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mathematics
mcgraw hills conquering sat math

McGraw Hills Conquering SAT Math 2nd Edition Robert Postman, Ryan Postman - Solutions

The height of triangle ABC is twice the height of parallelogram ADEC. If the area of triangle ABC is 14, what is the area of parallelogram ADEC?A. 1/2B. 2C. 7D. 14E. 28 D A в E с
A box contains metal and plastic paper clips. There are 16 fewer metal paper clips than plastic paper clips. If there are 100 paper clips in the box, how many plastic paper clips are there?A. 84B. 58C. 42D. 29E. 21
If x8/xk = x15 and (x7)z = x21, what is the product of k and z?A. −23B. −21C. −11D. −7E. −3
The cost of a pen decreases as the number of pens purchased increases. Which of the following could be the segment that best fits the scatterplot representing the number of pens purchased against the cost per pen? A. B. Cost Cost Number Purchased Number Purchased
The quantity of beans used in a stew is proportional to the number of servings. If three cups of beans are used for 8 servings, how many cups of beans will be used for 12 servings?A. 36B. 12C. 9D. 5.5E. 4.5
If there are no gaps between tiles used for a kitchen floor, how many 8-square-inch tiles are needed to cover a kitchen floor that is 10 feet wide and 14 feet long?A. 120B. 168C. 210D. 2,520E. 20,160
A statistics class has 10 sophomores, 5 juniors, and 15 seniors. What is the probability that a student chosen at random form the class is not a sophomore? A. B. C. D. E. 1|32|3 1256 -16
The circle graph below shows the percent of an exercise routine that is spent on each body part. If approximately 37 minutes is spent on shoulders and back, which of the following choices best approximates the amount of time spent on arms and legs?A. 25 minutesB. 26 minutesC. 27 minutesD. 28
The average of six consecutive positive integers is 14.5. What is the value of the smallest positive integer?
The scatter plot below shows the relationship between the weight of a car and average miles per gallon of the car. Which of the following accurately describes the relationship?A. As the weight of the car increases the miles per gallon increase.B. As the weight of the car increases the miles per
Jill bought a bracelet for $83.74. The price includes the 6% sales tax. What was the sticker price of the bracelet?
A password is formed with two letters followed by three one-digit numbers (0–9). If no letter and no number can be repeated, how many passwords ofthis type can be formed?A. 676,000B. 650,000C. 585,000D. 520,000E. 468,000
x − y = 3, what is the value of x2 − 2xy + y2?
The shaded part of the rectangular figure below has a constant width. What is the area of the shaded part? 5, 3 7
The perimeter of the regular hexagon below is 12. What is the length of ĀB̄ if A is equidistant from each vertex?A. 1B. 2C. 4D. 6E. 8 B A
The figure below is made up of a square and four congruent triangles. The height of each triangle is half the base. What is the probability that a point in the figure picked at random will be inside the shaded area?A. 1/2B. 1/3C. 1/4D. 2/3E. 3/4
A. 1/2B. 2C. 3D. 4E. 8 x4 1 16 and y = ₁ xy = 1 2
When k is divided by 6 the remainder is 5. What is the remainder when k + 7 is divided by 6?A. 0B. 1C. 2D. 3E. 4
The price of a shirt was discounted by 15%, and then again by 20% to a final price of $27.20. What was the original price of the shirt?A. $18B. $32C. $34D. $36E. $40
In the figure below x = 130. Which of the following is not true?A. l ∥ mB. y C. x + y = 180D. y = 40E. x + y > 90 m to 210 50°
Which of the following could be the quadratic equation of the graph shown below?A. y = −x2 − 2x − 3B. y = x2 − 2x − 3C. y = x2 + 2x − 3D. y = x2 + 2x + 3E. y = −x2 + 2x + 3 -6 4 -2 4 2 0 -4 N 6 x
A. −9B. −3C. 0D. 3E. 24 f(x) = x² + 8x + 15 x + 5 for x = 5, f(-3) =
Choose a number and continuously add a constant to form a sequence with an even number of elements. Which of the following lists all the true statements about the sequence?I. The mean is equal to the median.II. The mode is equal to the median.III. The mean is equal to the average of
Decreasing the price of an item by 20% is the same as decreasing the price by $14. What would be the discounted price of the item if the original price was decreased by 50%?A. $33B. $34C. $35D. $36E. $37
The area of a right triangle is 48 square inches, and the longer leg is 4 more than the shorter leg. What is the length of hypotenuse of this right triangle? A. 2√13 inches B. 4√13 inches C. 16√13 inches D. 4√26 inches E. 16√ 26 inches
A. 2B. 4C. 6D. 8E. 12 aΔb = a? - bl a? + 2ab + b2 * x^4 - 5' X =
The age of the wife is 36 in the married couple represented by point A. How old is the husband?A. 37B. 36C. 35D. 34E. 33
In what percent of the couples is the husband older than the wife? 2 A. 26-% ادن B. 331 3 C. 40% D. 60% E. 2 66-% 3
The radius of the circle O below is 4. What is the area of triangle AOB?A. 2√3B. 4C. 4√3E. 12 A 60° B
A. −12B. −4C. 2D. 4E. 12 If x= 2 then (-x)-³+ 2 - | به
A rectangle with height 16 is inscribed in a circle whose area is 100π. What is the of the rectangle?
