Daniel rides to school each day on a path that takes him first to a point directly east of his house and then from there directly north to his school.. How much shorter would his ride to
Trang 158 Is x + y 2z ?
(1) ABC is equilateral
(2) AD ⊥ BC
59 The circles in the diagram are concentric circles What is the area of the shaded region?
(1) The area of the inner circle is 25
(2) The diameter of the larger circle is 20
60 Find the value of x.
(1) The length of BC is 23.
A
30°
x
A
z
x y
Trang 261 What is the value of a + b?
(1) a 2 + b2 = 13
(2)
62 Between what two numbers is the measure of the third side of the triangle?
(1) The sum of the two known sides is 10
(2) The difference between the two known sides is 6
63 What is the area of the circle?
(1) The radius is 6
(2) The circumference is 12
64 What is the positive value of z ?
(1) 3y + z = 4
(2) z2– z = 12
65 Two cars leave the same city traveling on the same road in the same direction The second car leaves
one hour after the first How long will it take the second car to catch up with the first?
(1) The second car is traveling 10 miles per hour faster than the first car
(2) The second car averages 60 miles per hour
66 In right triangle XYZ, the m∠y = 90 What is the length of XZ?
(1) The length of YZ = 6.
(2) m ∠z = 45
67 Is ?
(1) 3x = 6y
(2)
68 What is the total cost of six pencils and four notebooks?
(1) Ten pencils and nine notebooks cost $11.50
(2) Twelve pencils and eight notebooks cost $11.00
69 What is the ratio of the corresponding sides of two similar triangles?
(1) The ratio of the perimeters of the two triangles is 3:1
(2) The ratio of the areas of the two triangles is 9:1
x
y 7 1
x
y 7 x y
2b12
a
Trang 370 What percent of the class period is over?
(1) The time remaining is 14of the time that has passed
(2) The class period is 42 minutes long
71 Daniel rides to school each day on a path that takes him first to a point directly east of his house and
then from there directly north to his school How much shorter would his ride to school be if he could walk on a straight-line path directly to school from his home, instead of east and then north?
(1) The direct straight-line distance from home to school is 17 miles
(2) The distance he rides to the east is 7 miles less than the distance he rides going north
72 What is the slope of line m?
(1) Line m intersects the x-axis at the point (4, 0).
(2) The equation of line m is 3y = x – 4.
73 Jacob is a salesperson He earns a monthly salary plus a commission on all sales over $4,000 How
much did he earn this month?
(1) His monthly salary is $855 and his total sales over $4,000 were $4,532.30
(2) His total sales for the month were $8,532.30
74 Is ABC similar to ADE?
(1) BC is parallel to DE
(2) AD = AE
75 The formula for compounded interest can be defined as A = p (1 + r) n , where A is the total value of the investment, p is the principle invested, r is the interest rate per period, and n is the number of periods.
If a $1,000 principle is invested, which bank gives a better interest rate for a savings account, Bank A or Bank B?
(1) The interest rate at Bank A is 4% compounded annually
(2) The total amount of interest earned at Bank B over a period of five years is $276.28
A
Trang 476 A fence has a square gate What is the height of the gate?
(1) The width of the gate is 30 inches
(2) The length of the diagonal brace of the gate is 30 2 inches
77 Find the area of the shaded region.
(1) m ∠A = 43°
(2) AB = 10 cm.
78 A circle and a straight line are drawn on the same coordinate graph In how many places do the two
graphs intersect?
(1) The equation of the circle is x2+ y2= 25
(2) The y-intercept of the straight line is 6.
79 Michael left a city in a car traveling directly west Katie left the same city two hours later going directly
east traveling at the same rate as Michael How long after Katie left will they be 350 miles apart? (1) An hour and a half after Katie left they are 250 miles apart
(2) Michael’s destination is 150 miles farther than Katie’s
80 What is the area of the shaded region?
(1) ABC is equilateral
(2) The length of BC is 16 inches
B
C
D
C
Trang 5A n s w e r E x p l a n a t i o n s
1 d The only prime numbers that satisfy this condition are 2 and 5 Since x y, x = 5 and y = 2
There-fore, by substitution, 2 (5) + 2 = 10 + 2 = 12
2 b Convert 6% to its decimal equivalent of 0.06 and 14% to 0.14 The key word “product” tells you to
multiply, so 0.06 × 0.14 = 0.0084, which is choice b
3 b 212miles divided by 14is ten quarter miles Since the first quarter mile costs x amount, the other nine
quarter miles cost 14x, so 9 ×14x = 94x x + 94x = 44x + 94x = 134x
4 a.The sum of the measures of the two shorter sides of a triangle must be greater than the longest side.
