**PSAT Practice Test Math :**

Here we are going to see some sample questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.

PSAT Practice Test Math

**Question 11 :**

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

**Solution :**

Let "x" be the even integer

1^{st} even integer = x

2^{nd} even integer = x + 2

3^{rd} 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 12 :**

What is 0.003815 in scientific notation ?

**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 13 :**

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

**Solution :**

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

BC^{2} = AB^{2} + AC^{2}

17^{2} = 5^{2} + AC^{2}

AC^{2 }= 289 - 25

AC^{2 }= 264

AC = √264

AC = √(2 ⋅ 2 ⋅ 66)

AC = 2√66

**Question 14 :**

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

**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 15 :**

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

**Solution :**

Radius of the circle = 5

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

Area of circle (y) = πr^{2}

x/y = 10 π/πr^{2}

= 10/r^{2}

= 10/5^{2}

= 10/25 = 2/5

**Question 16 :**

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

**Solution :**

1 milligram = (1/10^{6}) kilograms

98 = 98/10^{6} kilogram

= 9.8 x 10^{1} x 10^{-6}

= 9.8 x 10^{-5 }kilogram

**Question 17 :**

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

**Solution :**

Let "x" be the required score.

(72 + 92 + 80 + x)/4 = 85

(244 + x) = 340

x = 340 - 244

x = 96

**Question 18 :**

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

**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 19 :**

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 ?

**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,

CB^{2} = CD^{2} + DB^{2}

10^{2} = CD^{2} + 6^{2}

100 - 36 = CD^{2}

CD^{2 }= 64

CD = 8 (length of rectangle)

Area of rectangle = length (width)

= 8 (6) = 48

**Question 20 : **

√81 √25 + √16 =

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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