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SHSAT Math ( Section 1) (25 questions with 37 minutes)
1.  The figure below shows the number of cards owned by five students. Which two students own as many cards as Ed?
A) Richard and Ben
B) Richard and Josh
C) Eric and Josh
D) Eric and Richard
E) Eric and Ben
2.  The school bought a large number of pencils and distributed 3 to each of the students in the school with no pencil left. Which of the following could be the number of the pencils?
A) 896
B) 887
C) 890
D) 889
E) 891
3.  36 + 36 + 36
A) 36 − 1
B) 33 × 6
C) 96
D) 36 + 3
E) 36 + 1
4.  All the customers to the restaurant ordered either hamburgers or fries or both in some day. 36 customers ordered hamburgers, 45 ordered fries, and 34 ordered both. What was the total number of customers in the day to the restaurant?
A) 48
B) 81
C) 115
D) 47
E) 45
5.  Let @ represent one of the four basic operations (+, −, ×, ÷) such that, for any non-zero number n,
n @ 1 = n and 0 @ n = 0
Which arithmetic operation(s) will the symbol @ represent?
A) + only
B) ÷ only
C) × and ÷
D) − and ×
E) × only
6.  When a whole number is divided by 8, the quotient is 18 and the remainder is 2. What is the whole number?
A) 143
B) 150
C) 146
D) 147
E) 144
7.  A house was bought with a down payment of $67,000 and a monthly payment of $1,883 with a 30-year loan. Which of the following functions f models the total amount, in dollars, that would have been paid at the end of x months after the purchase, where x is positive integer less than or equal to 360?
A) f(x) = 1883 + 67000x
B) f(x) = 67000 + 1883x
C) f(x) = 67000 + 
1883x
12
 
D) f(x) = 67000 − 1883x
E) f(x) = 1883x − 67000
8.  Which of the following is the correct representation of phrase "7 less than 9 times x"?
A) 9x − 7
B) 7x − 9
C) 9x + 7
D) 7 − 9x
E) 7 < 9x
9.  
In the figure above, a line intersects with x-axis and y-axis with the given angles. What is the value of x?
10.  ABC is a right triangle. AD bisects ∠BAC and CE bisects ∠ACB. If ∠ECD = 10°, what is the degree measure of ∠ADB? Note that the diagram might not be drawn to scale.
Best GT Prep
A) 54
B) 58
C) 55
D) 53
E) can not be determined
11.  (
4
10
 )1 + (
3
10
 )2 + (
2
10
 )3 + (
1
10
 )4 =
A) 0.4981
B) 0.4881
C) 0.4971
D) 0.5981
E) 0.498
12.  If 8 hours ago was 6 A.M., what time will it be 90 hours from now?
A) 8 A.M.
B) 7 A.M.
C) 8 P.M.
D) 6 A.M.
E) 9 P.M.
13.  Which of the following numbers could be the product of two 2-digit odd numbers?
A) 74
B) 9,803
C) 65
D) 931
E) 7,634
14.  ABCD is a trapezoid. If CD = 12, AE = 6, and EB = 3. What is the area ratio of the triangle ADE to the trapezoid ABCD? Note that the diagram might not be drawn to scale.
Best GT Prep
A)
3
7
 
B)
1
3
 
C)
2
3
 
D)
2
7
 
E)
8
21
 
15.  Steve and Tom raised money for a field trip. Steve raised 50% more than Tom. The two together raised a total of $425. How much did Steve raise?
A) $258
B) $254
C) $255
D) $257
E) $170
16.  Which of the following points in the Cartesian coordinate system is closest to point (8, 9)?
A) (12, 9)
B) (4, 9)
C) (5, 13)
D) (8, 12)
E) (8, 5)
17.  What is the smallest positive integer n for which 22n − 1 is evaluated as a composite number?
A) 2
B) 4
C) 1
D) 6
E) 5
18.  The decimal number 0.58588588858888... consists of only 5's and 8's to the right of the decimal point. The first 5 is followed by one 8, the second 5 followed by two 8's, the third 5 is followed by three 8's, and so on. What is the total number of 8's between the 85th and the 87th 5 in this decimal number?
A) 171
B) 161
C) 166
D) 188
E) 185
19.  In the xy-plane, two parallel lines are 4x − 3y = 8 and 5y − kx = 8, where k is a constant. What is the value of k?
A) 4
B)
22
3
 
C) 5
D)
20
3
 
E) 7
20.  The average (arithmetic mean) of three positive numbers, a, b, and c, is 13. When the smallest of these numbers is subtracted from the sum of the other two, the result is 33. If a < b, which of the following pairs of equations could correctly express the information above?
A)
a + b + c = 39
b − (a + c) = 33
B)
a + b + c = 13
a + c − b = 33
C)
a + b + c = 39
a + b − c = 33
D)
a + b + c = 13
a + b − c = 33
E)
a + b + c = 39
a + c − b = 33
21.  All the faces of a cube are either painted white or black. There are 4 faces less in black than in white. If the volume of the cube is 1 cubic foot, what is the total area of white face(s) in square feet?
A) 1
B) 2
C) 6
D) 7
E) 5
22.  
A seven-segment display is a form of electronic display device for displaying decimal numerals. Above figure shows the numbers from 0 to 9 that are displayed with seven-segment display. Number 8 uses all the seven segments, while number 1 uses only two segments. If each number from 1 to 9 are displayed with the seven-segment displays, what is the median number of segments to display those numbers?
A) 6.5
B) 5
C) 3
D) 4.5
E) 4
23.  
In the figure above, what is the value of
AE
BE
 ? Note that the figure is not drawn to scale.
A)
1
9
 
B)
1
8
 
C)
1
3
 
D)
1
7
 
E)
1
10
 
24.  A spinner shown in the diagram has 6 equal sections. The probability of the pointer falling into each section is the same (Assume the pointer will never fall on a line between two sections). What is the probability that the product of the two numbers that occur in two tries is a prime?
Best GT Prep
A)
7
36
 
B)
1
2
 
C)
1
6
 
D)
1
12
 
E)
1
9
 
25.  Four congruent larger circles A, B, C, and D are connected with no overlapping. If the diameter of the circles is 10, what is the area of the shaded area?
Best GT Prep
A) 25 − 100π
B) 100 − 15π
C) 100π
D) 25π
E) 100 − 25π



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