PSAT PRACTICE TEST MATH

Question 1 :

The average of 7 consecutive even integers is 20. What is the median ?

(A)  18  (B)  20  (C)  20.5  (D)  22  (E)  24

Solution :

Let "x" be the even integer

1st even integer  =  x 

2nd even integer  =  x + 2

3rd even integer  =  x + 4

4th, 5th, 6th, 7th numbers are x + 6, x + 8, x + 10 and  x + 12 respectively.

Average of 7 consecutive even integer 

=  (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12)/7

20  =  (7x + 42)/7

140  =  7x + 42

7x  =  140 - 42

7x  =  98

x  =  14

Median  =  x + 6  

  =  14 + 6

  =  20

Question 2 :

What is 0.003815 in scientific notation ?

(A)  3815 x 10-2  (B)  3.815 x 10-3  (C)  3.85 x 10

(D)  0.003815 x 102    (E)  3.815 x 103

Solution :

In order to convert the given number in scientific notation, we have to move the decimal point to the right side

 0.003815  =  3.815 x 10-3

Question 3 :

In the figure above, what is the length of AC ?

(A)  8  (B)  12  (C)  2√66  (D)  2√289  (E)  √314

Solution :

Since the given triangle is right triangle, we may use the Pythagorean theorem.

BC2  =  AB2 + AC2

172  =  52 + AC2

AC=  289 - 25

AC2  =  264

AC  =  √264

AC  =  √(2 ⋅ 2 ⋅ 66)

AC  =  2√66

Question 4 :

What time will it be 53 hours after 3 : 30 P.M on Thursday ?

(A)  10 π/25  (B)  5/2  (C)  2/5  (D)  25 π/10  (E)  5π/25

Solution :

First let us divide 53 by 24.

3 : 30 PM - 3 : 30 PM (Thursday - Friday)

3 : 30 PM - 3 : 30 PM (Friday - Saturday)

53  =  2 (24) + 5

5 hours after 3 : 30 P.M on Saturday

8 : 30 PM on Saturday

Question 5 :

If x represents the circumference of the above figure and y represents the area, what is x/y ?

(A)  9.8 x 105 kg  (B)  9.8 x 103 kg  (C)  9.8 kg

(D)  9.8 x 10-3 kg  (E)  9.8 x 10-5 kg

Solution :

Radius of the circle  =  5

Circumference of circle (x) =  2πr  =  2 π (5)  =  10 π

Area of circle (y) =  πr2

x/y  =  10 π/πr2

  =  10/r2

  =  10/52

  =  10/25  =  2/5

Question 6 :

A certain substance has a mass of 98 milligrams. What is the mass of this substance in kilograms ?

Solution :

1 milligram  =  (1/106) kilograms

98  =  98/106 kilogram

  =  9.8 x 101 x 10-6

  =  9.8 x 10-5 kilogram

Question 7 :

Samuel scored 72, 92 and 80 on his first three exams. What is the minimum score he needs to get an average of 85 ?

(A)  85  (B)  90  (C)  93  (D)  96  (E)  100

Solution :

Let "x" be the required score.

(72 + 92 + 80 + x)/4  =  85

(244 + x)  =  340

x  =  340 - 244

x  =  96

Question 8 :

Five out of 10 marbles in a bag are red. What percentage of the marbles is not red ?

(A)  50%  (B)  55%  (C)  60%  (D)  75%  (E)  80%

Solution :

Total number of marbles  =  10

Number of red marble  =  5

Percentage of red marble  =  (5/10) x 100 %

  =  50%

What percentage of the marbles it is not red  =  50%

Question 9 :

In the figure above, the rectangle ABCD is inscribed in the circle.Where E is the center and the radius is 5. If the length of BD is 6, what is the area of rectangle ABCD ?

(A)  30  (B)  48  (C)  60  (D)  25   (E)  180

Solution :

In order to find the area of rectangle, we must know the dimension of rectangle.

width of rectangle  =  6

radius of circle  =  5 (EB)

EB  =  EC   =  5  

CB  =  10

In right triangle CDB,

CB2 = CD2 + DB2

102 = CD2 + 62

100 - 36 = CD2

CD=  64

CD  =  8 (length of rectangle)

Area of rectangle  = length (width)

  =  8 (6)  =  48

Question 10 : 

 √81 √25 + √16  =  

(A)  5  (B)  40  (C)  49  (D)  56  (E)  64

Solution :

  =  √81 √25 + √16

  =  √(9 ⋅ 9) √(5 ⋅ 5) + √(4 ⋅ 4)

  =  (9 ⋅ 5) + 4

  =  45 + 4

  =  49

Hence the answer is 49.

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