If n is an odd number, which of the following is not odd?I. n + 2.II. 2n.III. n + 1.A. I onlyB. II onlyC. I and IIID. II and IIIE. I, II, and III
Jim is a car salesman who gets a base monthly salary and a commission for car he sells. Jim’s monthly earnings are given by the function f(x) = c(4 + x), where x represents the number of cars he sold for the month. If Jim sells 6 cars in a month he earns $2,000. How much is Jim’s base
f(x) = 2x + 3, f (c + 2) = 15, f (c) =
The area of the base of Cylinder A is 4 times the area of the base of Cylinder B. What is the radius of Cylinder A (rA) in terms of the radius of Cylinder B (rB)? A. TA= B. B. TA = 4TB. C. TA= 2TB- YB D. TA E. TA 1 + 2/
The figure below is formed by two overlapping equilateral triangles, each having area 36√3. The shaded region is made up of six congruent equilateral triangles. What is the perimeter of the shaded region?A. 6B. 12C. 36D. 48E. 72
A jar contains blue, red, and green marbles. The ratio of blue:red:green = 3:5:4. What is the probability that a marble chosen at random is NOT red? A. B. C. D. E. 4 5 12 3 4 7 12 2 4
The graphs of f (x) and g(x) are shown below. What is the value of g[ f (5)]?A. −1B. -1/2C. 0D. 1/2E. 2 d + 24 0 -2 4 f(x) ty
The product xy equals every value in the interval [−2,4] and no values outside the interval. Which of the following describes possible values for x and y?A. −4 ≤ x ≤ 8 and 0 ≤ y ≤ 2.B. −1 ≤ x ≤ 2 and −2 ≤ y ≤ 0.C. −2 ≤ x ≤ 1 and 0 ≤ y ≤ 2.D. −1 ≤ x ≤ 2 and
Which of the following statements must be true about the x and y coordinates that satisfy the equation ay + ax = 0, a ≠ 0, x ≠ 0, y ≠ 0?A. x > yB. x = yC. x = −yD. x < yE. x = 1/y
In triangle ABC, shown below. ĀB̄ ≈ ̄C̄D̄. What is the value of x? C 0 2 S 130° B 145° A
In the figure below, what is the value of x in terms of a and b?A. a − 180B. b − 180C. 180 − aD. 180 − bE. a + b − 180 aº to, bº
What is the area of the triangle below?A. 25√3B. 50√3C. 100√3D. 25E. 50 60° 10 10
A jar contains green, red, and blue marbles. The probability of choosing a blue marble is 1/3, the probability of choosing a red marble is 1/2, the probability of choosing a green marble is 1/6 If there are 12 marbles in the jar, and then three green marbles are added, what is the new probability
A network with n points and a segment joining each point to every other point is called a complete network of size n. If k is the number of segments in a complete network of size n, which of the following is the number of segments in a complete network of size n + 1?A. k + nB. k + n + 1C. k + n +
If x2 + 2xy + y2 = 81, x + y =A. 7B. 8C. 9D. 10E. 11
Increasing x by 19% is equal to decreasing y by 15%. x/y = .
