Scholastic Aptitude Test (SAT)
-
Upload
quamar-sexton -
Category
Documents
-
view
49 -
download
4
description
Transcript of Scholastic Aptitude Test (SAT)
![Page 1: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/1.jpg)
SCHOLASTIC APTITUDE TEST (SAT)
PREP
![Page 2: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/2.jpg)
PRACTICE PROBLEMS
VERSION 3
![Page 3: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/3.jpg)
1. ( 1 + 1 ) ÷ 1 = 5 3 2
(A) 18
(B) 14
(C) 415
(D) 12
(E) 16 15
( 1 + 1 ) ÷ 1 =
5 3 2
3 + 5 ÷ 1 =
15 2
8 • 2 = 16
15 1 15
(E) 1615
SAT
![Page 4: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/4.jpg)
2. x 2 – 2 x when x = – 2 ?
(A) – 8
(B) – 4
(C) 0
(D) 4
(E) 8
x 2 – 2 x when x = – 2 ? (– 2 ) 2 – 2 (– 2 ) =4 + 4 = 8
(E) 8
SAT
![Page 5: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/5.jpg)
3. Kate read 96 pages in 2 hours and 40 minutes. What was Kate’s average rate of pages per hour?
(A) 24
(B) 30
(C) 36
(D) 42
(E) 48
x = 96 60 160
x = 96 • 60 160
x = 6 • 60 10
x = 6 • 6 = 36
(C) 36
SAT
![Page 6: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/6.jpg)
4. For how many integer values of x will 7/8 be greater than ¼ and less than 1/3 ?
(A) 6
(B) 7
(C) 12
(D) 28
(E) Infinite many
1 > 7 > 1 3 x 4
( 1 > 7 > 1 ) 12 x 3 x 4 4 x > 84 > 3 x _______________________________________________________________________________________
4 (22) > 84 > 3 (22) --- 88 > 84 > 66
4 (23) > 84 > 3 (23) --- 92 > 84 > 69
4 (24) > 84 > 3 (24) --- 96 > 84 > 72
4 (25) > 84 > 3 (25) --- 100 > 84 > 75
4 (26) > 84 > 3 (26) --- 104 > 84 > 78
4 (27) > 84 > 3 (27) --- 108 > 84 > 81
(A) 6
SAT
![Page 7: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/7.jpg)
5. What is the average (arithmetic mean) of 2 x + 5, 5 x – 6 , – 4 x + 2 ?
(A) x + 1 3
(B) x + 1
(C) 3 x + 1 3
(D) 3 x + 3
(E) 3 x + 3 1 3
2 x + 5 5 x – 6– 4 x + 2 3 x + 1
3 x + 1 = x + 1 3 3
(A) x + 1 3
SAT
![Page 8: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/8.jpg)
7. In this triangle, what is the degree measure of angle B ?
(A) 45
(B) 60
(C) 65
(D) 75
(E) 80
< B + < C + < A = 180⁰
< B + 45⁰ + 70⁰ = 180⁰
< B + 115⁰ = 180⁰
< B = 180⁰ – 115⁰ = 65⁰
(C) 65⁰
SAT
45⁰BC
A
70⁰
![Page 9: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/9.jpg)
8. For all x ≠ 0, x2 + x2 + x2 = x2
(A) 3
(B) 3 x
(C) x2
(D) x3
(E) x4
x2 + x2 + x2 = x2
3 x2 = 3 x2
(A) 3
SAT
![Page 10: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/10.jpg)
8. For all x ≠ 0, x2 + x2 + x2 = x2
(A) 3
(B) 3 x
(C) x2
(D) x3
(E) x4
x2 + x2 + x2 = x2
3 x2 = 3 x2
(A) 3
SAT
![Page 11: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/11.jpg)
9. The equation x2 = 5x – 4 has how many distinct real solutions ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) Infinitely many
x2 = 5 x – 4 x2 – 5 x + 4 = 0
( x – 4 ) ( x – 1 ) = 0
x = 4 or 1 (C) 2
SAT
![Page 12: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/12.jpg)
10.Which of the following sets of numbers has the property that the sum of any two numbers in the set is also a number in the set ?
