One year later the house was appraised at $335,000. At what percent did the appraised price of the house increase? A. 11²% 3 B. 11-% 3 C. 11% D. 13²% 3 E. 13-% 3
A television set is on sale for 15% off the original price. If the sale price is $340, what was the original price of the televisions set?A. $340B. $370C. $400D. $440E. $470
Dan needs to gain 8% of his current body weight to wrestle in weight Class A. Dan needs to lose the same percent of his current weight to wrestle in weight Class B. What percent of Dan’s Class A weight, to the nearest tenth, does he need to lose to get to his Class B weight?
The percent increase from 8 to 14 is equal to the percent decrease from 35 to x. What is the value of x?A. 7.5B. 7.75C. 8.25D. 8.5E. 8.75
If x percent of 80 is 12, then x percent of what number is 18?A. 112B. 115C. 117D. 118E. 120
16% of s equals t. 10% of t equals 40. What is the value of s − t?
Alex weighs 185 pounds. If he decreases his weight by 10%, what will be his new weight?A. 160 poundsB. 166.5 poundsC. 170 poundsD. 170.5 poundsE. 175.5 pounds
Jerry, Will, and Al all work at the same company. Jerry earns 80% of Will’s salary, and Will earns 75% of Al’s salary. What percent of Al’s salary is equal to Jerry’s salary?A. 80%B. 75%C. 70%D. 65%E. 60%
A camping tent went on sale from $80 to $60. A camping chair that originally cost $20 was discounted by the same percent. What is the new price of the camping chair?A. 25B. 20C. 15D. 10E. 5
Erin received a raise at her job from $14 per hour to $17 per hour. What is the percent increase of her raise?
60% of the students at the high school play sports. 14% of the students who play sports play baseball. What percent of the students in the school playbaseball?A. 4.6%B. 4.8%C. 6.4%D. 8.4%E. 10.6%
What percent of 42 is 25% of 56?
There are 15 students on a yearbook committee. 40% of the students are females. How many students on the committee are males?A. 6B. 9C. 12D. 13E. 15
The cost of grapes at a grocery store is normally $2.99 a pound. There was a sale on grapes for 65% off the normal price. What is the sale price of the grapes to the nearest cent?
Last season a certain basketball player averaged 25 points a game. This season the basketball player increased her average by 12%. What is the basketball player’s new scoring average?
Over the summer Jason grew from 70 inches to 73.5 inches. What percent has Jason’s height increased?
What is 12% of 70?A. 8.4B. 8.5C. 8.6D. 8.7E. 8.8
A jacket went on sale. The original price was $24, and the sale price was $18. At what percent was the jacket discounted?
13 of the 18 players on the varsity soccer team are seniors. What percent of the players on the team are not seniors? 7 A.27-% 9 B. 270% C.27.7% D. 272% E. 27.8%
During last year’s baseball season, a certain player has 625 at bats and gets a hit 32% of the time. This season the player increased the at bats by 12%, and got a hit 34% of the time. What is the percent increase in the number of hits?
On a school trip there must be 2 chaperones for every 25 students. How many chaperones need to be on a trip if 180 students are on the trip?A. 12B. 13C. 14D. 15E. 16
A computer store sells 3 computer CDs for $2. How much would 15 computer CDs costs?
Jordan swam 4 laps. Each lap is 100 meters. Jordan’s average speed for the first 3/4 of his swim was 40 meters per minute, and for the rest of his swim he averaged 35 meters per minute. What is Jordan’s average rate for the entire 4 laps, rounded to the nearest whole number?
When Drew goes to the grocery store for every 2 oranges he buys, he purchases 3 peaches and 1 apple. Drew bought 8 oranges. How many peaches and how many apples did Drew buy?
Jason ran for 5 miles. He ran the first 3 miles at an average rate of 8 miles per hour, and then he ran the final 2 miles at an average rate of 6 miles per hour. What is Jason’s average speed for the entire 5 miles?
State whether the following numbers are prime or composite.A. 31B. 45C. 63D. 59
List the factors of the following numbers and then identify the greatest common factor.A. 34B. 52
Write the prime factorization for each number.A. 44B. 195
What is the LCM of the numbers that satisfy these conditions?Factor of 48Multiple of 8
What is the sum of all the factors of 24?A. 46B. 49C. 50D. 60E. 66
If a, b, and c are distinct integers such that a < b < c, b < 0, and c = a · b, then which of the following must be true?A. c is a positive number.B. −a is a prime number.C. b is a prime number.D. c is a factor of a.E. c is a prime number.
What is the greatest number of 3s that can be multiplied together and still have a result less than 250?A. 3B. 4C. 5D. 6E. 7
Which of the following must be true about the sum of all the prime numbers between 20 and 30?A. It is a prime number.B. It is an odd number.C. It is a factor of 156.D. It is a multiple of 5.E. It is a factor of 10.
