PSAT PRACTICE MATH WORKSHEET 7

(1)  It takes George 3 minutes to read 300 words. If each page in a book that he is reading has 750 words, how long will it take George to read 6 pages ?

(A)  30 minutes  (B)  45 minutes  (C)  60 minutes 

(D)  90 minutes  (E)  250 minutes

Solution

(2)  [(1/2) - (3/4)]² + (5/10)  =  

(A)  9/16  (B)  1/2  (C)  1/16  (D)  3/4  (E)  1/4

Solution

(3)  If x = 2⁵ ⋅ 3² ⋅ 7, then what is the value of x ?

(A)  1150  (B)  2000  (C)  2015  (D)  2016  (E)  3050

Solution

(4)  A right cylindrical can is being filled with water. At 1 P.M, it is half full. At 2 P.M, it is 3/4^th full. At this rate, when was it empty ?

(A)  11 : 00 A.M  (B)  11 : 30 A.M  (C)  12 : 00 P.M

(D)  12 : 30 P.M  (E)  3 : 00  P.M

Solution

(5)  If x⁸  =  (2²) ⁴, what is x² ?

(A)  2  (B)  4  (C)  8  (D)  64  (E)  128

Solution

(6)  James has a work to finish. He finishes 1/8 of the total work on the first day. What fraction of the work is left ?

(A)  1/8  (B)  3/8  (C)  7/8  (D)  3/4  (E)  1/4

Solution

(7)  

There are two different pathways connecting 1 and and 2. How many fewer steps is the solid line path than the dotted line path. (A step is defined as a line segment connecting 2 circles)

(A)  -4  (B)  -1  (C)  1  (D)  4  (E)  7

Solution

(8)  Jackie and Jesse each solve the same problem in a different way 

Problem √(a + b)  =  ?

Jackie's way  =  √(a + b)  =  √a + √b

Jesse's way : √(a + b)  =  √(a+b)

If a = 9 and b = 25, how much bigger is Jakie's way than Jesse's way ?

(A)  -2  (B)  0  (C)  2  (D)  √36  (E)  8 - √34

Solution

(9)  If  θ { a, b, c, d, e, f, g, h, i }  =  [ab - cd + (ef)² (gh)²]/i

Which cannot be value of θ ?

(A)  θ (0, 0, 0, 0, 0, 0, 0, 0, 1)

(B)  θ (1, 1, 1, 1, 1, 1, 1, 1, 0)

(C)  θ (2, 2, 2, 2, 2, 2, 2, 2, 10)

(D)  θ (2,3, 1, 4, 5, 6, 7, 0, 10)

(E)  0

Solution

(10)  If James grows by 20 inches every day starting Monday. What is the difference in his height between Wednesday and Monday ?

(A)  0 inches  (B)  20 inches  (C)  30 inches 

(D)  40 inches  (E) 60 inches

(1)  Evaluate ([1/2)-(3/4)] ÷ (1/2)  =  

(A)  1/2  (B)  3/2  (C)  -1/2  (D)  -3/4  (E)  1

Solution

(2)  

Line q intersects the parallel lines p and l. What is y³/3 ?

(A)  x⁴/3  (B)  x⁶  (C)  x⁹  (D)  x⁴/9  (E)  x⁶/3

Solution

(3)   Given the arithmetic sequence x, y, 30, z, f then find the value of x + y + z + f

(A)  60  (B)  80  (C)  120  (D)  130  (E)  140

Solution

(4)  If (-1)²  =  1, then the value (-1) ²⁰²³ is

(A)  -2023  (B)  -1  (C)  0  (D)  1  (E)  2023

Solution

(5)  Caroline has two times as many marbles as Jake. Jake has 12 less than 7 times as many marbles James has. James has 14 marbles. How many marbles dies Caroline have ?

(A)  52  (B)  54  (C)  86  (D)  98  (E)  172

Solution

(6)  John is trying to escape a ditch. Every time he jumps 10 meters, he falls back 5 meters right after. The ditch is 19 meters long. What is the minimum number of jumps he needs to make to escape ?

(A) 3  (B) 4  (C) 5  (D) 7  (E) 8

Solution

(7)  What is the largest number of digits that the product of  3 digit and 2 digit number has ?

(A)  4  digit  (B)  5 digit  (C)  6 digit 

(D)  7 digit  (E)  8 digit

Solution

(8)  If Fn  =  2 F_n-1 + 3 F_n-2, then what is F₃ if F₁  =  F₂  =  1 ?

(A)  2  (B)  3  (C)  4  (D)  5  (E)  10

Solution

(9)  Sam walks 3m to the west, then 4m south, then 4 m North. How far is he from his original location ?

(A)  3 m (B)  5 m (C)  7 m  (D)  8 m  (E)  12 m

Solution

(10)  If a =  3 and b = 5, what is the value of 9a/(b-a) ?

(A)  9  (B)  27  (C)  13/5  (D)  27/2  (E)  26/5

Solution

(11)  If (x - 2)² + 5(x - 2) = -6 Which of the following could be the value of x - 2?

(A)  -1      (B)  -3     (C)  -4    (D)  -5

Solution

(12) At a science museum, a robotics club hosted a fund raising event for no more than 650 people. The club sold member tickets and y nonmember tickets. Member tickets sold for $20 each and nonmember tickets sold for $40 each. The cost to rent the museum for the event was a flat fee of $3,000 plus $12.50 per ticket sold. The equation shown gives the total profit P in dollars, earned from selling tickets to the event.

P = (20 - 12.50)x + (40 - 12.50)y - 3000

The robotics club made a total profit of $8,125 from selling tickets to the event. If 200 member tickets were sold, how many nonmember tickets were sold?

A) 450      B) 350       C) 240        D) 131

Solution

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