I. The set of even integersII. The set of odd integersIII. The set of prime numbers
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
1 + 3 = 4 Ex where odd integers doesn’t work
3 + 5 = 8 Ex where prime doesn’t work
2 + 4 = 6 Even Integers does work
(A) I only
SAT
![Page 13: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/13.jpg)
11.Bob’s average (arithmetic mean) score after 4 tests is 89. What score on the 5th test would bring Bob’s average up to exactly 90?
(A) 90
(B) 91
(C) 92
(D) 93
(E) 94
89 x 4 = 356 90 x 5 = 450
So, the difference between the 2 gives us the total needed to average 90
450 – 356 = 94(F) 94
SAT
![Page 14: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/14.jpg)
12.The price s of a sweater is reduced by 25% for a sale. After the sale, the reduced price is increased by 20%. Which of the following represents the final priceo f the sweater ?
(A) 1.05 s
(B) .95 s
(C) .90 s
(D) .85 s
(E) .80 s
Sale price is 25 % off or .75 s
Post sale price is increased by 20 %
The increase = .75 s x .2 = .15 s
Then we add .75 s + .15 s = 90 s
(C) .90 s
SAT
![Page 15: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/15.jpg)
13. How many distinct prime factors does the number 36 have ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
362 x 182 x 3 x 62 x 3 x 2 x 3
(A) 2
SAT
![Page 16: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/16.jpg)
15. If the area of a triangle is 36 and its base is 9, what is the length of the altitude to that base?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 12
AT = 1 hb = 36 2 1 h (9) = 36 2 h (9) = 36 2 h = 36 • 2 9 h = 8
(D) 8
SAT
![Page 17: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/17.jpg)
15.Let a be defined for all positive integers a by the equation a = a – a If x = 3, what is the value of x ? 4 6
(A) 18
(B) 28
(C) 36
(D) 40
(E) 54
If a = a – a 4 6 x = x – x 4 6If x = 3 3 = x – x 4 612 (3 = x – x ) 4 636 = 3 x – 2 x
36 = x
(C) 36
SAT
![Page 18: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/18.jpg)
16. Betty has q quarters, d dimes, n nickels and no other coins in her pocket. Which of the following represents the total number of coins in Joan’s pocket ?
(A) q + d + n
(B) 5q + 2d + n
(C) .25q + .10d + .05n
(D) (25 + 10 + 5) (q + d + n )
(E) 25q + 10d + 5n
This is a “TRAP” question:The problem only asks for the total # of coins, NOT the total value of coins, which is what you are lead to think.
(A) q + d + n
SAT
![Page 19: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/19.jpg)
17. Which of the following is an equation for the graph above ?
(A) y = –2 x + 1
(B) y = x + 1
(C) y = x + 2
(D) y = 2 x + 1
(E) y = 2 x + 2
The slope is 2 and the y-intercept is 2, so the answer is y = 2 x + 2
(E) y = 2 x + 2
SAT
•
•
![Page 20: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/20.jpg)
18.If an integer is divisible by 6 and 9, then the integer must be divisible by which of the following ?
I. 12II. 18III. 36
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Prime factors of 6 are 2 x 3, so any # divisible should have at least one 2 and one 3 as factors
Prime factors of 9 are 3 x 3, so any # divisible should have at least two 3’s as factors
Any # divisible by both should have at least one 2 and two 3’s and the first possibility is 2 x 32 or 18
12 and 36 require two 2’s in its prime factorization
12 doesn’t have a 2nd prime factor of 336 does work in some cases by NOT all, such as the most obvious one, 6 x 9 or 54.