In the xy-plane, line q and line r are parallel. Line q passes through the point (3,7), and line r passes through the point (3,2). If the y-intercept for line r is −2, what is the equation of a line perpendicular to line q, which intersects line q on the y-axis? 4 3 У-- А. У В. У с. у -x +
What is the diameter of a circle whose area is 4? A. B. 2 №₁ 4 JT C. 4√ D. 2t E. 4t
What is the area of a circle whose circumference is 12π?A. 9πB. 12πC. 16πD. 25πE. 36π
The inner circle is tangent to the outer circle at point P. Point O is the center of the outer circle and P̄Ō is the diameter the inner circle. What is the ratio of the area of the outer circle to the area of the inner circle?A. 2:1B. 3:1C. 3:2D. 4:1E. 5:2 P
What is the area of the circle O if the length of ArcPQR is 8π?A. 24πB. 60πC. 90πD. 120πE. 144π P 0 120° R Q
The area of the circle O below is 81π. What is the length of B̄Ā?A. 4.5B. 5C. 5.5D. 6E. 6.5 A B 30% C 60%
The area of the ΔABC is 18, what is the area of the shaded region?A. 18B. 9πC. 9π − 18D. 9π + 18E. 27π B 90° A С
Point O is the center of both circles seen below. What is the area of the shaded regions?A. 100πB. 50πC. 36πD. 16πE. 4π O 4
The area of circle P is 64π. QR tangent to circle P at point Q. If QR = 12, then PR = P R
The area of a circle is doubled. What is the ratio of the circle’s new radius to the circle’s original radius? A. B. C. D. E. 뷔 뷔
What is the value of x in circle O seen below?A. 20B. 30C. 40D. 50E. 60 100°
The diameter of the large circle is 12. The center of each of the three congruent smaller circles lies on the diameter of the larger circle. What is the area of the shaded region?A. 36πB. 24πC. 18πD. 12πE. 6π ӨӨ
The area of the outer square is 256. What is the area of the inner square? c
In the figure above, l ∣∣ m, x =A. 30B. 40C. 50D. 60E. 70 14 m 150°
x + y =A. 90B. 110C. 120D. 150E. 170 to 30%
Using the above diagram with p ∣∣ q, what is the value of x?A. −2B. −3C. −4D. −5E. −6 Р 9 (3x + 5)° /(2x+3)
l ∣∣ m, m∠4 = (3x + 5)° and m∠6 = (4x − 7)°m∠4 = and m∠6 = 14 m 1/2 3/4 5/6 7/8
B̄D̄ bisects ∠ABC, x =A. 40B. 45C. 50D. 55E. 60 80% B A, C D
m∠5 = (4x + 6)° and m∠8 = (7x − 15) m∠5 = and m∠8 =
All the circles below are congruent. The total area of the nine congruent circles is 324π. The square passes through the center of eight circles as shown. What is the area of the shaded region?A. 1,296 − 144πB. 576 − 144πC. 324 − 144πD. 576 − 72πE. 324 − 72π 88
Which of the following statements must be true?I. a = dII. a + c = 180III. a + d = 90A. IB. IIC. I and IID. I and IIIE. I, II, and III 60 aº do
The product of x and x increased by 5 is equal to −6. What is the product of the possible values of x?
The product of a and 4 is twice the sum of 3 and 5. a =
The sum of x and y is twice x. y =A. xB. 2xC. x2D. x/2E. x - 2
2 times x plus 6 is equal to 5 times x less 3. x =A. 1B. 2C. 3D. 4E. 5
Car A travels 300 miles in 5 hours. Car B traveled the same distance in 7 hours. If RA is the rate of Car A, and RB is the rate of Car B, what is the rate of Car B with respect to the rate of Car A?
4 times x is equal to x increased by 6. x =A. 1B. 2C. 3D. 4E. 5
Jack earns twice as much as Phil. Don earns 3 times as much as Phil. If J is Jack’s salary, what is Don’s salary with respect to J?
On Tuesday Ray rode his bike 10 miles. On Wednesday he increased Tuesday’s distance by 5 miles. On Thursday he decreased Wednesday’s distance by 7 miles. On Friday he increased Thursday’s distance by 12 miles. How many total miles did Ray ride over the 4-day period?A. 50B. 51C. 52D. 53E. 54
Sarah ran 1 mile in 8 minutes, at a constant rate. There are 5,280 feet in a mile. How many feet did Sarah run in 120 seconds?