List the first eight multiples of each number and then identify the least common multiple of the two numbers.A. 5B. 7
At a dinner party each table can seat eight people. If 100 people attend the party, what is the minimum number of tables that are needed?A. 12B. 13C. 14D. 15E. 16
What is the greatest integer that evenly divides both 48 and 64?
Let P be a prime number greater than 4. How many distinct prime factors does 9 · P have?A. 2B. 3C. 4D. 5E. 6
When x is divided by 8, the remainder is 3. What is the remainder when 4x is divided by 8?A. 1B. 2C. 3D. 4E. 5
Let x, y, and z be positive integers such that y is a multiple of x and z. All of the following statements are true except for:A. y · z is a multiple of x.B. x is a factor of y.C. x · z is a factor of y.D. z divides evenly into y.E. x divides evenly into y · z.
When a two-digit number is divided by 5 the remainder is 2. Which of the following statements must be true about the two-digit number?A. The sum of all the digits is odd.B. The digit in the one’s place is odd.C. The number is prime.D. The number is odd.E. The digit in the one’s place is prim
The sum of 3 consecutive integers is 15. How many distinct prime factors does the product of these three numbers have?A. 2B. 3C. 4D. 5E. 6
How many positive integers less than 20 have an odd number of distinct factors?A. 12B. 10C. 8D. 6E. 4
If a, b, and c are all integers greater than 1 and a b = 21 and b · c = 39, then which of the following choices gives the correct ordering of the numbers?A. b < a < cB. c < a < bC. a < b < cD. b < c < aE. a < c < b
In the repeating decimal 0.714285714285 . . . , what is the 50th digit to the right of the decimal point?
How many distinct composite numbers can be formed by adding 2 of the first 5 prime numbers?
A rope is 13 feet long. How many ways can the rope be cut into more than one piece so that the length of each piece is a prime number?A. 4B. 5C. 6D. 7E. 8
In which of the following choices would the symbol > create an incorrect statement? A. D. E. a ml Na
In a certain geometric sequence, 5 is the first term and 45 is the 3rd term. What term is 3,645?
Which of the following is not equal to 5/9? A. B. C. D. E.
Simplify the following questions: - (들 + 을) + (틀-2)
What is the difference between the largest and smallest number in the set below? E. D. A. 디 - SEE !! u
Which of the following has the smallest result? E. D. +-+ C. - || A| 8/735 ∞0 AW W/N B. + A. + + 5/6 N/- N/W aju + 1|22|3 54
(17 − 3) ÷ 7 − 2 (−4 − 8) =A. -20B. -2C. 26D. 31E. 34
Order the fractions 7/13, 8/15 and 9/17 from least to greatest.
Which of the following choices could be equal to set Z if X = {2,5,6,7,9} and Y = {2,5,7} XUYUZ = {1,2,3,4,5,6,7,8,9} xnz = {2,6} yn z = {2} A. Z= {1,4,8} B. Z= {1,3,8} C. Z= {1,3,4,8} D. Z= {1,2,3,4,6,8} E. Z= {1,2,3,5,6,8}
X = {−7,−3,2,1,5,8} and Y = {−8,−3,−1,2,5,8,9}. Which of the following is equal to the sum of the elements of X ∩ Y?A. 0B. 4C. 6D. 12E. 16
3/4 / 3/8 =a. 9/32b. 1/2c. 32/9d. 2 e. 3/2
Let the set X be all the positive composite numbers less than 10 and the set Y be all positive even numbers less than 10. Find X ∪ Y and X ∩ Y.
What is the value of b − a 8 5 a +4 24 85 8 5 b +4 36
Find the next three terms in the sequence: 7, 11, 15.
For which of the following values of x is x3 < x not a true statement? A. B. C. D. E. -3 -2 دی که ان 113 112
What is the next term in the sequence: 2,8,32,128 . . . ?
Set X = even integers and Set Y = odd integers. Therefore X ∩ Y =A. Prime numbersB. IntegersC. Empty setD. Composite numbersE. Whole numbers
Find the next three terms in the sequence: 5, 15, 45.
If 3x+2 = 81, then x =A. 5B. 4C. 3D. 2E. 1
The first term in a geometric sequence is 3 and the 4th term is 81. What is the 10th term of the sequence?A. 177,147B. 59,049C. 19,683D. 6,561E. 2,187
Multiplying a number by 4/5 and then dividing by 2/5 is the same as doing what to the number?A. Dividing by 4B. Multiplying by 1/2C. Multiplying by 2D. Dividing by 5E. Multiplying by 5
Which of the following number sets has the property that the sum of any two numbers in the set is also in the set?I. Even integersII. Odd integersIII. Composite numbersA. IB. IIC. IIID. I and IIE. I and III
The first term in a geometric sequence is 2, and the common ratio is 3. The first term in an arithmetic sequence is 3, and the common difference is 3. Let set X be the set containing the first six terms of the geometric sequence and set Y be the set containing the first six terms of the arithmetic
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