(B) II only
SAT
![Page 21: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/21.jpg)
19. In this figure, O is the center of the circle and P, O, and Q are collinear. If < ROQ measures 50⁰, what is the degree measure of <RPQ ?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
< POR =180⁰ – 50 ⁰ = 130 ⁰PO = OR (all radii are =) < RPQ = <PRO (base <‘s of Isosceles are =)and < QPR + <PRO = 50 ⁰ < RPQ =25
(B) 25
SAT
QOP
R
50⁰?
![Page 22: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/22.jpg)
20.A wooden cube with volume 64 is sliced in half horizontally,. The two halves are then glued together to form a rectangle solid which is not a cube. What is the surface area of this new solid?
(A) 128
(B) 112
(C) 96
(D) 56
(E) 48
E3 = 4 x 4 x 4 = 64Two rectangle solids 4 x 4 x 2, when glued 2 x 4 x 8Then Top and Bottom = 8 x 4 = 32 or 64 totalThen Front and Back = 8 x 2 = 16 or 32 totalThen two sides = 4 x 2 = 8 or 16 total
(B) 112
SAT
64
E3 = 4 x 4 x 4 = 64
2
2
44
24
4 4
Grand total of 6 sides = 64 + 32 + 16 = 112
![Page 23: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/23.jpg)
21.A drawer contains 6 blue socks, 12 black socks and 15 white socks. If one sock is chosen at random, what is the probability that it will be black?
(A) 14
(B) 13
(C) 38
(D) 12
(E) 58
6 blue12 black15 white32 Total
Black 12 = 3Total 32 8
(C) 38
SAT
![Page 24: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/24.jpg)
22.Danielle drives from here home to the store at an average speed of 40 miles per hour. She returns home along the same route at an average speed of 60 miles per hour. What is her average speed, in miles per hour, for her entire trip ?
(A) 45
(B) 48
(C) 50
(D) 52
(E) 55
This is a TRAP question ! We are NOT given enough information to use a distance formula. So we need to improvise by selecting a distance that is easy to work with. Since we have speeds of 40 and 60 mph, why not use a multiple of both, such as, 120
Distance = rate x time(going trip) 120 = 40 t where t = 3 hours(return trip) 120 = 60 t where t = 2 hours Now 240 = 5 r, where r = 48 miles per hour
(A) 48
SAT
![Page 25: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/25.jpg)
23. What is the area of a right triangle if the length of one leg is a and the length of the hypotenuse is c ?
(A) ac 2
(B) ac – a2
2
(C) a3 + c3
2
(D) a c2– a2
2
(E) a2 + c2
c2 = a2 + b2
c2 – a2 = b2
√ c2 – a2 = b
AT = ½ h b
A = 1 a ( √ c2 – a2 ) 2
SAT
c2
b2
a2
(D)
![Page 26: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/26.jpg)
24. In ∆ PRS, RT is the altitude to side PS and QS is the altitude to side PR. If RT = 7, PR – 8 and QS = 9, what is the length of PS ?
(A) 5 1 7
(B) 6 2 9
(C) 7 7 8
(D) 10 2 7
(E) 13 4 9
AT = ½ h b
Using altitude QS and side PR = ½ • 9 • 8 = 36
Using altitude RT with side PS = ½ • 7 • PS = 36
7 PS = 36 then, PS = 36 • 2 = 10 2 2 7 7
(D) 10 2 7
SAT
P
Q
R
ST
![Page 27: Scholastic Aptitude Test (SAT)](https://reader033.fdocuments.us/reader033/viewer/2022061616/56813320550346895d99f479/html5/thumbnails/27.jpg)
25.There are 3 routes from River City to Bayville.There are 4 routes from Bayville to Eagles Mere.There are 3 routes from Eagles Mere to Twin Peaks.If a driver must pass through Bayville, and Eagles Mere exactly once, how many possible ways are there to go from River City to Twin Peaks.
(A) 6
(B) 10
(C) 12
(D) 24
(E) 36
River City1 2 3 [ 3 ]
xBayville1 2 3 4 [ 4 ] x Eagles Mere1 2 3 [ 3 ] = Twin Peaks [ 36 ]
(E) 36
SAT