Zach earns $1,400 plus 15% commission of his sales every month. What was Zach’s total sales for a month when he earned $2,000 in that month?
Bob invested in a stock that increased in value by 17% to 25.74. What was the actual increase in the stock’s value?
Lindsey earns $15 hour for the first 40 hours she works in a week and 50% more for every hour over 40. How many hours did Lindsey work in a week, when she was paid $937.50 before taxes?A. 15 hoursB. 30 hoursC. 40 hoursD. 45 hoursE. 55 hours
40% of the students in a class are female. If there are 10 females in the class, how many males are there in the class?A. 5B. 10C. 15D. 20E. 25
Julie worked 3 less than twice as many hours as Bruce. Which of the following choices represents the number of hours that Julie, J, worked based on the number of hours that Bruce, B, worked?A. J = 2B − 3B. J = 2 − 3BC. J = 2B + 3D. J = 3 − 2BE. J = −2B − 3
It takes a copy machine 6 minutes to complete a certain copy job. How minutes until the copy machine is finished with the job after 2/3 of the job has been completed?A. 4 minutesB. 3.5 minutesC. 3 minutesD. 2.5 minutesE. 2 minutes
Every day before work Matt buys a cup of coffee at the local coffee shop. If Matt has spent $27 on his last 20 cups of coffee, each cup the same price, how much is each cup of coffee?
On a varsity baseball team 1/2 of the players are seniors, 1/4 of the players are juniors, and the remaining 5 players are sophomores. How many players are on the team? A. 16B. 17C. 18D. 19E. 20
Gary’s winning time in a 100-yard race is 11 seconds. Frank is 3 yards behind Gary Gary finishes the race. What is Frank’s average speed in feet per second when Gary crosses the finish line, to the nearest tenth?
During a 4-week proper eating and exercise program, Bill lost 9 pounds. If the amount he lost in the second 2-week period is half the amount he lost in the first 2-week period, how many pounds did Bill lose in the second 2-week period?A. 3 poundsB. 4 poundsC. 5 poundsD. 6 poundsE. 7 pounds
n + 5 = 8, 3(n + 5) =A. 8B. 15C. 16D. 24E. 30
If x + y = 4, then 2(x + y) =A. 2B. 4C. 6D. 8E. 10
If 2x + 6 = 4x − 1, what is the value of x?A. 2.5B. 3C. 3.5D. 4E. 4.5
During a baseball season Andrew got a hit in 35% of his at-bats, 12.5% of which were doubles. If Andrew hit 21 doubles in the season, how many at-bats did he have?A. 168B. 240C. 360D. 480E. 540
Tim earns $2,000 more a year than Pete. If Pete gets a 5% raise, their earnings would be equal. How much money does Pete earn a year?A. $30,000B. $35,000C. $40,000D. $45,000E. $50,000
A theater charges $5 for children and $7 for adults to attend a children’s play. A total of 1,600 tickets were sold for a total of $9,200. How many children’s tickets were sold?A. 600B. 700C. 800D. 900E. 1,000
There is an inverse relationship between the squirrel (s) and the fox (f) population in a certain wooded area. The point (s, f) represents the number of squirrels and foxes. If the point (200,100) correctly represents these two populations at a certain time of the year, which of the following
k divided by 4 has a remainder of 3. What is the remainder when k + 3 is divided by 4?
If 4a − 7 > 9, then which of the following cannot be equal to a?A. 3B. 5C. 7D. 9E. 11
Which of the following graphs of a quadratic function has a negative y-intercept positive x-intercepts? A. B. C. -6 4 -2 -6 4 -2 -6 a 2 0 -2 y 4 0 2 y 4 B 4 -2 0 -2 2 4 6 6 X x X
(y + 7) + k = y − 2, k =A. −2.5B. −4.5C. −5D. −9E. −18
Which of the following figures could not be formed when the cone shown below is intersected with a plane? A. O
75% of n is 45. n is what percent of 90?A. 30%B. 33%C. 33 1/3%D. 50%E. 66 2/3%

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