Since 3 + 3 5, statement I works Since 6 + 6 = 12 and 1 + 2 = 3, they do not form the sides of the triangle The answer is statement I only
5 a If the average of four rounds is 78, then the total points scored is 78 × 4 = 312 If his score were to drop 2 points, that means his new average would be 76 A 76 average for five rounds is a total of 380 points The difference between these two point totals is 380 – 312 = 68 He needs a score of 68 on the fifth round
6 e Suppose Celeste worked for 8 hours each day for 5 consecutive days Her total pay would be found
by finding her total hours (8 × 5 = 40) and then multiplying 40 by her pay per hour ($9.50) Since you are only multiplying to solve the problem, the expression is 9.50 × d × h or 9.50dh
7 e To make this problem easier, assume the initial cost of the jacket was $100 The first markdown of
20% would save you $20, bringing the cost of the jacket to $80 For the second markdown, you should
be finding 20% of $80, the new cost of the jacket 20% of 80 = 0.20 × 80 = 16 If you save $16 the sec-ond time, the final cost of the jacket is 80 – 16 = $64 Since the initial cost was $100, $64 is 64% of this price
8 d First calculate the number of letters completed by 30 typists in 20 minutes Let x = the number of
letters typed by 30 typists and set up the proportion Cross-multiply to get
20x = 1,440 Divide both sides by 20 and get x = 72 Since 20 minutes is one-third of an hour, multiply
72 × 3 = 216 to get the total letters for one hour
9 d This problem can be solved by using the simple interest formula: interest = principal × rate × time Remember to change the interest rate to a decimal before using it in the formula I = (1,000)(0.05)(2)
= $100 Since $100 was made in interest, the total in the bank account is $1,000 + $100 = $1,100
10 a Using the rules for exponents, choice a simplifies to 25and choices b, c, and d simplify to 26= 64
Choice e becomes 27 × 81, which is obviously much larger than 64
typists letters 20
48 30
x
Trang 611 d Let x = the number of liters of the 40% solution Use the equation 0.40x + 0.20(35) = 0.35 (x + 35)
to show the two amounts mixed equal the 35% solution
Solve the equation: 0.40x + 0.20(35) = 0.35(x + 35)
Multiply both sides by 100 in order to work with more compatible numbers:
40x + 20(35) = 35(x + 35) 40x + 700 = 35x + 1,225
Subtract 700 on both sides: 40x + 700 – 700 = 35x + 1,225 – 700
Subtract 35x from both sides 40x – 35x = 35x – 35x + 525
Divide both sides by 5:
x = 105 liters of 35% iodine solution
12 b Let x = the part of the floor that can be tiled in 1 hour Since Steve can tile a floor in 6 hours, he can
tile of the floor in 1 hour Since Cheryl can tile the same floor in 4 hours, she can tile of the floor
in 1 hour Use the equation , where represents the part of the floor they can tile in an
hour together Multiply each term by the LCD = 12x. The equation
simplifies to 2x + 3x = 12 5x = 12 Divide each side by 5 to get hours Since 0.4 times 60 minutes equals 24 minutes, the final answer is 2 hours 24 minutes
13 a The length of one side of a square is equal to the square root of the area of the square Since the area
of the squares is 9, 16, and 25, the lengths of the sides of the squares are 3, 4, and 5, respectively The triangle is formed by the sides of the three squares; therefore, the perimeter, or distance around the tri-angle, is 3 + 4 + 5 = 12
14 c Suppose that the shoes cost $10 $10 – 10% = 10 – 1 = $9 When the shoes are marked back up, 10%
of $9 is only 90 cents Therefore, the markup must be greater than 10% = , or about 11%
15 b Note that the figure is not drawn to scale, so do not rely on the diagram to calculate the answer.
Since the angles are adjacent and formed by two intersecting lines, they are also supplementary
Com-bine the two angles and set the sum equal to 180 2x + 3x – 40 = 180 ComCom-bine like terms and add 40
to both sides 5x – 40 + 40 = 180 + 40 5x = 220 Divide both sides by 5 to get x = 44 Then 2x = 88 and 3x – 40 = 92 The smaller angle is 88.
16 b x, x + 2, and x + 4 are each two numbers apart This would make x + 2 the average of the three
numbers If x + 2 = 33, then x = 31.
17 d It costs d for the first 100 posters plus the cost of 25 additional posters This translates to d + 25e,
since e is the cost of each poster over the initial 100.
18 d If the volume of the cube is x3, then one edge of the cube is x The surface area of a cube is six times the area of one face, which is x times x The total surface area is 6x2
19 c The next larger multiple of two would be x – 3 + 2, which is x – 1 In this case, remember that any
even number is a multiple of two and all evens are two numbers apart If x – 3 is a multiple of two,
you can assume that it is also an even number This number plus two would also produce an even
1119%
$1
$9
x12
5 2.4
12x×1
6 12x ×1
4 12x ×1
x
1
x
1
61
4 1
x
1 4 1
6
5x
5 525 5